id sid tid token lemma pos work_ln56cwsp7ffppl4wxeq7osqfuu 1 1 ON on IN work_ln56cwsp7ffppl4wxeq7osqfuu 1 2 THE the DT work_ln56cwsp7ffppl4wxeq7osqfuu 1 3 JUSTICE JUSTICE NNP work_ln56cwsp7ffppl4wxeq7osqfuu 1 4 OF of IN work_ln56cwsp7ffppl4wxeq7osqfuu 1 5 DECISION DECISION NNP work_ln56cwsp7ffppl4wxeq7osqfuu 1 6 RULES∗ RULES∗ NNP work_ln56cwsp7ffppl4wxeq7osqfuu 1 7 JOSE JOSE NNP work_ln56cwsp7ffppl4wxeq7osqfuu 1 8 APESTEGUIA† APESTEGUIA† VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 1 9 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 1 10 MIGUEL MIGUEL NNP work_ln56cwsp7ffppl4wxeq7osqfuu 1 11 A. a. NN work_ln56cwsp7ffppl4wxeq7osqfuu 1 12 BALLESTER‡ BALLESTER‡ NNP work_ln56cwsp7ffppl4wxeq7osqfuu 1 13 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 1 14 AND and CC work_ln56cwsp7ffppl4wxeq7osqfuu 1 15 ROSA ROSA NNP work_ln56cwsp7ffppl4wxeq7osqfuu 1 16 FERRER§ FERRER§ `` work_ln56cwsp7ffppl4wxeq7osqfuu 1 17 Abstract Abstract NNP work_ln56cwsp7ffppl4wxeq7osqfuu 1 18 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 2 1 Which which WDT work_ln56cwsp7ffppl4wxeq7osqfuu 2 2 decision decision NN work_ln56cwsp7ffppl4wxeq7osqfuu 2 3 rules rule NNS work_ln56cwsp7ffppl4wxeq7osqfuu 2 4 are be VBP work_ln56cwsp7ffppl4wxeq7osqfuu 2 5 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 2 6 most most RBS work_ln56cwsp7ffppl4wxeq7osqfuu 2 7 efficient efficient JJ work_ln56cwsp7ffppl4wxeq7osqfuu 2 8 ? ? . work_ln56cwsp7ffppl4wxeq7osqfuu 3 1 Which which WDT work_ln56cwsp7ffppl4wxeq7osqfuu 3 2 are be VBP work_ln56cwsp7ffppl4wxeq7osqfuu 3 3 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 3 4 best good JJS work_ln56cwsp7ffppl4wxeq7osqfuu 3 5 in in IN work_ln56cwsp7ffppl4wxeq7osqfuu 3 6 terms term NNS work_ln56cwsp7ffppl4wxeq7osqfuu 3 7 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 3 8 maximin maximin NN work_ln56cwsp7ffppl4wxeq7osqfuu 3 9 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 3 10 or or CC work_ln56cwsp7ffppl4wxeq7osqfuu 3 11 maximax maximax NNP work_ln56cwsp7ffppl4wxeq7osqfuu 3 12 ? ? . work_ln56cwsp7ffppl4wxeq7osqfuu 4 1 We -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 4 2 study study VBP work_ln56cwsp7ffppl4wxeq7osqfuu 4 3 these these DT work_ln56cwsp7ffppl4wxeq7osqfuu 4 4 questions question NNS work_ln56cwsp7ffppl4wxeq7osqfuu 4 5 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 4 6 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 4 7 case case NN work_ln56cwsp7ffppl4wxeq7osqfuu 4 8 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 4 9 a a DT work_ln56cwsp7ffppl4wxeq7osqfuu 4 10 group group NN work_ln56cwsp7ffppl4wxeq7osqfuu 4 11 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 4 12 individuals individual NNS work_ln56cwsp7ffppl4wxeq7osqfuu 4 13 faced face VBN work_ln56cwsp7ffppl4wxeq7osqfuu 4 14 with with IN work_ln56cwsp7ffppl4wxeq7osqfuu 4 15 a a DT work_ln56cwsp7ffppl4wxeq7osqfuu 4 16 choice choice NN work_ln56cwsp7ffppl4wxeq7osqfuu 4 17 from from IN work_ln56cwsp7ffppl4wxeq7osqfuu 4 18 a a DT work_ln56cwsp7ffppl4wxeq7osqfuu 4 19 set set NN work_ln56cwsp7ffppl4wxeq7osqfuu 4 20 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 4 21 alternatives alternative NNS work_ln56cwsp7ffppl4wxeq7osqfuu 4 22 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 5 1 First first RB work_ln56cwsp7ffppl4wxeq7osqfuu 5 2 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 5 3 we -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 5 4 show show VBP work_ln56cwsp7ffppl4wxeq7osqfuu 5 5 that that IN work_ln56cwsp7ffppl4wxeq7osqfuu 5 6 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 5 7 set set NN work_ln56cwsp7ffppl4wxeq7osqfuu 5 8 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 5 9 optimal optimal JJ work_ln56cwsp7ffppl4wxeq7osqfuu 5 10 decision decision NN work_ln56cwsp7ffppl4wxeq7osqfuu 5 11 rules rule NNS work_ln56cwsp7ffppl4wxeq7osqfuu 5 12 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 5 13 well well RB work_ln56cwsp7ffppl4wxeq7osqfuu 5 14 - - HYPH work_ln56cwsp7ffppl4wxeq7osqfuu 5 15 defined define VBN work_ln56cwsp7ffppl4wxeq7osqfuu 5 16 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 5 17 particularly particularly RB work_ln56cwsp7ffppl4wxeq7osqfuu 5 18 simple simple JJ work_ln56cwsp7ffppl4wxeq7osqfuu 5 19 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 5 20 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 5 21 well well RB work_ln56cwsp7ffppl4wxeq7osqfuu 5 22 - - HYPH work_ln56cwsp7ffppl4wxeq7osqfuu 5 23 known know VBN work_ln56cwsp7ffppl4wxeq7osqfuu 5 24 : : : work_ln56cwsp7ffppl4wxeq7osqfuu 5 25 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 5 26 class class NN work_ln56cwsp7ffppl4wxeq7osqfuu 5 27 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 5 28 scoring score VBG work_ln56cwsp7ffppl4wxeq7osqfuu 5 29 rules rule NNS work_ln56cwsp7ffppl4wxeq7osqfuu 5 30 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 6 1 Second second JJ work_ln56cwsp7ffppl4wxeq7osqfuu 6 2 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 6 3 we -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 6 4 provide provide VBP work_ln56cwsp7ffppl4wxeq7osqfuu 6 5 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 6 6 optimal optimal JJ work_ln56cwsp7ffppl4wxeq7osqfuu 6 7 decision decision NN work_ln56cwsp7ffppl4wxeq7osqfuu 6 8 rules rule NNS work_ln56cwsp7ffppl4wxeq7osqfuu 6 9 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 6 10 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 6 11 three three CD work_ln56cwsp7ffppl4wxeq7osqfuu 6 12 different different JJ work_ln56cwsp7ffppl4wxeq7osqfuu 6 13 ideals ideal NNS work_ln56cwsp7ffppl4wxeq7osqfuu 6 14 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 6 15 justice justice NN work_ln56cwsp7ffppl4wxeq7osqfuu 6 16 under under IN work_ln56cwsp7ffppl4wxeq7osqfuu 6 17 consideration consideration NN work_ln56cwsp7ffppl4wxeq7osqfuu 6 18 : : : work_ln56cwsp7ffppl4wxeq7osqfuu 6 19 utilitarianism utilitarianism NN work_ln56cwsp7ffppl4wxeq7osqfuu 6 20 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 6 21 efficiency efficiency NN work_ln56cwsp7ffppl4wxeq7osqfuu 6 22 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 6 23 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 6 24 maximin maximin NN work_ln56cwsp7ffppl4wxeq7osqfuu 6 25 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 6 26 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 6 27 maximax maximax NNP work_ln56cwsp7ffppl4wxeq7osqfuu 6 28 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 7 1 We -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 7 2 show show VBP work_ln56cwsp7ffppl4wxeq7osqfuu 7 3 that that DT work_ln56cwsp7ffppl4wxeq7osqfuu 7 4 plurality plurality NN work_ln56cwsp7ffppl4wxeq7osqfuu 7 5 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 7 6 arguably arguably RB work_ln56cwsp7ffppl4wxeq7osqfuu 7 7 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 7 8 most most RBS work_ln56cwsp7ffppl4wxeq7osqfuu 7 9 widely widely RB work_ln56cwsp7ffppl4wxeq7osqfuu 7 10 used use VBN work_ln56cwsp7ffppl4wxeq7osqfuu 7 11 voting voting NN work_ln56cwsp7ffppl4wxeq7osqfuu 7 12 sys- sys- NNP work_ln56cwsp7ffppl4wxeq7osqfuu 7 13 tem tem NNP work_ln56cwsp7ffppl4wxeq7osqfuu 7 14 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 7 15 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 7 16 optimal optimal JJ work_ln56cwsp7ffppl4wxeq7osqfuu 7 17 in in IN work_ln56cwsp7ffppl4wxeq7osqfuu 7 18 terms term NNS work_ln56cwsp7ffppl4wxeq7osqfuu 7 19 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 7 20 maximax maximax NNP work_ln56cwsp7ffppl4wxeq7osqfuu 7 21 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 7 22 while while IN work_ln56cwsp7ffppl4wxeq7osqfuu 7 23 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 7 24 best good JJS work_ln56cwsp7ffppl4wxeq7osqfuu 7 25 way way NN work_ln56cwsp7ffppl4wxeq7osqfuu 7 26 to to TO work_ln56cwsp7ffppl4wxeq7osqfuu 7 27 achieve achieve VB work_ln56cwsp7ffppl4wxeq7osqfuu 7 28 maximin maximin NN work_ln56cwsp7ffppl4wxeq7osqfuu 7 29 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 7 30 by by IN work_ln56cwsp7ffppl4wxeq7osqfuu 7 31 means mean NNS work_ln56cwsp7ffppl4wxeq7osqfuu 7 32 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 7 33 negative negative JJ work_ln56cwsp7ffppl4wxeq7osqfuu 7 34 voting voting NN work_ln56cwsp7ffppl4wxeq7osqfuu 7 35 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 7 36 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 7 37 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 7 38 optimal optimal JJ work_ln56cwsp7ffppl4wxeq7osqfuu 7 39 utilitarian utilitarian JJ work_ln56cwsp7ffppl4wxeq7osqfuu 7 40 decision decision NN work_ln56cwsp7ffppl4wxeq7osqfuu 7 41 rule rule NN work_ln56cwsp7ffppl4wxeq7osqfuu 7 42 depends depend VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 7 43 on on IN work_ln56cwsp7ffppl4wxeq7osqfuu 7 44 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 7 45 culture culture NN work_ln56cwsp7ffppl4wxeq7osqfuu 7 46 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 7 47 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 7 48 society society NN work_ln56cwsp7ffppl4wxeq7osqfuu 7 49 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 8 1 We -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 8 2 then then RB work_ln56cwsp7ffppl4wxeq7osqfuu 8 3 provide provide VBP work_ln56cwsp7ffppl4wxeq7osqfuu 8 4 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 8 5 mapping mapping NN work_ln56cwsp7ffppl4wxeq7osqfuu 8 6 between between IN work_ln56cwsp7ffppl4wxeq7osqfuu 8 7 cultures culture NNS work_ln56cwsp7ffppl4wxeq7osqfuu 8 8 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 8 9 optimal optimal JJ work_ln56cwsp7ffppl4wxeq7osqfuu 8 10 decision decision NN work_ln56cwsp7ffppl4wxeq7osqfuu 8 11 rules rule NNS work_ln56cwsp7ffppl4wxeq7osqfuu 8 12 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 9 1 Keywords keyword NNS work_ln56cwsp7ffppl4wxeq7osqfuu 9 2 : : : work_ln56cwsp7ffppl4wxeq7osqfuu 9 3 Decision decision NN work_ln56cwsp7ffppl4wxeq7osqfuu 9 4 rules rule NNS work_ln56cwsp7ffppl4wxeq7osqfuu 9 5 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 9 6 Scoring score VBG work_ln56cwsp7ffppl4wxeq7osqfuu 9 7 Rules Rules NNPS work_ln56cwsp7ffppl4wxeq7osqfuu 9 8 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 9 9 Voting Voting NNP work_ln56cwsp7ffppl4wxeq7osqfuu 9 10 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 9 11 Utilitarianism Utilitarianism NNP work_ln56cwsp7ffppl4wxeq7osqfuu 9 12 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 9 13 Maximin Maximin NNP work_ln56cwsp7ffppl4wxeq7osqfuu 9 14 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 9 15 Maxi- Maxi- NNP work_ln56cwsp7ffppl4wxeq7osqfuu 9 16 max max NNP work_ln56cwsp7ffppl4wxeq7osqfuu 9 17 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 10 1 JEL JEL NNP work_ln56cwsp7ffppl4wxeq7osqfuu 10 2 classification classification NN work_ln56cwsp7ffppl4wxeq7osqfuu 10 3 numbers number NNS work_ln56cwsp7ffppl4wxeq7osqfuu 10 4 : : : work_ln56cwsp7ffppl4wxeq7osqfuu 10 5 D00 D00 NNP work_ln56cwsp7ffppl4wxeq7osqfuu 10 6 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 10 7 D63 D63 NNP work_ln56cwsp7ffppl4wxeq7osqfuu 10 8 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 10 9 D71 D71 NNP work_ln56cwsp7ffppl4wxeq7osqfuu 10 10 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 10 11 D72 D72 NNP work_ln56cwsp7ffppl4wxeq7osqfuu 10 12 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 11 1 1 1 LS work_ln56cwsp7ffppl4wxeq7osqfuu 11 2 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 12 1 Introduction introduction NN work_ln56cwsp7ffppl4wxeq7osqfuu 12 2 Should Should MD work_ln56cwsp7ffppl4wxeq7osqfuu 12 3 I -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 12 4 implement implement VB work_ln56cwsp7ffppl4wxeq7osqfuu 12 5 a a DT work_ln56cwsp7ffppl4wxeq7osqfuu 12 6 plurality plurality NN work_ln56cwsp7ffppl4wxeq7osqfuu 12 7 voting voting NN work_ln56cwsp7ffppl4wxeq7osqfuu 12 8 rule rule NN work_ln56cwsp7ffppl4wxeq7osqfuu 12 9 if if IN work_ln56cwsp7ffppl4wxeq7osqfuu 12 10 I -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 12 11 aim aim VBP work_ln56cwsp7ffppl4wxeq7osqfuu 12 12 to to TO work_ln56cwsp7ffppl4wxeq7osqfuu 12 13 maximize maximize VB work_ln56cwsp7ffppl4wxeq7osqfuu 12 14 efficiency efficiency NN work_ln56cwsp7ffppl4wxeq7osqfuu 12 15 ? ? . work_ln56cwsp7ffppl4wxeq7osqfuu 13 1 If if IN work_ln56cwsp7ffppl4wxeq7osqfuu 13 2 I -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 13 3 am be VBP work_ln56cwsp7ffppl4wxeq7osqfuu 13 4 persuaded persuade VBN work_ln56cwsp7ffppl4wxeq7osqfuu 13 5 by by IN work_ln56cwsp7ffppl4wxeq7osqfuu 13 6 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 13 7 maximin maximin NN work_ln56cwsp7ffppl4wxeq7osqfuu 13 8 ideal ideal NN work_ln56cwsp7ffppl4wxeq7osqfuu 13 9 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 13 10 justice justice NN work_ln56cwsp7ffppl4wxeq7osqfuu 13 11 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 13 12 should should MD work_ln56cwsp7ffppl4wxeq7osqfuu 13 13 I -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 13 14 implement implement VB work_ln56cwsp7ffppl4wxeq7osqfuu 13 15 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 13 16 Borda Borda NNP work_ln56cwsp7ffppl4wxeq7osqfuu 13 17 count count NN work_ln56cwsp7ffppl4wxeq7osqfuu 13 18 ? ? . work_ln56cwsp7ffppl4wxeq7osqfuu 14 1 What what WP work_ln56cwsp7ffppl4wxeq7osqfuu 14 2 should should MD work_ln56cwsp7ffppl4wxeq7osqfuu 14 3 I -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 14 4 use use VB work_ln56cwsp7ffppl4wxeq7osqfuu 14 5 if if IN work_ln56cwsp7ffppl4wxeq7osqfuu 14 6 it -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 14 7 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 14 8 maximax maximax NNP work_ln56cwsp7ffppl4wxeq7osqfuu 14 9 that that WDT work_ln56cwsp7ffppl4wxeq7osqfuu 14 10 I -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 14 11 wish wish VBP work_ln56cwsp7ffppl4wxeq7osqfuu 14 12 to to TO work_ln56cwsp7ffppl4wxeq7osqfuu 14 13 optimize optimize VB work_ln56cwsp7ffppl4wxeq7osqfuu 14 14 ? ? . work_ln56cwsp7ffppl4wxeq7osqfuu 15 1 These these DT work_ln56cwsp7ffppl4wxeq7osqfuu 15 2 are be VBP work_ln56cwsp7ffppl4wxeq7osqfuu 15 3 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 15 4 type type NN work_ln56cwsp7ffppl4wxeq7osqfuu 15 5 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 15 6 questions question NNS work_ln56cwsp7ffppl4wxeq7osqfuu 15 7 addressed address VBN work_ln56cwsp7ffppl4wxeq7osqfuu 15 8 in in IN work_ln56cwsp7ffppl4wxeq7osqfuu 15 9 this this DT work_ln56cwsp7ffppl4wxeq7osqfuu 15 10 paper paper NN work_ln56cwsp7ffppl4wxeq7osqfuu 15 11 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 16 1 Our -PRON- PRP$ work_ln56cwsp7ffppl4wxeq7osqfuu 16 2 aim aim NN work_ln56cwsp7ffppl4wxeq7osqfuu 16 3 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 16 4 to to TO work_ln56cwsp7ffppl4wxeq7osqfuu 16 5 identify identify VB work_ln56cwsp7ffppl4wxeq7osqfuu 16 6 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 16 7 best good JJS work_ln56cwsp7ffppl4wxeq7osqfuu 16 8 decision decision NN work_ln56cwsp7ffppl4wxeq7osqfuu 16 9 rules rule NNS work_ln56cwsp7ffppl4wxeq7osqfuu 16 10 in in IN work_ln56cwsp7ffppl4wxeq7osqfuu 16 11 terms term NNS work_ln56cwsp7ffppl4wxeq7osqfuu 16 12 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 16 13 these these DT work_ln56cwsp7ffppl4wxeq7osqfuu 16 14 three three CD work_ln56cwsp7ffppl4wxeq7osqfuu 16 15 ideals ideal NNS work_ln56cwsp7ffppl4wxeq7osqfuu 16 16 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 16 17 justice justice NN work_ln56cwsp7ffppl4wxeq7osqfuu 16 18 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 17 1 In in IN work_ln56cwsp7ffppl4wxeq7osqfuu 17 2 our -PRON- PRP$ work_ln56cwsp7ffppl4wxeq7osqfuu 17 3 setting setting NN work_ln56cwsp7ffppl4wxeq7osqfuu 17 4 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 17 5 individuals individual NNS work_ln56cwsp7ffppl4wxeq7osqfuu 17 6 ’ ’ POS work_ln56cwsp7ffppl4wxeq7osqfuu 17 7 preferences preference NNS work_ln56cwsp7ffppl4wxeq7osqfuu 17 8 are be VBP work_ln56cwsp7ffppl4wxeq7osqfuu 17 9 cardinal cardinal JJ work_ln56cwsp7ffppl4wxeq7osqfuu 17 10 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 17 11 interpersonally interpersonally RB work_ln56cwsp7ffppl4wxeq7osqfuu 17 12 comparable comparable JJ work_ln56cwsp7ffppl4wxeq7osqfuu 17 13 utility utility NN work_ln56cwsp7ffppl4wxeq7osqfuu 17 14 random random JJ work_ln56cwsp7ffppl4wxeq7osqfuu 17 15 variables variable NNS work_ln56cwsp7ffppl4wxeq7osqfuu 17 16 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 18 1 The the DT work_ln56cwsp7ffppl4wxeq7osqfuu 18 2 realization realization NN work_ln56cwsp7ffppl4wxeq7osqfuu 18 3 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 18 4 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 18 5 individual individual JJ work_ln56cwsp7ffppl4wxeq7osqfuu 18 6 utility utility NN work_ln56cwsp7ffppl4wxeq7osqfuu 18 7 values value NNS work_ln56cwsp7ffppl4wxeq7osqfuu 18 8 depends depend VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 18 9 on on IN work_ln56cwsp7ffppl4wxeq7osqfuu 18 10 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 18 11 culture culture NN work_ln56cwsp7ffppl4wxeq7osqfuu 18 12 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 18 13 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 18 14 society society NN work_ln56cwsp7ffppl4wxeq7osqfuu 18 15 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 18 16 which which WDT work_ln56cwsp7ffppl4wxeq7osqfuu 18 17 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 18 18 simply simply RB work_ln56cwsp7ffppl4wxeq7osqfuu 18 19 a a DT work_ln56cwsp7ffppl4wxeq7osqfuu 18 20 probability probability NN work_ln56cwsp7ffppl4wxeq7osqfuu 18 21 distribution distribution NN work_ln56cwsp7ffppl4wxeq7osqfuu 18 22 over over IN work_ln56cwsp7ffppl4wxeq7osqfuu 18 23 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 18 24 range range NN work_ln56cwsp7ffppl4wxeq7osqfuu 18 25 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 18 26 utility utility NN work_ln56cwsp7ffppl4wxeq7osqfuu 18 27 intensities intensity NNS work_ln56cwsp7ffppl4wxeq7osqfuu 18 28 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 19 1 We -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 19 2 consider consider VBP work_ln56cwsp7ffppl4wxeq7osqfuu 19 3 three three CD work_ln56cwsp7ffppl4wxeq7osqfuu 19 4 prominent prominent JJ work_ln56cwsp7ffppl4wxeq7osqfuu 19 5 ideals ideal NNS work_ln56cwsp7ffppl4wxeq7osqfuu 19 6 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 19 7 justice justice NN work_ln56cwsp7ffppl4wxeq7osqfuu 19 8 defined define VBN work_ln56cwsp7ffppl4wxeq7osqfuu 19 9 in in IN work_ln56cwsp7ffppl4wxeq7osqfuu 19 10 cardinal cardinal JJ work_ln56cwsp7ffppl4wxeq7osqfuu 19 11 Date date NN work_ln56cwsp7ffppl4wxeq7osqfuu 19 12 : : : work_ln56cwsp7ffppl4wxeq7osqfuu 19 13 September September NNP work_ln56cwsp7ffppl4wxeq7osqfuu 19 14 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 19 15 2008 2008 CD work_ln56cwsp7ffppl4wxeq7osqfuu 19 16 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 20 1 ∗ ∗ NFP work_ln56cwsp7ffppl4wxeq7osqfuu 20 2 We -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 20 3 thank thank VBP work_ln56cwsp7ffppl4wxeq7osqfuu 20 4 Toni Toni NNP work_ln56cwsp7ffppl4wxeq7osqfuu 20 5 Calvo Calvo NNP work_ln56cwsp7ffppl4wxeq7osqfuu 20 6 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 20 7 Gabor Gabor NNP work_ln56cwsp7ffppl4wxeq7osqfuu 20 8 Lugosi Lugosi NNP work_ln56cwsp7ffppl4wxeq7osqfuu 20 9 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 20 10 Larry Larry NNP work_ln56cwsp7ffppl4wxeq7osqfuu 20 11 Samuelson Samuelson NNP work_ln56cwsp7ffppl4wxeq7osqfuu 20 12 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 20 13 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 20 14 Rann Rann NNP work_ln56cwsp7ffppl4wxeq7osqfuu 20 15 Smorodinsky Smorodinsky NNP work_ln56cwsp7ffppl4wxeq7osqfuu 20 16 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 20 17 valu- valu- NNS work_ln56cwsp7ffppl4wxeq7osqfuu 20 18 able able JJ work_ln56cwsp7ffppl4wxeq7osqfuu 20 19 comments comment NNS work_ln56cwsp7ffppl4wxeq7osqfuu 20 20 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 21 1 Financial financial JJ work_ln56cwsp7ffppl4wxeq7osqfuu 21 2 support support NN work_ln56cwsp7ffppl4wxeq7osqfuu 21 3 by by IN work_ln56cwsp7ffppl4wxeq7osqfuu 21 4 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 21 5 Spanish Spanish NNP work_ln56cwsp7ffppl4wxeq7osqfuu 21 6 Commission Commission NNP work_ln56cwsp7ffppl4wxeq7osqfuu 21 7 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 21 8 Science Science NNP work_ln56cwsp7ffppl4wxeq7osqfuu 21 9 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 21 10 Technology Technology NNP work_ln56cwsp7ffppl4wxeq7osqfuu 21 11 CICYT CICYT NNP work_ln56cwsp7ffppl4wxeq7osqfuu 21 12 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 21 13 SEJ2006 SEJ2006 NNP work_ln56cwsp7ffppl4wxeq7osqfuu 21 14 - - HYPH work_ln56cwsp7ffppl4wxeq7osqfuu 21 15 11510 11510 CD work_ln56cwsp7ffppl4wxeq7osqfuu 21 16 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 21 17 SEJ2005 SEJ2005 NNP work_ln56cwsp7ffppl4wxeq7osqfuu 21 18 - - HYPH work_ln56cwsp7ffppl4wxeq7osqfuu 21 19 01481 01481 NNP work_ln56cwsp7ffppl4wxeq7osqfuu 21 20 / / SYM work_ln56cwsp7ffppl4wxeq7osqfuu 21 21 ECON ECON NNP work_ln56cwsp7ffppl4wxeq7osqfuu 21 22 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 21 23 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 21 24 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 21 25 Barcelona Barcelona NNP work_ln56cwsp7ffppl4wxeq7osqfuu 21 26 GSE GSE NNP work_ln56cwsp7ffppl4wxeq7osqfuu 21 27 research research NN work_ln56cwsp7ffppl4wxeq7osqfuu 21 28 network network NN work_ln56cwsp7ffppl4wxeq7osqfuu 21 29 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 21 30 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 21 31 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 21 32 Generalitat Generalitat NNP work_ln56cwsp7ffppl4wxeq7osqfuu 21 33 de de NNP work_ln56cwsp7ffppl4wxeq7osqfuu 21 34 Catalunya Catalunya NNP work_ln56cwsp7ffppl4wxeq7osqfuu 21 35 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 21 36 gratefully gratefully RB work_ln56cwsp7ffppl4wxeq7osqfuu 21 37 acknowledged acknowledge VBN work_ln56cwsp7ffppl4wxeq7osqfuu 21 38 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 22 1 † † `` work_ln56cwsp7ffppl4wxeq7osqfuu 22 2 Universitat Universitat NNP work_ln56cwsp7ffppl4wxeq7osqfuu 22 3 Pompeu Pompeu NNP work_ln56cwsp7ffppl4wxeq7osqfuu 22 4 Fabra Fabra NNP work_ln56cwsp7ffppl4wxeq7osqfuu 22 5 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 23 1 E e NN work_ln56cwsp7ffppl4wxeq7osqfuu 23 2 - - NN work_ln56cwsp7ffppl4wxeq7osqfuu 23 3 mail mail NN work_ln56cwsp7ffppl4wxeq7osqfuu 23 4 : : : work_ln56cwsp7ffppl4wxeq7osqfuu 23 5 jose.apesteguia@upf.edu jose.apesteguia@upf.edu NNP work_ln56cwsp7ffppl4wxeq7osqfuu 23 6 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 24 1 ‡ ‡ : work_ln56cwsp7ffppl4wxeq7osqfuu 24 2 Universitat Universitat NNP work_ln56cwsp7ffppl4wxeq7osqfuu 24 3 Autonoma Autonoma NNP work_ln56cwsp7ffppl4wxeq7osqfuu 24 4 de de IN work_ln56cwsp7ffppl4wxeq7osqfuu 24 5 Barcelona Barcelona NNP work_ln56cwsp7ffppl4wxeq7osqfuu 24 6 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 25 1 E e NN work_ln56cwsp7ffppl4wxeq7osqfuu 25 2 - - NN work_ln56cwsp7ffppl4wxeq7osqfuu 25 3 mail mail NN work_ln56cwsp7ffppl4wxeq7osqfuu 25 4 : : : work_ln56cwsp7ffppl4wxeq7osqfuu 25 5 miguelangel.ballester@uab.es miguelangel.ballester@uab.es NN work_ln56cwsp7ffppl4wxeq7osqfuu 25 6 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 26 1 § § ADD work_ln56cwsp7ffppl4wxeq7osqfuu 26 2 Vanderbilt Vanderbilt NNP work_ln56cwsp7ffppl4wxeq7osqfuu 26 3 University University NNP work_ln56cwsp7ffppl4wxeq7osqfuu 26 4 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 27 1 E e NN work_ln56cwsp7ffppl4wxeq7osqfuu 27 2 - - NN work_ln56cwsp7ffppl4wxeq7osqfuu 27 3 mail mail NN work_ln56cwsp7ffppl4wxeq7osqfuu 27 4 : : : work_ln56cwsp7ffppl4wxeq7osqfuu 27 5 rosa.ferrer@vanderbilt.edu rosa.ferrer@vanderbilt.edu ADD work_ln56cwsp7ffppl4wxeq7osqfuu 27 6 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 28 1 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 28 2 2 2 CD work_ln56cwsp7ffppl4wxeq7osqfuu 28 3 terms term NNS work_ln56cwsp7ffppl4wxeq7osqfuu 28 4 : : : work_ln56cwsp7ffppl4wxeq7osqfuu 28 5 utilitarianism utilitarianism NN work_ln56cwsp7ffppl4wxeq7osqfuu 28 6 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 28 7 or or CC work_ln56cwsp7ffppl4wxeq7osqfuu 28 8 efficiency efficiency NN work_ln56cwsp7ffppl4wxeq7osqfuu 28 9 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 28 10 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 28 11 maximin maximin NN work_ln56cwsp7ffppl4wxeq7osqfuu 28 12 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 28 13 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 28 14 maximax maximax NNP work_ln56cwsp7ffppl4wxeq7osqfuu 28 15 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 29 1 In in IN work_ln56cwsp7ffppl4wxeq7osqfuu 29 2 short short JJ work_ln56cwsp7ffppl4wxeq7osqfuu 29 3 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 29 4 utilitarian- utilitarian- JJ work_ln56cwsp7ffppl4wxeq7osqfuu 29 5 ism ism NN work_ln56cwsp7ffppl4wxeq7osqfuu 29 6 evaluates evaluate VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 29 7 an an DT work_ln56cwsp7ffppl4wxeq7osqfuu 29 8 alternative alternative NN work_ln56cwsp7ffppl4wxeq7osqfuu 29 9 in in IN work_ln56cwsp7ffppl4wxeq7osqfuu 29 10 terms term NNS work_ln56cwsp7ffppl4wxeq7osqfuu 29 11 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 29 12 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 29 13 average average NN work_ln56cwsp7ffppl4wxeq7osqfuu 29 14 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 29 15 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 29 16 individual individual JJ work_ln56cwsp7ffppl4wxeq7osqfuu 29 17 utility utility NN work_ln56cwsp7ffppl4wxeq7osqfuu 29 18 values value NNS work_ln56cwsp7ffppl4wxeq7osqfuu 29 19 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 30 1 The the DT work_ln56cwsp7ffppl4wxeq7osqfuu 30 2 maximin maximin NN work_ln56cwsp7ffppl4wxeq7osqfuu 30 3 principle principle NN work_ln56cwsp7ffppl4wxeq7osqfuu 30 4 disregards disregard VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 30 5 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 30 6 utility utility NN work_ln56cwsp7ffppl4wxeq7osqfuu 30 7 values value NNS work_ln56cwsp7ffppl4wxeq7osqfuu 30 8 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 30 9 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 30 10 most most RBS work_ln56cwsp7ffppl4wxeq7osqfuu 30 11 favored favored JJ work_ln56cwsp7ffppl4wxeq7osqfuu 30 12 individuals individual NNS work_ln56cwsp7ffppl4wxeq7osqfuu 30 13 to to TO work_ln56cwsp7ffppl4wxeq7osqfuu 30 14 evaluate evaluate VB work_ln56cwsp7ffppl4wxeq7osqfuu 30 15 an an DT work_ln56cwsp7ffppl4wxeq7osqfuu 30 16 alternative alternative NN work_ln56cwsp7ffppl4wxeq7osqfuu 30 17 on on IN work_ln56cwsp7ffppl4wxeq7osqfuu 30 18 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 30 19 basis basis NN work_ln56cwsp7ffppl4wxeq7osqfuu 30 20 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 30 21 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 30 22 utility utility NN work_ln56cwsp7ffppl4wxeq7osqfuu 30 23 value value NN work_ln56cwsp7ffppl4wxeq7osqfuu 30 24 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 30 25 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 30 26 worst worst RBS work_ln56cwsp7ffppl4wxeq7osqfuu 30 27 - - HYPH work_ln56cwsp7ffppl4wxeq7osqfuu 30 28 off off RP work_ln56cwsp7ffppl4wxeq7osqfuu 30 29 agent agent NN work_ln56cwsp7ffppl4wxeq7osqfuu 30 30 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 31 1 In in IN work_ln56cwsp7ffppl4wxeq7osqfuu 31 2 contrast contrast NN work_ln56cwsp7ffppl4wxeq7osqfuu 31 3 with with IN work_ln56cwsp7ffppl4wxeq7osqfuu 31 4 maximin maximin NN work_ln56cwsp7ffppl4wxeq7osqfuu 31 5 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 31 6 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 31 7 maximax maximax NNP work_ln56cwsp7ffppl4wxeq7osqfuu 31 8 rule rule NN work_ln56cwsp7ffppl4wxeq7osqfuu 31 9 focuses focus VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 31 10 on on IN work_ln56cwsp7ffppl4wxeq7osqfuu 31 11 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 31 12 best well RBS work_ln56cwsp7ffppl4wxeq7osqfuu 31 13 - - HYPH work_ln56cwsp7ffppl4wxeq7osqfuu 31 14 off off RP work_ln56cwsp7ffppl4wxeq7osqfuu 31 15 individuals individual NNS work_ln56cwsp7ffppl4wxeq7osqfuu 31 16 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 32 1 Maxi- Maxi- NNP work_ln56cwsp7ffppl4wxeq7osqfuu 32 2 max max NNP work_ln56cwsp7ffppl4wxeq7osqfuu 32 3 as as IN work_ln56cwsp7ffppl4wxeq7osqfuu 32 4 an an DT work_ln56cwsp7ffppl4wxeq7osqfuu 32 5 ideal ideal NN work_ln56cwsp7ffppl4wxeq7osqfuu 32 6 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 32 7 justice justice NN work_ln56cwsp7ffppl4wxeq7osqfuu 32 8 may may MD work_ln56cwsp7ffppl4wxeq7osqfuu 32 9 appear appear VB work_ln56cwsp7ffppl4wxeq7osqfuu 32 10 a a DT work_ln56cwsp7ffppl4wxeq7osqfuu 32 11 mere mere JJ work_ln56cwsp7ffppl4wxeq7osqfuu 32 12 formal formal JJ work_ln56cwsp7ffppl4wxeq7osqfuu 32 13 curiosity curiosity NN work_ln56cwsp7ffppl4wxeq7osqfuu 32 14 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 33 1 However however RB work_ln56cwsp7ffppl4wxeq7osqfuu 33 2 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 33 3 we -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 33 4 will will MD work_ln56cwsp7ffppl4wxeq7osqfuu 33 5 see see VB work_ln56cwsp7ffppl4wxeq7osqfuu 33 6 that that DT work_ln56cwsp7ffppl4wxeq7osqfuu 33 7 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 33 8 because because IN work_ln56cwsp7ffppl4wxeq7osqfuu 33 9 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 33 10 its -PRON- PRP$ work_ln56cwsp7ffppl4wxeq7osqfuu 33 11 close close JJ work_ln56cwsp7ffppl4wxeq7osqfuu 33 12 connection connection NN work_ln56cwsp7ffppl4wxeq7osqfuu 33 13 to to IN work_ln56cwsp7ffppl4wxeq7osqfuu 33 14 plurality plurality NN work_ln56cwsp7ffppl4wxeq7osqfuu 33 15 voting voting NN work_ln56cwsp7ffppl4wxeq7osqfuu 33 16 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 33 17 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 33 18 maximax maximax NNP work_ln56cwsp7ffppl4wxeq7osqfuu 33 19 principle principle NN work_ln56cwsp7ffppl4wxeq7osqfuu 33 20 plays play VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 33 21 a a DT work_ln56cwsp7ffppl4wxeq7osqfuu 33 22 more more RBR work_ln56cwsp7ffppl4wxeq7osqfuu 33 23 important important JJ work_ln56cwsp7ffppl4wxeq7osqfuu 33 24 role role NN work_ln56cwsp7ffppl4wxeq7osqfuu 33 25 in in IN work_ln56cwsp7ffppl4wxeq7osqfuu 33 26 democratic democratic JJ work_ln56cwsp7ffppl4wxeq7osqfuu 33 27 political political JJ work_ln56cwsp7ffppl4wxeq7osqfuu 33 28 institutions institution NNS work_ln56cwsp7ffppl4wxeq7osqfuu 33 29 than than IN work_ln56cwsp7ffppl4wxeq7osqfuu 33 30 might may MD work_ln56cwsp7ffppl4wxeq7osqfuu 33 31 be be VB work_ln56cwsp7ffppl4wxeq7osqfuu 33 32 expected expect VBN work_ln56cwsp7ffppl4wxeq7osqfuu 33 33 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 34 1 In in IN work_ln56cwsp7ffppl4wxeq7osqfuu 34 2 our -PRON- PRP$ work_ln56cwsp7ffppl4wxeq7osqfuu 34 3 model model NN work_ln56cwsp7ffppl4wxeq7osqfuu 34 4 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 34 5 n n JJ work_ln56cwsp7ffppl4wxeq7osqfuu 34 6 individuals individual NNS work_ln56cwsp7ffppl4wxeq7osqfuu 34 7 must must MD work_ln56cwsp7ffppl4wxeq7osqfuu 34 8 choose choose VB work_ln56cwsp7ffppl4wxeq7osqfuu 34 9 an an DT work_ln56cwsp7ffppl4wxeq7osqfuu 34 10 alternative alternative NN work_ln56cwsp7ffppl4wxeq7osqfuu 34 11 from from IN work_ln56cwsp7ffppl4wxeq7osqfuu 34 12 a a DT work_ln56cwsp7ffppl4wxeq7osqfuu 34 13 set set NN work_ln56cwsp7ffppl4wxeq7osqfuu 34 14 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 34 15 k k NN work_ln56cwsp7ffppl4wxeq7osqfuu 34 16 ≥ ≥ DT work_ln56cwsp7ffppl4wxeq7osqfuu 34 17 3 3 CD work_ln56cwsp7ffppl4wxeq7osqfuu 34 18 alter- alter- JJ work_ln56cwsp7ffppl4wxeq7osqfuu 34 19 natives native NNS work_ln56cwsp7ffppl4wxeq7osqfuu 34 20 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 35 1 Decision decision NN work_ln56cwsp7ffppl4wxeq7osqfuu 35 2 rules rule NNS work_ln56cwsp7ffppl4wxeq7osqfuu 35 3 serve serve VBP work_ln56cwsp7ffppl4wxeq7osqfuu 35 4 precisely precisely RB work_ln56cwsp7ffppl4wxeq7osqfuu 35 5 this this DT work_ln56cwsp7ffppl4wxeq7osqfuu 35 6 purpose purpose NN work_ln56cwsp7ffppl4wxeq7osqfuu 35 7 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 36 1 A a DT work_ln56cwsp7ffppl4wxeq7osqfuu 36 2 decision decision NN work_ln56cwsp7ffppl4wxeq7osqfuu 36 3 rule rule NN work_ln56cwsp7ffppl4wxeq7osqfuu 36 4 transforms transform VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 36 5 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 36 6 ordinal ordinal JJ work_ln56cwsp7ffppl4wxeq7osqfuu 36 7 preferences preference NNS work_ln56cwsp7ffppl4wxeq7osqfuu 36 8 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 36 9 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 36 10 individuals individual NNS work_ln56cwsp7ffppl4wxeq7osqfuu 36 11 into into IN work_ln56cwsp7ffppl4wxeq7osqfuu 36 12 a a DT work_ln56cwsp7ffppl4wxeq7osqfuu 36 13 selection selection NN work_ln56cwsp7ffppl4wxeq7osqfuu 36 14 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 36 15 alternatives alternative NNS work_ln56cwsp7ffppl4wxeq7osqfuu 36 16 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 37 1 We -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 37 2 impose impose VBP work_ln56cwsp7ffppl4wxeq7osqfuu 37 3 no no DT work_ln56cwsp7ffppl4wxeq7osqfuu 37 4 restriction restriction NN work_ln56cwsp7ffppl4wxeq7osqfuu 37 5 on on IN work_ln56cwsp7ffppl4wxeq7osqfuu 37 6 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 37 7 possible possible JJ work_ln56cwsp7ffppl4wxeq7osqfuu 37 8 set set NN work_ln56cwsp7ffppl4wxeq7osqfuu 37 9 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 37 10 decision decision NN work_ln56cwsp7ffppl4wxeq7osqfuu 37 11 rules rule NNS work_ln56cwsp7ffppl4wxeq7osqfuu 37 12 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 37 13 other other JJ work_ln56cwsp7ffppl4wxeq7osqfuu 37 14 than than IN work_ln56cwsp7ffppl4wxeq7osqfuu 37 15 assuming assume VBG work_ln56cwsp7ffppl4wxeq7osqfuu 37 16 that that IN work_ln56cwsp7ffppl4wxeq7osqfuu 37 17 it -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 37 18 uses use VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 37 19 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 37 20 actual actual JJ work_ln56cwsp7ffppl4wxeq7osqfuu 37 21 ordinal ordinal JJ work_ln56cwsp7ffppl4wxeq7osqfuu 37 22 preferences preference NNS work_ln56cwsp7ffppl4wxeq7osqfuu 37 23 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 37 24 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 37 25 individuals individual NNS work_ln56cwsp7ffppl4wxeq7osqfuu 37 26 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 38 1 The the DT work_ln56cwsp7ffppl4wxeq7osqfuu 38 2 question question NN work_ln56cwsp7ffppl4wxeq7osqfuu 38 3 arises arise VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 38 4 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 38 5 what what WP work_ln56cwsp7ffppl4wxeq7osqfuu 38 6 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 38 7 optimal optimal JJ work_ln56cwsp7ffppl4wxeq7osqfuu 38 8 decision decision NN work_ln56cwsp7ffppl4wxeq7osqfuu 38 9 rules rule NNS work_ln56cwsp7ffppl4wxeq7osqfuu 38 10 are be VBP work_ln56cwsp7ffppl4wxeq7osqfuu 38 11 in in IN work_ln56cwsp7ffppl4wxeq7osqfuu 38 12 terms term NNS work_ln56cwsp7ffppl4wxeq7osqfuu 38 13 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 38 14 a a DT work_ln56cwsp7ffppl4wxeq7osqfuu 38 15 particular particular JJ work_ln56cwsp7ffppl4wxeq7osqfuu 38 16 cardinal cardinal JJ work_ln56cwsp7ffppl4wxeq7osqfuu 38 17 ideal ideal NN work_ln56cwsp7ffppl4wxeq7osqfuu 38 18 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 38 19 justice justice NN work_ln56cwsp7ffppl4wxeq7osqfuu 38 20 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 39 1 That that RB work_ln56cwsp7ffppl4wxeq7osqfuu 39 2 is is RB work_ln56cwsp7ffppl4wxeq7osqfuu 39 3 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 39 4 we -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 39 5 explore explore VBP work_ln56cwsp7ffppl4wxeq7osqfuu 39 6 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 39 7 connection connection NN work_ln56cwsp7ffppl4wxeq7osqfuu 39 8 between between IN work_ln56cwsp7ffppl4wxeq7osqfuu 39 9 a a DT work_ln56cwsp7ffppl4wxeq7osqfuu 39 10 given give VBN work_ln56cwsp7ffppl4wxeq7osqfuu 39 11 ideal ideal NN work_ln56cwsp7ffppl4wxeq7osqfuu 39 12 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 39 13 justice justice NN work_ln56cwsp7ffppl4wxeq7osqfuu 39 14 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 39 15 different different JJ work_ln56cwsp7ffppl4wxeq7osqfuu 39 16 decision decision NN work_ln56cwsp7ffppl4wxeq7osqfuu 39 17 rules rule NNS work_ln56cwsp7ffppl4wxeq7osqfuu 39 18 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 39 19 with with IN work_ln56cwsp7ffppl4wxeq7osqfuu 39 20 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 39 21 aim aim NN work_ln56cwsp7ffppl4wxeq7osqfuu 39 22 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 39 23 identifying identify VBG work_ln56cwsp7ffppl4wxeq7osqfuu 39 24 those those DT work_ln56cwsp7ffppl4wxeq7osqfuu 39 25 that that WDT work_ln56cwsp7ffppl4wxeq7osqfuu 39 26 best good JJS work_ln56cwsp7ffppl4wxeq7osqfuu 39 27 serve serve VBP work_ln56cwsp7ffppl4wxeq7osqfuu 39 28 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 39 29 pursued pursue VBN work_ln56cwsp7ffppl4wxeq7osqfuu 39 30 ideal ideal NN work_ln56cwsp7ffppl4wxeq7osqfuu 39 31 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 39 32 justice justice NN work_ln56cwsp7ffppl4wxeq7osqfuu 39 33 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 40 1 There there EX work_ln56cwsp7ffppl4wxeq7osqfuu 40 2 are be VBP work_ln56cwsp7ffppl4wxeq7osqfuu 40 3 different different JJ work_ln56cwsp7ffppl4wxeq7osqfuu 40 4 options option NNS work_ln56cwsp7ffppl4wxeq7osqfuu 40 5 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 40 6 measuring measure VBG work_ln56cwsp7ffppl4wxeq7osqfuu 40 7 decision decision NN work_ln56cwsp7ffppl4wxeq7osqfuu 40 8 rule rule NN work_ln56cwsp7ffppl4wxeq7osqfuu 40 9 performance performance NN work_ln56cwsp7ffppl4wxeq7osqfuu 40 10 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 41 1 A a DT work_ln56cwsp7ffppl4wxeq7osqfuu 41 2 natural natural JJ work_ln56cwsp7ffppl4wxeq7osqfuu 41 3 index index NN work_ln56cwsp7ffppl4wxeq7osqfuu 41 4 can can MD work_ln56cwsp7ffppl4wxeq7osqfuu 41 5 be be VB work_ln56cwsp7ffppl4wxeq7osqfuu 41 6 obtained obtain VBN work_ln56cwsp7ffppl4wxeq7osqfuu 41 7 by by IN work_ln56cwsp7ffppl4wxeq7osqfuu 41 8 evaluating evaluate VBG work_ln56cwsp7ffppl4wxeq7osqfuu 41 9 decision decision NN work_ln56cwsp7ffppl4wxeq7osqfuu 41 10 rules rule NNS work_ln56cwsp7ffppl4wxeq7osqfuu 41 11 in in IN work_ln56cwsp7ffppl4wxeq7osqfuu 41 12 terms term NNS work_ln56cwsp7ffppl4wxeq7osqfuu 41 13 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 41 14 their -PRON- PRP$ work_ln56cwsp7ffppl4wxeq7osqfuu 41 15 expected expect VBN work_ln56cwsp7ffppl4wxeq7osqfuu 41 16 attainable attainable JJ work_ln56cwsp7ffppl4wxeq7osqfuu 41 17 value value NN work_ln56cwsp7ffppl4wxeq7osqfuu 41 18 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 41 19 a a DT work_ln56cwsp7ffppl4wxeq7osqfuu 41 20 given give VBN work_ln56cwsp7ffppl4wxeq7osqfuu 41 21 ideal ideal NN work_ln56cwsp7ffppl4wxeq7osqfuu 41 22 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 41 23 justice justice NN work_ln56cwsp7ffppl4wxeq7osqfuu 41 24 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 42 1 Another another DT work_ln56cwsp7ffppl4wxeq7osqfuu 42 2 index index NN work_ln56cwsp7ffppl4wxeq7osqfuu 42 3 emerges emerge VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 42 4 by by IN work_ln56cwsp7ffppl4wxeq7osqfuu 42 5 judging judge VBG work_ln56cwsp7ffppl4wxeq7osqfuu 42 6 decision decision NN work_ln56cwsp7ffppl4wxeq7osqfuu 42 7 rules rule NNS work_ln56cwsp7ffppl4wxeq7osqfuu 42 8 on on IN work_ln56cwsp7ffppl4wxeq7osqfuu 42 9 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 42 10 basis basis NN work_ln56cwsp7ffppl4wxeq7osqfuu 42 11 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 42 12 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 42 13 probability probability NN work_ln56cwsp7ffppl4wxeq7osqfuu 42 14 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 42 15 their -PRON- PRP$ work_ln56cwsp7ffppl4wxeq7osqfuu 42 16 selecting select VBG work_ln56cwsp7ffppl4wxeq7osqfuu 42 17 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 42 18 best good JJS work_ln56cwsp7ffppl4wxeq7osqfuu 42 19 alternative alternative NN work_ln56cwsp7ffppl4wxeq7osqfuu 42 20 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 42 21 a a DT work_ln56cwsp7ffppl4wxeq7osqfuu 42 22 given give VBN work_ln56cwsp7ffppl4wxeq7osqfuu 42 23 theory theory NN work_ln56cwsp7ffppl4wxeq7osqfuu 42 24 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 42 25 justice justice NN work_ln56cwsp7ffppl4wxeq7osqfuu 42 26 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 43 1 Yet yet RB work_ln56cwsp7ffppl4wxeq7osqfuu 43 2 a a DT work_ln56cwsp7ffppl4wxeq7osqfuu 43 3 third third JJ work_ln56cwsp7ffppl4wxeq7osqfuu 43 4 possibility possibility NN work_ln56cwsp7ffppl4wxeq7osqfuu 43 5 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 43 6 to to TO work_ln56cwsp7ffppl4wxeq7osqfuu 43 7 measure measure VB work_ln56cwsp7ffppl4wxeq7osqfuu 43 8 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 43 9 probability probability NN work_ln56cwsp7ffppl4wxeq7osqfuu 43 10 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 43 11 avoiding avoid VBG work_ln56cwsp7ffppl4wxeq7osqfuu 43 12 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 43 13 worst bad JJS work_ln56cwsp7ffppl4wxeq7osqfuu 43 14 alternatives alternative NNS work_ln56cwsp7ffppl4wxeq7osqfuu 43 15 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 44 1 The the DT work_ln56cwsp7ffppl4wxeq7osqfuu 44 2 three three CD work_ln56cwsp7ffppl4wxeq7osqfuu 44 3 criteria criterion NNS work_ln56cwsp7ffppl4wxeq7osqfuu 44 4 approach approach VBP work_ln56cwsp7ffppl4wxeq7osqfuu 44 5 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 44 6 same same JJ work_ln56cwsp7ffppl4wxeq7osqfuu 44 7 problem problem NN work_ln56cwsp7ffppl4wxeq7osqfuu 44 8 from from IN work_ln56cwsp7ffppl4wxeq7osqfuu 44 9 different different JJ work_ln56cwsp7ffppl4wxeq7osqfuu 44 10 angles angle NNS work_ln56cwsp7ffppl4wxeq7osqfuu 44 11 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 44 12 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 44 13 hence hence RB work_ln56cwsp7ffppl4wxeq7osqfuu 44 14 in in IN work_ln56cwsp7ffppl4wxeq7osqfuu 44 15 principle principle NN work_ln56cwsp7ffppl4wxeq7osqfuu 44 16 complement complement NN work_ln56cwsp7ffppl4wxeq7osqfuu 44 17 each each DT work_ln56cwsp7ffppl4wxeq7osqfuu 44 18 other other JJ work_ln56cwsp7ffppl4wxeq7osqfuu 44 19 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 45 1 It -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 45 2 could could MD work_ln56cwsp7ffppl4wxeq7osqfuu 45 3 be be VB work_ln56cwsp7ffppl4wxeq7osqfuu 45 4 argued argue VBN work_ln56cwsp7ffppl4wxeq7osqfuu 45 5 that that IN work_ln56cwsp7ffppl4wxeq7osqfuu 45 6 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 45 7 first first JJ work_ln56cwsp7ffppl4wxeq7osqfuu 45 8 index index NN work_ln56cwsp7ffppl4wxeq7osqfuu 45 9 adopts adopt VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 45 10 a a DT work_ln56cwsp7ffppl4wxeq7osqfuu 45 11 risk risk NN work_ln56cwsp7ffppl4wxeq7osqfuu 45 12 - - HYPH work_ln56cwsp7ffppl4wxeq7osqfuu 45 13 neutral neutral JJ work_ln56cwsp7ffppl4wxeq7osqfuu 45 14 approach approach NN work_ln56cwsp7ffppl4wxeq7osqfuu 45 15 to to TO work_ln56cwsp7ffppl4wxeq7osqfuu 45 16 measure measure VB work_ln56cwsp7ffppl4wxeq7osqfuu 45 17 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 45 18 success success NN work_ln56cwsp7ffppl4wxeq7osqfuu 45 19 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 45 20 decision decision NN work_ln56cwsp7ffppl4wxeq7osqfuu 45 21 rules rule NNS work_ln56cwsp7ffppl4wxeq7osqfuu 45 22 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 45 23 while while IN work_ln56cwsp7ffppl4wxeq7osqfuu 45 24 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 45 25 second second JJ work_ln56cwsp7ffppl4wxeq7osqfuu 45 26 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 45 27 third third JJ work_ln56cwsp7ffppl4wxeq7osqfuu 45 28 indices index NNS work_ln56cwsp7ffppl4wxeq7osqfuu 45 29 could could MD work_ln56cwsp7ffppl4wxeq7osqfuu 45 30 be be VB work_ln56cwsp7ffppl4wxeq7osqfuu 45 31 understood understand VBN work_ln56cwsp7ffppl4wxeq7osqfuu 45 32 as as IN work_ln56cwsp7ffppl4wxeq7osqfuu 45 33 representative representative NN work_ln56cwsp7ffppl4wxeq7osqfuu 45 34 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 45 35 risk risk NN work_ln56cwsp7ffppl4wxeq7osqfuu 45 36 - - HYPH work_ln56cwsp7ffppl4wxeq7osqfuu 45 37 loving loving NN work_ln56cwsp7ffppl4wxeq7osqfuu 45 38 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 45 39 risk risk NN work_ln56cwsp7ffppl4wxeq7osqfuu 45 40 - - HYPH work_ln56cwsp7ffppl4wxeq7osqfuu 45 41 averse averse JJ work_ln56cwsp7ffppl4wxeq7osqfuu 45 42 positions position NNS work_ln56cwsp7ffppl4wxeq7osqfuu 45 43 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 45 44 respectively respectively RB work_ln56cwsp7ffppl4wxeq7osqfuu 45 45 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 46 1 Firstly firstly RB work_ln56cwsp7ffppl4wxeq7osqfuu 46 2 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 46 3 we -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 46 4 show show VBP work_ln56cwsp7ffppl4wxeq7osqfuu 46 5 that that IN work_ln56cwsp7ffppl4wxeq7osqfuu 46 6 a a DT work_ln56cwsp7ffppl4wxeq7osqfuu 46 7 particularly particularly RB work_ln56cwsp7ffppl4wxeq7osqfuu 46 8 prominent prominent JJ work_ln56cwsp7ffppl4wxeq7osqfuu 46 9 class class NN work_ln56cwsp7ffppl4wxeq7osqfuu 46 10 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 46 11 decision decision NN work_ln56cwsp7ffppl4wxeq7osqfuu 46 12 rules rule NNS work_ln56cwsp7ffppl4wxeq7osqfuu 46 13 emerges emerge VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 46 14 as as IN work_ln56cwsp7ffppl4wxeq7osqfuu 46 15 optimal optimal NN work_ln56cwsp7ffppl4wxeq7osqfuu 46 16 : : : work_ln56cwsp7ffppl4wxeq7osqfuu 46 17 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 46 18 class class NN work_ln56cwsp7ffppl4wxeq7osqfuu 46 19 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 46 20 scoring score VBG work_ln56cwsp7ffppl4wxeq7osqfuu 46 21 rules rule NNS work_ln56cwsp7ffppl4wxeq7osqfuu 46 22 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 47 1 A a DT work_ln56cwsp7ffppl4wxeq7osqfuu 47 2 scoring score VBG work_ln56cwsp7ffppl4wxeq7osqfuu 47 3 rule rule NN work_ln56cwsp7ffppl4wxeq7osqfuu 47 4 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 47 5 a a DT work_ln56cwsp7ffppl4wxeq7osqfuu 47 6 vector vector NN work_ln56cwsp7ffppl4wxeq7osqfuu 47 7 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 47 8 fixed fix VBN work_ln56cwsp7ffppl4wxeq7osqfuu 47 9 points point NNS work_ln56cwsp7ffppl4wxeq7osqfuu 47 10 that that IN work_ln56cwsp7ffppl4wxeq7osqfuu 47 11 individuals individual NNS work_ln56cwsp7ffppl4wxeq7osqfuu 47 12 assign assign VBP work_ln56cwsp7ffppl4wxeq7osqfuu 47 13 to to IN work_ln56cwsp7ffppl4wxeq7osqfuu 47 14 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 47 15 different different JJ work_ln56cwsp7ffppl4wxeq7osqfuu 47 16 alternatives alternative NNS work_ln56cwsp7ffppl4wxeq7osqfuu 47 17 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 48 1 The the DT work_ln56cwsp7ffppl4wxeq7osqfuu 48 2 plurality plurality NN work_ln56cwsp7ffppl4wxeq7osqfuu 48 3 scoring score VBG work_ln56cwsp7ffppl4wxeq7osqfuu 48 4 rule rule NN work_ln56cwsp7ffppl4wxeq7osqfuu 48 5 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 48 6 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 48 7 negative negative JJ work_ln56cwsp7ffppl4wxeq7osqfuu 48 8 scoring score VBG work_ln56cwsp7ffppl4wxeq7osqfuu 48 9 rule rule NN work_ln56cwsp7ffppl4wxeq7osqfuu 48 10 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 48 11 Borda Borda NNP work_ln56cwsp7ffppl4wxeq7osqfuu 48 12 ’s ’s POS work_ln56cwsp7ffppl4wxeq7osqfuu 48 13 scoring score VBG work_ln56cwsp7ffppl4wxeq7osqfuu 48 14 rule rule NN work_ln56cwsp7ffppl4wxeq7osqfuu 48 15 are be VBP work_ln56cwsp7ffppl4wxeq7osqfuu 48 16 especially especially RB work_ln56cwsp7ffppl4wxeq7osqfuu 48 17 salient salient JJ work_ln56cwsp7ffppl4wxeq7osqfuu 48 18 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 49 1 This this DT work_ln56cwsp7ffppl4wxeq7osqfuu 49 2 result result NN work_ln56cwsp7ffppl4wxeq7osqfuu 49 3 significantly significantly RB work_ln56cwsp7ffppl4wxeq7osqfuu 49 4 restricts restrict VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 49 5 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 49 6 class class NN work_ln56cwsp7ffppl4wxeq7osqfuu 49 7 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 49 8 decision decision NN work_ln56cwsp7ffppl4wxeq7osqfuu 49 9 rules rule NNS work_ln56cwsp7ffppl4wxeq7osqfuu 49 10 from from IN work_ln56cwsp7ffppl4wxeq7osqfuu 49 11 which which WDT work_ln56cwsp7ffppl4wxeq7osqfuu 49 12 to to TO work_ln56cwsp7ffppl4wxeq7osqfuu 49 13 seek seek VB work_ln56cwsp7ffppl4wxeq7osqfuu 49 14 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 49 15 optimal optimal JJ work_ln56cwsp7ffppl4wxeq7osqfuu 49 16 ones one NNS work_ln56cwsp7ffppl4wxeq7osqfuu 49 17 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 50 1 A a DT work_ln56cwsp7ffppl4wxeq7osqfuu 50 2 further further JJ work_ln56cwsp7ffppl4wxeq7osqfuu 50 3 point point NN work_ln56cwsp7ffppl4wxeq7osqfuu 50 4 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 50 5 that that IN work_ln56cwsp7ffppl4wxeq7osqfuu 50 6 scoring score VBG work_ln56cwsp7ffppl4wxeq7osqfuu 50 7 rules rule NNS work_ln56cwsp7ffppl4wxeq7osqfuu 50 8 are be VBP work_ln56cwsp7ffppl4wxeq7osqfuu 50 9 relatively relatively RB work_ln56cwsp7ffppl4wxeq7osqfuu 50 10 easy easy JJ work_ln56cwsp7ffppl4wxeq7osqfuu 50 11 to to TO work_ln56cwsp7ffppl4wxeq7osqfuu 50 12 implement implement VB work_ln56cwsp7ffppl4wxeq7osqfuu 50 13 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 50 14 widely widely RB work_ln56cwsp7ffppl4wxeq7osqfuu 50 15 used use VBN work_ln56cwsp7ffppl4wxeq7osqfuu 50 16 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 51 1 Secondly secondly RB work_ln56cwsp7ffppl4wxeq7osqfuu 51 2 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 51 3 our -PRON- PRP$ work_ln56cwsp7ffppl4wxeq7osqfuu 51 4 results result NNS work_ln56cwsp7ffppl4wxeq7osqfuu 51 5 indicate indicate VBP work_ln56cwsp7ffppl4wxeq7osqfuu 51 6 that that IN work_ln56cwsp7ffppl4wxeq7osqfuu 51 7 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 51 8 message message NN work_ln56cwsp7ffppl4wxeq7osqfuu 51 9 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 51 10 each each DT work_ln56cwsp7ffppl4wxeq7osqfuu 51 11 ideal ideal NN work_ln56cwsp7ffppl4wxeq7osqfuu 51 12 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 51 13 justice justice NN work_ln56cwsp7ffppl4wxeq7osqfuu 51 14 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 51 15 robust robust JJ work_ln56cwsp7ffppl4wxeq7osqfuu 51 16 across across IN work_ln56cwsp7ffppl4wxeq7osqfuu 51 17 indices index NNS work_ln56cwsp7ffppl4wxeq7osqfuu 51 18 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 52 1 That that RB work_ln56cwsp7ffppl4wxeq7osqfuu 52 2 is is RB work_ln56cwsp7ffppl4wxeq7osqfuu 52 3 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 52 4 what what WP work_ln56cwsp7ffppl4wxeq7osqfuu 52 5 matters matter VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 52 6 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 52 7 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 52 8 nature nature NN work_ln56cwsp7ffppl4wxeq7osqfuu 52 9 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 52 10 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 52 11 ideal ideal NN work_ln56cwsp7ffppl4wxeq7osqfuu 52 12 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 52 13 justice justice NN work_ln56cwsp7ffppl4wxeq7osqfuu 52 14 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 52 15 not not RB work_ln56cwsp7ffppl4wxeq7osqfuu 52 16 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 52 17 particular particular JJ work_ln56cwsp7ffppl4wxeq7osqfuu 52 18 way way NN work_ln56cwsp7ffppl4wxeq7osqfuu 52 19 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 52 20 measuring measure VBG work_ln56cwsp7ffppl4wxeq7osqfuu 52 21 decision decision NN work_ln56cwsp7ffppl4wxeq7osqfuu 52 22 rule rule NN work_ln56cwsp7ffppl4wxeq7osqfuu 52 23 performance performance NN work_ln56cwsp7ffppl4wxeq7osqfuu 52 24 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 53 1 Thirdly thirdly RB work_ln56cwsp7ffppl4wxeq7osqfuu 53 2 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 53 3 we -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 53 4 provide provide VBP work_ln56cwsp7ffppl4wxeq7osqfuu 53 5 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 53 6 optimal optimal JJ work_ln56cwsp7ffppl4wxeq7osqfuu 53 7 decision decision NN work_ln56cwsp7ffppl4wxeq7osqfuu 53 8 rules rule NNS work_ln56cwsp7ffppl4wxeq7osqfuu 53 9 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 53 10 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 53 11 three three CD work_ln56cwsp7ffppl4wxeq7osqfuu 53 12 ideals ideal NNS work_ln56cwsp7ffppl4wxeq7osqfuu 53 13 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 53 14 justice justice NN work_ln56cwsp7ffppl4wxeq7osqfuu 53 15 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 54 1 In in IN work_ln56cwsp7ffppl4wxeq7osqfuu 54 2 utilitarian utilitarian JJ work_ln56cwsp7ffppl4wxeq7osqfuu 54 3 terms term NNS work_ln56cwsp7ffppl4wxeq7osqfuu 54 4 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 54 5 we -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 54 6 show show VBP work_ln56cwsp7ffppl4wxeq7osqfuu 54 7 that that IN work_ln56cwsp7ffppl4wxeq7osqfuu 54 8 there there EX work_ln56cwsp7ffppl4wxeq7osqfuu 54 9 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 54 10 a a DT work_ln56cwsp7ffppl4wxeq7osqfuu 54 11 mapping mapping NN work_ln56cwsp7ffppl4wxeq7osqfuu 54 12 from from IN work_ln56cwsp7ffppl4wxeq7osqfuu 54 13 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 54 14 culture culture NN work_ln56cwsp7ffppl4wxeq7osqfuu 54 15 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 54 16 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 54 17 society society NN work_ln56cwsp7ffppl4wxeq7osqfuu 54 18 to to IN work_ln56cwsp7ffppl4wxeq7osqfuu 54 19 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 54 20 optimal optimal JJ work_ln56cwsp7ffppl4wxeq7osqfuu 54 21 decision decision NN work_ln56cwsp7ffppl4wxeq7osqfuu 54 22 rule rule NN work_ln56cwsp7ffppl4wxeq7osqfuu 54 23 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 55 1 Moreover moreover RB work_ln56cwsp7ffppl4wxeq7osqfuu 55 2 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 55 3 we -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 55 4 find find VBP work_ln56cwsp7ffppl4wxeq7osqfuu 55 5 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 55 6 exact exact JJ work_ln56cwsp7ffppl4wxeq7osqfuu 55 7 shape shape NN work_ln56cwsp7ffppl4wxeq7osqfuu 55 8 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 55 9 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 55 10 optimal optimal JJ work_ln56cwsp7ffppl4wxeq7osqfuu 55 11 decision decision NN work_ln56cwsp7ffppl4wxeq7osqfuu 55 12 rule rule NN work_ln56cwsp7ffppl4wxeq7osqfuu 55 13 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 55 14 conditional conditional JJ work_ln56cwsp7ffppl4wxeq7osqfuu 55 15 on on IN work_ln56cwsp7ffppl4wxeq7osqfuu 55 16 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 55 17 culture culture NN work_ln56cwsp7ffppl4wxeq7osqfuu 55 18 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 55 19 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 55 20 society society NN work_ln56cwsp7ffppl4wxeq7osqfuu 55 21 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 56 1 We -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 56 2 then then RB work_ln56cwsp7ffppl4wxeq7osqfuu 56 3 illustrate illustrate VBP work_ln56cwsp7ffppl4wxeq7osqfuu 56 4 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 56 5 result result NN work_ln56cwsp7ffppl4wxeq7osqfuu 56 6 with with IN work_ln56cwsp7ffppl4wxeq7osqfuu 56 7 a a DT work_ln56cwsp7ffppl4wxeq7osqfuu 56 8 number number NN work_ln56cwsp7ffppl4wxeq7osqfuu 56 9 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 56 10 examples example NNS work_ln56cwsp7ffppl4wxeq7osqfuu 56 11 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 57 1 In in IN work_ln56cwsp7ffppl4wxeq7osqfuu 57 2 particular particular JJ work_ln56cwsp7ffppl4wxeq7osqfuu 57 3 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 57 4 we -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 57 5 show show VBP work_ln56cwsp7ffppl4wxeq7osqfuu 57 6 that that IN work_ln56cwsp7ffppl4wxeq7osqfuu 57 7 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 57 8 a a DT work_ln56cwsp7ffppl4wxeq7osqfuu 57 9 range range NN work_ln56cwsp7ffppl4wxeq7osqfuu 57 10 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 57 11 cultures culture NNS work_ln56cwsp7ffppl4wxeq7osqfuu 57 12 satisfying satisfy VBG work_ln56cwsp7ffppl4wxeq7osqfuu 57 13 3 3 CD work_ln56cwsp7ffppl4wxeq7osqfuu 57 14 a a DT work_ln56cwsp7ffppl4wxeq7osqfuu 57 15 certain certain JJ work_ln56cwsp7ffppl4wxeq7osqfuu 57 16 regularity regularity NN work_ln56cwsp7ffppl4wxeq7osqfuu 57 17 condition condition NN work_ln56cwsp7ffppl4wxeq7osqfuu 57 18 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 57 19 a a DT work_ln56cwsp7ffppl4wxeq7osqfuu 57 20 prominent prominent JJ work_ln56cwsp7ffppl4wxeq7osqfuu 57 21 scoring score VBG work_ln56cwsp7ffppl4wxeq7osqfuu 57 22 rule rule NN work_ln56cwsp7ffppl4wxeq7osqfuu 57 23 emerges emerge VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 57 24 as as IN work_ln56cwsp7ffppl4wxeq7osqfuu 57 25 optimal optimal JJ work_ln56cwsp7ffppl4wxeq7osqfuu 57 26 : : : work_ln56cwsp7ffppl4wxeq7osqfuu 57 27 Borda Borda NNP work_ln56cwsp7ffppl4wxeq7osqfuu 57 28 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 58 1 When when WRB work_ln56cwsp7ffppl4wxeq7osqfuu 58 2 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 58 3 culture culture NN work_ln56cwsp7ffppl4wxeq7osqfuu 58 4 follows follow VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 58 5 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 58 6 normal normal JJ work_ln56cwsp7ffppl4wxeq7osqfuu 58 7 distribution distribution NN work_ln56cwsp7ffppl4wxeq7osqfuu 58 8 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 58 9 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 58 10 optimal optimal JJ work_ln56cwsp7ffppl4wxeq7osqfuu 58 11 decision decision NN work_ln56cwsp7ffppl4wxeq7osqfuu 58 12 rule rule NN work_ln56cwsp7ffppl4wxeq7osqfuu 58 13 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 58 14 util- util- JJ work_ln56cwsp7ffppl4wxeq7osqfuu 58 15 itarianism itarianism NN work_ln56cwsp7ffppl4wxeq7osqfuu 58 16 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 58 17 not not RB work_ln56cwsp7ffppl4wxeq7osqfuu 58 18 Borda Borda NNP work_ln56cwsp7ffppl4wxeq7osqfuu 58 19 but but CC work_ln56cwsp7ffppl4wxeq7osqfuu 58 20 a a DT work_ln56cwsp7ffppl4wxeq7osqfuu 58 21 scoring score VBG work_ln56cwsp7ffppl4wxeq7osqfuu 58 22 rule rule NN work_ln56cwsp7ffppl4wxeq7osqfuu 58 23 where where WRB work_ln56cwsp7ffppl4wxeq7osqfuu 58 24 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 58 25 differences difference NNS work_ln56cwsp7ffppl4wxeq7osqfuu 58 26 in in IN work_ln56cwsp7ffppl4wxeq7osqfuu 58 27 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 58 28 values value NNS work_ln56cwsp7ffppl4wxeq7osqfuu 58 29 given give VBN work_ln56cwsp7ffppl4wxeq7osqfuu 58 30 to to IN work_ln56cwsp7ffppl4wxeq7osqfuu 58 31 consecutive consecutive JJ work_ln56cwsp7ffppl4wxeq7osqfuu 58 32 alternatives alternative NNS work_ln56cwsp7ffppl4wxeq7osqfuu 58 33 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 58 34 a a DT work_ln56cwsp7ffppl4wxeq7osqfuu 58 35 symmetric symmetric JJ work_ln56cwsp7ffppl4wxeq7osqfuu 58 36 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 58 37 strictly strictly RB work_ln56cwsp7ffppl4wxeq7osqfuu 58 38 convex convex NNP work_ln56cwsp7ffppl4wxeq7osqfuu 58 39 function function NN work_ln56cwsp7ffppl4wxeq7osqfuu 58 40 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 59 1 That that RB work_ln56cwsp7ffppl4wxeq7osqfuu 59 2 is is RB work_ln56cwsp7ffppl4wxeq7osqfuu 59 3 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 59 4 with with IN work_ln56cwsp7ffppl4wxeq7osqfuu 59 5 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 59 6 normal normal JJ work_ln56cwsp7ffppl4wxeq7osqfuu 59 7 distribution distribution NN work_ln56cwsp7ffppl4wxeq7osqfuu 59 8 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 59 9 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 59 10 optimal optimal JJ work_ln56cwsp7ffppl4wxeq7osqfuu 59 11 scoring score VBG work_ln56cwsp7ffppl4wxeq7osqfuu 59 12 rule rule NN work_ln56cwsp7ffppl4wxeq7osqfuu 59 13 strongly strongly RB work_ln56cwsp7ffppl4wxeq7osqfuu 59 14 discriminates discriminate NNS work_ln56cwsp7ffppl4wxeq7osqfuu 59 15 between between IN work_ln56cwsp7ffppl4wxeq7osqfuu 59 16 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 59 17 very very RB work_ln56cwsp7ffppl4wxeq7osqfuu 59 18 best good JJS work_ln56cwsp7ffppl4wxeq7osqfuu 59 19 alternatives alternative NNS work_ln56cwsp7ffppl4wxeq7osqfuu 59 20 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 59 21 also also RB work_ln56cwsp7ffppl4wxeq7osqfuu 59 22 between between IN work_ln56cwsp7ffppl4wxeq7osqfuu 59 23 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 59 24 very very RB work_ln56cwsp7ffppl4wxeq7osqfuu 59 25 worst bad JJS work_ln56cwsp7ffppl4wxeq7osqfuu 59 26 alternatives alternative NNS work_ln56cwsp7ffppl4wxeq7osqfuu 59 27 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 60 1 Alternatives alternative NNS work_ln56cwsp7ffppl4wxeq7osqfuu 60 2 in in IN work_ln56cwsp7ffppl4wxeq7osqfuu 60 3 between between IN work_ln56cwsp7ffppl4wxeq7osqfuu 60 4 are be VBP work_ln56cwsp7ffppl4wxeq7osqfuu 60 5 treated treat VBN work_ln56cwsp7ffppl4wxeq7osqfuu 60 6 as as RB work_ln56cwsp7ffppl4wxeq7osqfuu 60 7 almost almost RB work_ln56cwsp7ffppl4wxeq7osqfuu 60 8 alike alike RB work_ln56cwsp7ffppl4wxeq7osqfuu 60 9 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 61 1 We -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 61 2 explore explore VBP work_ln56cwsp7ffppl4wxeq7osqfuu 61 3 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 61 4 connection connection NN work_ln56cwsp7ffppl4wxeq7osqfuu 61 5 between between IN work_ln56cwsp7ffppl4wxeq7osqfuu 61 6 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 61 7 optimal optimal JJ work_ln56cwsp7ffppl4wxeq7osqfuu 61 8 utilitarian utilitarian JJ work_ln56cwsp7ffppl4wxeq7osqfuu 61 9 decision decision NN work_ln56cwsp7ffppl4wxeq7osqfuu 61 10 rule rule NN work_ln56cwsp7ffppl4wxeq7osqfuu 61 11 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 61 12 other other JJ work_ln56cwsp7ffppl4wxeq7osqfuu 61 13 prominent prominent JJ work_ln56cwsp7ffppl4wxeq7osqfuu 61 14 cultures culture NNS work_ln56cwsp7ffppl4wxeq7osqfuu 61 15 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 61 16 such such JJ work_ln56cwsp7ffppl4wxeq7osqfuu 61 17 as as IN work_ln56cwsp7ffppl4wxeq7osqfuu 61 18 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 61 19 exponential exponential JJ work_ln56cwsp7ffppl4wxeq7osqfuu 61 20 or or CC work_ln56cwsp7ffppl4wxeq7osqfuu 61 21 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 61 22 logistic logistic JJ work_ln56cwsp7ffppl4wxeq7osqfuu 61 23 distribution distribution NN work_ln56cwsp7ffppl4wxeq7osqfuu 61 24 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 62 1 In in IN work_ln56cwsp7ffppl4wxeq7osqfuu 62 2 contrast contrast NN work_ln56cwsp7ffppl4wxeq7osqfuu 62 3 to to IN work_ln56cwsp7ffppl4wxeq7osqfuu 62 4 utilitarianism utilitarianism NN work_ln56cwsp7ffppl4wxeq7osqfuu 62 5 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 62 6 maximax maximax NNP work_ln56cwsp7ffppl4wxeq7osqfuu 62 7 offers offer VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 62 8 a a DT work_ln56cwsp7ffppl4wxeq7osqfuu 62 9 unique unique JJ work_ln56cwsp7ffppl4wxeq7osqfuu 62 10 optimal optimal JJ work_ln56cwsp7ffppl4wxeq7osqfuu 62 11 decision decision NN work_ln56cwsp7ffppl4wxeq7osqfuu 62 12 rule rule NN work_ln56cwsp7ffppl4wxeq7osqfuu 62 13 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 62 14 every every DT work_ln56cwsp7ffppl4wxeq7osqfuu 62 15 possible possible JJ work_ln56cwsp7ffppl4wxeq7osqfuu 62 16 culture culture NN work_ln56cwsp7ffppl4wxeq7osqfuu 62 17 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 63 1 It -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 63 2 proves prove VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 63 3 to to TO work_ln56cwsp7ffppl4wxeq7osqfuu 63 4 be be VB work_ln56cwsp7ffppl4wxeq7osqfuu 63 5 a a DT work_ln56cwsp7ffppl4wxeq7osqfuu 63 6 remarkably remarkably RB work_ln56cwsp7ffppl4wxeq7osqfuu 63 7 important important JJ work_ln56cwsp7ffppl4wxeq7osqfuu 63 8 decision decision NN work_ln56cwsp7ffppl4wxeq7osqfuu 63 9 rule rule NN work_ln56cwsp7ffppl4wxeq7osqfuu 63 10 : : : work_ln56cwsp7ffppl4wxeq7osqfuu 63 11 plurality plurality NN work_ln56cwsp7ffppl4wxeq7osqfuu 63 12 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 64 1 Although although IN work_ln56cwsp7ffppl4wxeq7osqfuu 64 2 plurality plurality NN work_ln56cwsp7ffppl4wxeq7osqfuu 64 3 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 64 4 probably probably RB work_ln56cwsp7ffppl4wxeq7osqfuu 64 5 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 64 6 most most RBS work_ln56cwsp7ffppl4wxeq7osqfuu 64 7 widely widely RB work_ln56cwsp7ffppl4wxeq7osqfuu 64 8 used use VBN work_ln56cwsp7ffppl4wxeq7osqfuu 64 9 voting voting NN work_ln56cwsp7ffppl4wxeq7osqfuu 64 10 system system NN work_ln56cwsp7ffppl4wxeq7osqfuu 64 11 in in IN work_ln56cwsp7ffppl4wxeq7osqfuu 64 12 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 64 13 democratic democratic JJ work_ln56cwsp7ffppl4wxeq7osqfuu 64 14 world world NN work_ln56cwsp7ffppl4wxeq7osqfuu 64 15 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 64 16 our -PRON- PRP$ work_ln56cwsp7ffppl4wxeq7osqfuu 64 17 results result NNS work_ln56cwsp7ffppl4wxeq7osqfuu 64 18 show show VBP work_ln56cwsp7ffppl4wxeq7osqfuu 64 19 that that IN work_ln56cwsp7ffppl4wxeq7osqfuu 64 20 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 64 21 instead instead RB work_ln56cwsp7ffppl4wxeq7osqfuu 64 22 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 64 23 maximizing maximize VBG work_ln56cwsp7ffppl4wxeq7osqfuu 64 24 efficiency efficiency NN work_ln56cwsp7ffppl4wxeq7osqfuu 64 25 or or CC work_ln56cwsp7ffppl4wxeq7osqfuu 64 26 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 64 27 well well NN work_ln56cwsp7ffppl4wxeq7osqfuu 64 28 - - HYPH work_ln56cwsp7ffppl4wxeq7osqfuu 64 29 being being NN work_ln56cwsp7ffppl4wxeq7osqfuu 64 30 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 64 31 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 64 32 worst worst RBS work_ln56cwsp7ffppl4wxeq7osqfuu 64 33 - - HYPH work_ln56cwsp7ffppl4wxeq7osqfuu 64 34 off off RP work_ln56cwsp7ffppl4wxeq7osqfuu 64 35 agents agent NNS work_ln56cwsp7ffppl4wxeq7osqfuu 64 36 in in IN work_ln56cwsp7ffppl4wxeq7osqfuu 64 37 a a DT work_ln56cwsp7ffppl4wxeq7osqfuu 64 38 society society NN work_ln56cwsp7ffppl4wxeq7osqfuu 64 39 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 64 40 plurality plurality NN work_ln56cwsp7ffppl4wxeq7osqfuu 64 41 maximizes maximize VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 64 42 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 64 43 well well NN work_ln56cwsp7ffppl4wxeq7osqfuu 64 44 - - HYPH work_ln56cwsp7ffppl4wxeq7osqfuu 64 45 being being NN work_ln56cwsp7ffppl4wxeq7osqfuu 64 46 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 64 47 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 64 48 best good JJS work_ln56cwsp7ffppl4wxeq7osqfuu 64 49 - - HYPH work_ln56cwsp7ffppl4wxeq7osqfuu 64 50 off off NN work_ln56cwsp7ffppl4wxeq7osqfuu 64 51 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 64 52 a a DT work_ln56cwsp7ffppl4wxeq7osqfuu 64 53 property property NN work_ln56cwsp7ffppl4wxeq7osqfuu 64 54 that that WDT work_ln56cwsp7ffppl4wxeq7osqfuu 64 55 may may MD work_ln56cwsp7ffppl4wxeq7osqfuu 64 56 be be VB work_ln56cwsp7ffppl4wxeq7osqfuu 64 57 considered consider VBN work_ln56cwsp7ffppl4wxeq7osqfuu 64 58 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 64 59 questionable questionable JJ work_ln56cwsp7ffppl4wxeq7osqfuu 64 60 merit merit NN work_ln56cwsp7ffppl4wxeq7osqfuu 64 61 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 65 1 Finally finally RB work_ln56cwsp7ffppl4wxeq7osqfuu 65 2 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 65 3 maximin maximin NN work_ln56cwsp7ffppl4wxeq7osqfuu 65 4 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 65 5 best well RBS work_ln56cwsp7ffppl4wxeq7osqfuu 65 6 approached approach VBN work_ln56cwsp7ffppl4wxeq7osqfuu 65 7 with with IN work_ln56cwsp7ffppl4wxeq7osqfuu 65 8 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 65 9 negative negative JJ work_ln56cwsp7ffppl4wxeq7osqfuu 65 10 scoring score VBG work_ln56cwsp7ffppl4wxeq7osqfuu 65 11 rule rule NN work_ln56cwsp7ffppl4wxeq7osqfuu 65 12 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 66 1 Given give VBN work_ln56cwsp7ffppl4wxeq7osqfuu 66 2 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 66 3 link link NN work_ln56cwsp7ffppl4wxeq7osqfuu 66 4 between between IN work_ln56cwsp7ffppl4wxeq7osqfuu 66 5 plurality plurality NN work_ln56cwsp7ffppl4wxeq7osqfuu 66 6 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 66 7 maximax maximax NNP work_ln56cwsp7ffppl4wxeq7osqfuu 66 8 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 66 9 it -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 66 10 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 66 11 not not RB work_ln56cwsp7ffppl4wxeq7osqfuu 66 12 surprising surprising JJ work_ln56cwsp7ffppl4wxeq7osqfuu 66 13 that that IN work_ln56cwsp7ffppl4wxeq7osqfuu 66 14 negative negative JJ work_ln56cwsp7ffppl4wxeq7osqfuu 66 15 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 66 16 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 66 17 symmetric symmetric JJ work_ln56cwsp7ffppl4wxeq7osqfuu 66 18 scoring score VBG work_ln56cwsp7ffppl4wxeq7osqfuu 66 19 rule rule NN work_ln56cwsp7ffppl4wxeq7osqfuu 66 20 to to IN work_ln56cwsp7ffppl4wxeq7osqfuu 66 21 plurality plurality NN work_ln56cwsp7ffppl4wxeq7osqfuu 66 22 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 66 23 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 66 24 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 66 25 best good JJS work_ln56cwsp7ffppl4wxeq7osqfuu 66 26 decision decision NN work_ln56cwsp7ffppl4wxeq7osqfuu 66 27 rule rule NN work_ln56cwsp7ffppl4wxeq7osqfuu 66 28 in in IN work_ln56cwsp7ffppl4wxeq7osqfuu 66 29 terms term NNS work_ln56cwsp7ffppl4wxeq7osqfuu 66 30 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 66 31 maximin maximin NN work_ln56cwsp7ffppl4wxeq7osqfuu 66 32 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 66 33 which which WDT work_ln56cwsp7ffppl4wxeq7osqfuu 66 34 can can MD work_ln56cwsp7ffppl4wxeq7osqfuu 66 35 be be VB work_ln56cwsp7ffppl4wxeq7osqfuu 66 36 shown show VBN work_ln56cwsp7ffppl4wxeq7osqfuu 66 37 to to TO work_ln56cwsp7ffppl4wxeq7osqfuu 66 38 be be VB work_ln56cwsp7ffppl4wxeq7osqfuu 66 39 in in IN work_ln56cwsp7ffppl4wxeq7osqfuu 66 40 a a DT work_ln56cwsp7ffppl4wxeq7osqfuu 66 41 way way NN work_ln56cwsp7ffppl4wxeq7osqfuu 66 42 symmetric symmetric JJ work_ln56cwsp7ffppl4wxeq7osqfuu 66 43 to to IN work_ln56cwsp7ffppl4wxeq7osqfuu 66 44 maximax maximax NNP work_ln56cwsp7ffppl4wxeq7osqfuu 66 45 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 67 1 Interestingly interestingly RB work_ln56cwsp7ffppl4wxeq7osqfuu 67 2 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 67 3 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 67 4 results result NNS work_ln56cwsp7ffppl4wxeq7osqfuu 67 5 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 67 6 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 67 7 three three CD work_ln56cwsp7ffppl4wxeq7osqfuu 67 8 ideals ideal NNS work_ln56cwsp7ffppl4wxeq7osqfuu 67 9 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 67 10 justice justice NN work_ln56cwsp7ffppl4wxeq7osqfuu 67 11 point point NN work_ln56cwsp7ffppl4wxeq7osqfuu 67 12 to to IN work_ln56cwsp7ffppl4wxeq7osqfuu 67 13 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 67 14 three three CD work_ln56cwsp7ffppl4wxeq7osqfuu 67 15 best well RBS work_ln56cwsp7ffppl4wxeq7osqfuu 67 16 - - HYPH work_ln56cwsp7ffppl4wxeq7osqfuu 67 17 known know VBN work_ln56cwsp7ffppl4wxeq7osqfuu 67 18 scoring score VBG work_ln56cwsp7ffppl4wxeq7osqfuu 67 19 rules rule NNS work_ln56cwsp7ffppl4wxeq7osqfuu 67 20 : : : work_ln56cwsp7ffppl4wxeq7osqfuu 67 21 plurality plurality NN work_ln56cwsp7ffppl4wxeq7osqfuu 67 22 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 67 23 Borda Borda NNP work_ln56cwsp7ffppl4wxeq7osqfuu 67 24 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 67 25 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 67 26 negative negative JJ work_ln56cwsp7ffppl4wxeq7osqfuu 67 27 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 68 1 We -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 68 2 are be VBP work_ln56cwsp7ffppl4wxeq7osqfuu 68 3 certainly certainly RB work_ln56cwsp7ffppl4wxeq7osqfuu 68 4 not not RB work_ln56cwsp7ffppl4wxeq7osqfuu 68 5 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 68 6 first first JJ work_ln56cwsp7ffppl4wxeq7osqfuu 68 7 to to TO work_ln56cwsp7ffppl4wxeq7osqfuu 68 8 evaluate evaluate VB work_ln56cwsp7ffppl4wxeq7osqfuu 68 9 decision decision NN work_ln56cwsp7ffppl4wxeq7osqfuu 68 10 rules rule NNS work_ln56cwsp7ffppl4wxeq7osqfuu 68 11 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 69 1 There there EX work_ln56cwsp7ffppl4wxeq7osqfuu 69 2 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 69 3 a a DT work_ln56cwsp7ffppl4wxeq7osqfuu 69 4 large large JJ work_ln56cwsp7ffppl4wxeq7osqfuu 69 5 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 69 6 still still RB work_ln56cwsp7ffppl4wxeq7osqfuu 69 7 growing grow VBG work_ln56cwsp7ffppl4wxeq7osqfuu 69 8 literature literature NN work_ln56cwsp7ffppl4wxeq7osqfuu 69 9 examining examine VBG work_ln56cwsp7ffppl4wxeq7osqfuu 69 10 decision decision NN work_ln56cwsp7ffppl4wxeq7osqfuu 69 11 rules rule NNS work_ln56cwsp7ffppl4wxeq7osqfuu 69 12 in in IN work_ln56cwsp7ffppl4wxeq7osqfuu 69 13 terms term NNS work_ln56cwsp7ffppl4wxeq7osqfuu 69 14 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 69 15 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 69 16 properties property NNS work_ln56cwsp7ffppl4wxeq7osqfuu 69 17 they -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 69 18 satisfy satisfy VBP work_ln56cwsp7ffppl4wxeq7osqfuu 69 19 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 70 1 In in IN work_ln56cwsp7ffppl4wxeq7osqfuu 70 2 other other JJ work_ln56cwsp7ffppl4wxeq7osqfuu 70 3 words word NNS work_ln56cwsp7ffppl4wxeq7osqfuu 70 4 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 70 5 decision decision NN work_ln56cwsp7ffppl4wxeq7osqfuu 70 6 rules rule NNS work_ln56cwsp7ffppl4wxeq7osqfuu 70 7 are be VBP work_ln56cwsp7ffppl4wxeq7osqfuu 70 8 judged judge VBN work_ln56cwsp7ffppl4wxeq7osqfuu 70 9 on on IN work_ln56cwsp7ffppl4wxeq7osqfuu 70 10 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 70 11 basis basis NN work_ln56cwsp7ffppl4wxeq7osqfuu 70 12 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 70 13 their -PRON- PRP$ work_ln56cwsp7ffppl4wxeq7osqfuu 70 14 capacity capacity NN work_ln56cwsp7ffppl4wxeq7osqfuu 70 15 to to TO work_ln56cwsp7ffppl4wxeq7osqfuu 70 16 meet meet VB work_ln56cwsp7ffppl4wxeq7osqfuu 70 17 cer- cer- JJ work_ln56cwsp7ffppl4wxeq7osqfuu 70 18 tain tain NN work_ln56cwsp7ffppl4wxeq7osqfuu 70 19 desirable desirable JJ work_ln56cwsp7ffppl4wxeq7osqfuu 70 20 properties property NNS work_ln56cwsp7ffppl4wxeq7osqfuu 70 21 such such JJ work_ln56cwsp7ffppl4wxeq7osqfuu 70 22 as as IN work_ln56cwsp7ffppl4wxeq7osqfuu 70 23 anonymity anonymity NN work_ln56cwsp7ffppl4wxeq7osqfuu 70 24 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 70 25 independence independence NN work_ln56cwsp7ffppl4wxeq7osqfuu 70 26 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 70 27 irrelevant irrelevant JJ work_ln56cwsp7ffppl4wxeq7osqfuu 70 28 alternatives alternative NNS work_ln56cwsp7ffppl4wxeq7osqfuu 70 29 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 70 30 strategy strategy NN work_ln56cwsp7ffppl4wxeq7osqfuu 70 31 - - HYPH work_ln56cwsp7ffppl4wxeq7osqfuu 70 32 proofness proofness NN work_ln56cwsp7ffppl4wxeq7osqfuu 70 33 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 70 34 consistency consistency NN work_ln56cwsp7ffppl4wxeq7osqfuu 70 35 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 70 36 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 70 37 social social JJ work_ln56cwsp7ffppl4wxeq7osqfuu 70 38 preference preference NN work_ln56cwsp7ffppl4wxeq7osqfuu 70 39 ordering ordering NN work_ln56cwsp7ffppl4wxeq7osqfuu 70 40 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 70 41 Pareto Pareto NNP work_ln56cwsp7ffppl4wxeq7osqfuu 70 42 - - HYPH work_ln56cwsp7ffppl4wxeq7osqfuu 70 43 dominance dominance NN work_ln56cwsp7ffppl4wxeq7osqfuu 70 44 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 70 45 path path NN work_ln56cwsp7ffppl4wxeq7osqfuu 70 46 - - HYPH work_ln56cwsp7ffppl4wxeq7osqfuu 70 47 independence independence NN work_ln56cwsp7ffppl4wxeq7osqfuu 70 48 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 70 49 probability probability NN work_ln56cwsp7ffppl4wxeq7osqfuu 70 50 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 70 51 selecting select VBG work_ln56cwsp7ffppl4wxeq7osqfuu 70 52 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 70 53 Condorcet Condorcet NNP work_ln56cwsp7ffppl4wxeq7osqfuu 70 54 winner winner NN work_ln56cwsp7ffppl4wxeq7osqfuu 70 55 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 70 56 etc.1 etc.1 NFP work_ln56cwsp7ffppl4wxeq7osqfuu 70 57 In in IN work_ln56cwsp7ffppl4wxeq7osqfuu 70 58 this this DT work_ln56cwsp7ffppl4wxeq7osqfuu 70 59 paper paper NN work_ln56cwsp7ffppl4wxeq7osqfuu 70 60 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 70 61 we -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 70 62 focus focus VBP work_ln56cwsp7ffppl4wxeq7osqfuu 70 63 not not RB work_ln56cwsp7ffppl4wxeq7osqfuu 70 64 on on IN work_ln56cwsp7ffppl4wxeq7osqfuu 70 65 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 70 66 specific specific JJ work_ln56cwsp7ffppl4wxeq7osqfuu 70 67 properties property NNS work_ln56cwsp7ffppl4wxeq7osqfuu 70 68 that that WDT work_ln56cwsp7ffppl4wxeq7osqfuu 70 69 voting voting NN work_ln56cwsp7ffppl4wxeq7osqfuu 70 70 systems system NNS work_ln56cwsp7ffppl4wxeq7osqfuu 70 71 may may MD work_ln56cwsp7ffppl4wxeq7osqfuu 70 72 or or CC work_ln56cwsp7ffppl4wxeq7osqfuu 70 73 may may MD work_ln56cwsp7ffppl4wxeq7osqfuu 70 74 not not RB work_ln56cwsp7ffppl4wxeq7osqfuu 70 75 satisfy satisfy VB work_ln56cwsp7ffppl4wxeq7osqfuu 70 76 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 70 77 but but CC work_ln56cwsp7ffppl4wxeq7osqfuu 70 78 on on IN work_ln56cwsp7ffppl4wxeq7osqfuu 70 79 how how WRB work_ln56cwsp7ffppl4wxeq7osqfuu 70 80 well well RB work_ln56cwsp7ffppl4wxeq7osqfuu 70 81 they -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 70 82 perform perform VBP work_ln56cwsp7ffppl4wxeq7osqfuu 70 83 in in IN work_ln56cwsp7ffppl4wxeq7osqfuu 70 84 terms term NNS work_ln56cwsp7ffppl4wxeq7osqfuu 70 85 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 70 86 an an DT work_ln56cwsp7ffppl4wxeq7osqfuu 70 87 ideal ideal NN work_ln56cwsp7ffppl4wxeq7osqfuu 70 88 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 70 89 justice justice NN work_ln56cwsp7ffppl4wxeq7osqfuu 70 90 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 71 1 If if IN work_ln56cwsp7ffppl4wxeq7osqfuu 71 2 there there EX work_ln56cwsp7ffppl4wxeq7osqfuu 71 3 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 71 4 agreement agreement NN work_ln56cwsp7ffppl4wxeq7osqfuu 71 5 over over IN work_ln56cwsp7ffppl4wxeq7osqfuu 71 6 which which WDT work_ln56cwsp7ffppl4wxeq7osqfuu 71 7 ideal ideal NN work_ln56cwsp7ffppl4wxeq7osqfuu 71 8 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 71 9 justice justice NN work_ln56cwsp7ffppl4wxeq7osqfuu 71 10 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 71 11 to to TO work_ln56cwsp7ffppl4wxeq7osqfuu 71 12 be be VB work_ln56cwsp7ffppl4wxeq7osqfuu 71 13 pursued pursue VBN work_ln56cwsp7ffppl4wxeq7osqfuu 71 14 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 71 15 it -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 71 16 seems seem VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 71 17 much much RB work_ln56cwsp7ffppl4wxeq7osqfuu 71 18 more more RBR work_ln56cwsp7ffppl4wxeq7osqfuu 71 19 relevant relevant JJ work_ln56cwsp7ffppl4wxeq7osqfuu 71 20 to to TO work_ln56cwsp7ffppl4wxeq7osqfuu 71 21 evaluate evaluate VB work_ln56cwsp7ffppl4wxeq7osqfuu 71 22 voting voting NN work_ln56cwsp7ffppl4wxeq7osqfuu 71 23 systems system NNS work_ln56cwsp7ffppl4wxeq7osqfuu 71 24 on on IN work_ln56cwsp7ffppl4wxeq7osqfuu 71 25 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 71 26 basis basis NN work_ln56cwsp7ffppl4wxeq7osqfuu 71 27 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 71 28 how how WRB work_ln56cwsp7ffppl4wxeq7osqfuu 71 29 well well RB work_ln56cwsp7ffppl4wxeq7osqfuu 71 30 they -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 71 31 serve serve VBP work_ln56cwsp7ffppl4wxeq7osqfuu 71 32 that that DT work_ln56cwsp7ffppl4wxeq7osqfuu 71 33 ideal ideal NN work_ln56cwsp7ffppl4wxeq7osqfuu 71 34 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 71 35 than than IN work_ln56cwsp7ffppl4wxeq7osqfuu 71 36 it -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 71 37 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 71 38 to to TO work_ln56cwsp7ffppl4wxeq7osqfuu 71 39 calculate calculate VB work_ln56cwsp7ffppl4wxeq7osqfuu 71 40 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 71 41 probability probability NN work_ln56cwsp7ffppl4wxeq7osqfuu 71 42 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 71 43 their -PRON- PRP$ work_ln56cwsp7ffppl4wxeq7osqfuu 71 44 electing elect VBG work_ln56cwsp7ffppl4wxeq7osqfuu 71 45 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 71 46 Condorcet Condorcet NNP work_ln56cwsp7ffppl4wxeq7osqfuu 71 47 winner winner NN work_ln56cwsp7ffppl4wxeq7osqfuu 71 48 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 71 49 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 71 50 example example NN work_ln56cwsp7ffppl4wxeq7osqfuu 71 51 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 72 1 In in IN work_ln56cwsp7ffppl4wxeq7osqfuu 72 2 other other JJ work_ln56cwsp7ffppl4wxeq7osqfuu 72 3 words word NNS work_ln56cwsp7ffppl4wxeq7osqfuu 72 4 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 72 5 in in IN work_ln56cwsp7ffppl4wxeq7osqfuu 72 6 this this DT work_ln56cwsp7ffppl4wxeq7osqfuu 72 7 paper paper NN work_ln56cwsp7ffppl4wxeq7osqfuu 72 8 we -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 72 9 shift shift VBP work_ln56cwsp7ffppl4wxeq7osqfuu 72 10 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 72 11 decision decision NN work_ln56cwsp7ffppl4wxeq7osqfuu 72 12 rule rule NN work_ln56cwsp7ffppl4wxeq7osqfuu 72 13 evaluation evaluation NN work_ln56cwsp7ffppl4wxeq7osqfuu 72 14 criterion criterion NN work_ln56cwsp7ffppl4wxeq7osqfuu 72 15 from from IN work_ln56cwsp7ffppl4wxeq7osqfuu 72 16 an an DT work_ln56cwsp7ffppl4wxeq7osqfuu 72 17 ordinal ordinal NN work_ln56cwsp7ffppl4wxeq7osqfuu 72 18 to to IN work_ln56cwsp7ffppl4wxeq7osqfuu 72 19 a a DT work_ln56cwsp7ffppl4wxeq7osqfuu 72 20 cardinal cardinal JJ work_ln56cwsp7ffppl4wxeq7osqfuu 72 21 approach approach NN work_ln56cwsp7ffppl4wxeq7osqfuu 72 22 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 73 1 The the DT work_ln56cwsp7ffppl4wxeq7osqfuu 73 2 problem problem NN work_ln56cwsp7ffppl4wxeq7osqfuu 73 3 therefore therefore RB work_ln56cwsp7ffppl4wxeq7osqfuu 73 4 reduces reduce VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 73 5 to to IN work_ln56cwsp7ffppl4wxeq7osqfuu 73 6 inferring infer VBG work_ln56cwsp7ffppl4wxeq7osqfuu 73 7 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 73 8 relevant relevant JJ work_ln56cwsp7ffppl4wxeq7osqfuu 73 9 utility utility NN work_ln56cwsp7ffppl4wxeq7osqfuu 73 10 intensities intensity NNS work_ln56cwsp7ffppl4wxeq7osqfuu 73 11 from from IN work_ln56cwsp7ffppl4wxeq7osqfuu 73 12 ordinal ordinal JJ work_ln56cwsp7ffppl4wxeq7osqfuu 73 13 rankings ranking NNS work_ln56cwsp7ffppl4wxeq7osqfuu 73 14 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 74 1 There there EX work_ln56cwsp7ffppl4wxeq7osqfuu 74 2 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 74 3 very very RB work_ln56cwsp7ffppl4wxeq7osqfuu 74 4 little little JJ work_ln56cwsp7ffppl4wxeq7osqfuu 74 5 work work NN work_ln56cwsp7ffppl4wxeq7osqfuu 74 6 on on IN work_ln56cwsp7ffppl4wxeq7osqfuu 74 7 evaluating evaluate VBG work_ln56cwsp7ffppl4wxeq7osqfuu 74 8 decision decision NN work_ln56cwsp7ffppl4wxeq7osqfuu 74 9 rules rule NNS work_ln56cwsp7ffppl4wxeq7osqfuu 74 10 on on IN work_ln56cwsp7ffppl4wxeq7osqfuu 74 11 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 74 12 basis basis NN work_ln56cwsp7ffppl4wxeq7osqfuu 74 13 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 74 14 some some DT work_ln56cwsp7ffppl4wxeq7osqfuu 74 15 cardinal cardinal JJ work_ln56cwsp7ffppl4wxeq7osqfuu 74 16 theory theory NN work_ln56cwsp7ffppl4wxeq7osqfuu 74 17 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 74 18 justice justice NN work_ln56cwsp7ffppl4wxeq7osqfuu 74 19 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 75 1 Notable notable JJ work_ln56cwsp7ffppl4wxeq7osqfuu 75 2 exceptions exception NNS work_ln56cwsp7ffppl4wxeq7osqfuu 75 3 are be VBP work_ln56cwsp7ffppl4wxeq7osqfuu 75 4 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 75 5 early early JJ work_ln56cwsp7ffppl4wxeq7osqfuu 75 6 simulation simulation NN work_ln56cwsp7ffppl4wxeq7osqfuu 75 7 studies study NNS work_ln56cwsp7ffppl4wxeq7osqfuu 75 8 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 75 9 Bordley Bordley NNP work_ln56cwsp7ffppl4wxeq7osqfuu 75 10 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 75 11 1983 1983 CD work_ln56cwsp7ffppl4wxeq7osqfuu 75 12 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 75 13 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 75 14 Merrill Merrill NNP work_ln56cwsp7ffppl4wxeq7osqfuu 75 15 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 75 16 1984 1984 CD work_ln56cwsp7ffppl4wxeq7osqfuu 75 17 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 75 18 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 75 19 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 75 20 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 75 21 theoretical theoretical JJ work_ln56cwsp7ffppl4wxeq7osqfuu 75 22 work work NN work_ln56cwsp7ffppl4wxeq7osqfuu 75 23 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 75 24 Weber Weber NNP work_ln56cwsp7ffppl4wxeq7osqfuu 75 25 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 75 26 1978 1978 CD work_ln56cwsp7ffppl4wxeq7osqfuu 75 27 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 75 28 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 76 1 Bordley Bordley NNP work_ln56cwsp7ffppl4wxeq7osqfuu 76 2 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 76 3 1Early 1early JJ work_ln56cwsp7ffppl4wxeq7osqfuu 76 4 studies study NNS work_ln56cwsp7ffppl4wxeq7osqfuu 76 5 are be VBP work_ln56cwsp7ffppl4wxeq7osqfuu 76 6 Brams Brams NNP work_ln56cwsp7ffppl4wxeq7osqfuu 76 7 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 76 8 Fishburn Fishburn NNP work_ln56cwsp7ffppl4wxeq7osqfuu 76 9 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 76 10 1978 1978 CD work_ln56cwsp7ffppl4wxeq7osqfuu 76 11 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 76 12 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 76 13 Caplin Caplin NNP work_ln56cwsp7ffppl4wxeq7osqfuu 76 14 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 76 15 Nalebuff Nalebuff NNP work_ln56cwsp7ffppl4wxeq7osqfuu 76 16 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 76 17 1988 1988 CD work_ln56cwsp7ffppl4wxeq7osqfuu 76 18 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 76 19 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 76 20 DeMeyer DeMeyer NNP work_ln56cwsp7ffppl4wxeq7osqfuu 76 21 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 76 22 Plott Plott NNP work_ln56cwsp7ffppl4wxeq7osqfuu 76 23 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 76 24 1970 1970 CD work_ln56cwsp7ffppl4wxeq7osqfuu 76 25 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 76 26 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 76 27 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 76 28 Nurmi Nurmi NNP work_ln56cwsp7ffppl4wxeq7osqfuu 76 29 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 76 30 1983 1983 CD work_ln56cwsp7ffppl4wxeq7osqfuu 76 31 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 76 32 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 77 1 See see VB work_ln56cwsp7ffppl4wxeq7osqfuu 77 2 also also RB work_ln56cwsp7ffppl4wxeq7osqfuu 77 3 Benoit Benoit NNP work_ln56cwsp7ffppl4wxeq7osqfuu 77 4 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 77 5 Kornhauser Kornhauser NNP work_ln56cwsp7ffppl4wxeq7osqfuu 77 6 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 77 7 2007 2007 CD work_ln56cwsp7ffppl4wxeq7osqfuu 77 8 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 77 9 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 77 10 Dasgupta Dasgupta NNP work_ln56cwsp7ffppl4wxeq7osqfuu 77 11 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 77 12 Maskin Maskin NNP work_ln56cwsp7ffppl4wxeq7osqfuu 77 13 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 77 14 2008 2008 CD work_ln56cwsp7ffppl4wxeq7osqfuu 77 15 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 77 16 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 77 17 Gehrlein Gehrlein NNP work_ln56cwsp7ffppl4wxeq7osqfuu 77 18 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 77 19 1997 1997 CD work_ln56cwsp7ffppl4wxeq7osqfuu 77 20 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 77 21 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 77 22 Levin Levin NNP work_ln56cwsp7ffppl4wxeq7osqfuu 77 23 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 77 24 Nalebuff Nalebuff NNP work_ln56cwsp7ffppl4wxeq7osqfuu 77 25 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 77 26 1995 1995 CD work_ln56cwsp7ffppl4wxeq7osqfuu 77 27 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 77 28 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 77 29 Myerson Myerson NNP work_ln56cwsp7ffppl4wxeq7osqfuu 77 30 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 77 31 2002 2002 CD work_ln56cwsp7ffppl4wxeq7osqfuu 77 32 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 77 33 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 77 34 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 77 35 Saari saari JJ work_ln56cwsp7ffppl4wxeq7osqfuu 77 36 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 77 37 1999 1999 CD work_ln56cwsp7ffppl4wxeq7osqfuu 77 38 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 77 39 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 78 1 4 4 CD work_ln56cwsp7ffppl4wxeq7osqfuu 78 2 Merrill Merrill NNP work_ln56cwsp7ffppl4wxeq7osqfuu 78 3 use use VBP work_ln56cwsp7ffppl4wxeq7osqfuu 78 4 simulations simulation NNS work_ln56cwsp7ffppl4wxeq7osqfuu 78 5 to to TO work_ln56cwsp7ffppl4wxeq7osqfuu 78 6 analyze analyze VB work_ln56cwsp7ffppl4wxeq7osqfuu 78 7 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 78 8 efficiency efficiency NN work_ln56cwsp7ffppl4wxeq7osqfuu 78 9 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 78 10 different different JJ work_ln56cwsp7ffppl4wxeq7osqfuu 78 11 voting voting NN work_ln56cwsp7ffppl4wxeq7osqfuu 78 12 systems system NNS work_ln56cwsp7ffppl4wxeq7osqfuu 78 13 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 78 14 including include VBG work_ln56cwsp7ffppl4wxeq7osqfuu 78 15 plurality plurality NN work_ln56cwsp7ffppl4wxeq7osqfuu 78 16 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 78 17 Borda Borda NNP work_ln56cwsp7ffppl4wxeq7osqfuu 78 18 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 79 1 Consistent consistent JJ work_ln56cwsp7ffppl4wxeq7osqfuu 79 2 with with IN work_ln56cwsp7ffppl4wxeq7osqfuu 79 3 our -PRON- PRP$ work_ln56cwsp7ffppl4wxeq7osqfuu 79 4 results result NNS work_ln56cwsp7ffppl4wxeq7osqfuu 79 5 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 79 6 they -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 79 7 show show VBP work_ln56cwsp7ffppl4wxeq7osqfuu 79 8 that that IN work_ln56cwsp7ffppl4wxeq7osqfuu 79 9 plurality plurality NN work_ln56cwsp7ffppl4wxeq7osqfuu 79 10 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 79 11 easily easily RB work_ln56cwsp7ffppl4wxeq7osqfuu 79 12 outperformed outperform VBN work_ln56cwsp7ffppl4wxeq7osqfuu 79 13 in in IN work_ln56cwsp7ffppl4wxeq7osqfuu 79 14 utilitarian utilitarian JJ work_ln56cwsp7ffppl4wxeq7osqfuu 79 15 terms term NNS work_ln56cwsp7ffppl4wxeq7osqfuu 79 16 by by IN work_ln56cwsp7ffppl4wxeq7osqfuu 79 17 other other JJ work_ln56cwsp7ffppl4wxeq7osqfuu 79 18 decision decision NN work_ln56cwsp7ffppl4wxeq7osqfuu 79 19 rules rule NNS work_ln56cwsp7ffppl4wxeq7osqfuu 79 20 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 80 1 Weber Weber NNP work_ln56cwsp7ffppl4wxeq7osqfuu 80 2 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 80 3 1978 1978 CD work_ln56cwsp7ffppl4wxeq7osqfuu 80 4 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 80 5 studies study VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 80 6 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 80 7 performance performance NN work_ln56cwsp7ffppl4wxeq7osqfuu 80 8 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 80 9 scoring score VBG work_ln56cwsp7ffppl4wxeq7osqfuu 80 10 rules rule NNS work_ln56cwsp7ffppl4wxeq7osqfuu 80 11 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 80 12 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 80 13 case case NN work_ln56cwsp7ffppl4wxeq7osqfuu 80 14 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 80 15 utilitarianism utilitarianism NN work_ln56cwsp7ffppl4wxeq7osqfuu 80 16 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 80 17 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 80 18 cultures culture NNS work_ln56cwsp7ffppl4wxeq7osqfuu 80 19 following follow VBG work_ln56cwsp7ffppl4wxeq7osqfuu 80 20 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 80 21 uniform uniform JJ work_ln56cwsp7ffppl4wxeq7osqfuu 80 22 distribution distribution NN work_ln56cwsp7ffppl4wxeq7osqfuu 80 23 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 81 1 He -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 81 2 shows show VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 81 3 that that IN work_ln56cwsp7ffppl4wxeq7osqfuu 81 4 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 81 5 asymptotically asymptotically RB work_ln56cwsp7ffppl4wxeq7osqfuu 81 6 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 81 7 Borda Borda NNP work_ln56cwsp7ffppl4wxeq7osqfuu 81 8 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 81 9 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 81 10 best good JJS work_ln56cwsp7ffppl4wxeq7osqfuu 81 11 scoring scoring JJ work_ln56cwsp7ffppl4wxeq7osqfuu 81 12 rule rule NN work_ln56cwsp7ffppl4wxeq7osqfuu 81 13 in in IN work_ln56cwsp7ffppl4wxeq7osqfuu 81 14 this this DT work_ln56cwsp7ffppl4wxeq7osqfuu 81 15 case case NN work_ln56cwsp7ffppl4wxeq7osqfuu 81 16 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 82 1 This this DT work_ln56cwsp7ffppl4wxeq7osqfuu 82 2 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 82 3 again again RB work_ln56cwsp7ffppl4wxeq7osqfuu 82 4 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 82 5 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 82 6 consistent consistent JJ work_ln56cwsp7ffppl4wxeq7osqfuu 82 7 with with IN work_ln56cwsp7ffppl4wxeq7osqfuu 82 8 our -PRON- PRP$ work_ln56cwsp7ffppl4wxeq7osqfuu 82 9 results result NNS work_ln56cwsp7ffppl4wxeq7osqfuu 82 10 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 83 1 In in IN work_ln56cwsp7ffppl4wxeq7osqfuu 83 2 another another DT work_ln56cwsp7ffppl4wxeq7osqfuu 83 3 related related JJ work_ln56cwsp7ffppl4wxeq7osqfuu 83 4 strand strand NN work_ln56cwsp7ffppl4wxeq7osqfuu 83 5 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 83 6 literature literature NN work_ln56cwsp7ffppl4wxeq7osqfuu 83 7 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 83 8 there there EX work_ln56cwsp7ffppl4wxeq7osqfuu 83 9 are be VBP work_ln56cwsp7ffppl4wxeq7osqfuu 83 10 papers paper NNS work_ln56cwsp7ffppl4wxeq7osqfuu 83 11 that that WDT work_ln56cwsp7ffppl4wxeq7osqfuu 83 12 study study VBP work_ln56cwsp7ffppl4wxeq7osqfuu 83 13 how how WRB work_ln56cwsp7ffppl4wxeq7osqfuu 83 14 to to TO work_ln56cwsp7ffppl4wxeq7osqfuu 83 15 select select VB work_ln56cwsp7ffppl4wxeq7osqfuu 83 16 a a DT work_ln56cwsp7ffppl4wxeq7osqfuu 83 17 voting voting NN work_ln56cwsp7ffppl4wxeq7osqfuu 83 18 rule rule NN work_ln56cwsp7ffppl4wxeq7osqfuu 83 19 in in IN work_ln56cwsp7ffppl4wxeq7osqfuu 83 20 a a DT work_ln56cwsp7ffppl4wxeq7osqfuu 83 21 constitutional constitutional JJ work_ln56cwsp7ffppl4wxeq7osqfuu 83 22 setting setting NN work_ln56cwsp7ffppl4wxeq7osqfuu 83 23 where where WRB work_ln56cwsp7ffppl4wxeq7osqfuu 83 24 there there EX work_ln56cwsp7ffppl4wxeq7osqfuu 83 25 are be VBP work_ln56cwsp7ffppl4wxeq7osqfuu 83 26 two two CD work_ln56cwsp7ffppl4wxeq7osqfuu 83 27 options option NNS work_ln56cwsp7ffppl4wxeq7osqfuu 83 28 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 83 29 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 83 30 status status NN work_ln56cwsp7ffppl4wxeq7osqfuu 83 31 quo quo NN work_ln56cwsp7ffppl4wxeq7osqfuu 83 32 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 83 33 a a DT work_ln56cwsp7ffppl4wxeq7osqfuu 83 34 second second JJ work_ln56cwsp7ffppl4wxeq7osqfuu 83 35 alternative alternative NN work_ln56cwsp7ffppl4wxeq7osqfuu 83 36 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 83 37 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 83 38 individual individual JJ work_ln56cwsp7ffppl4wxeq7osqfuu 83 39 preferences preference NNS work_ln56cwsp7ffppl4wxeq7osqfuu 83 40 are be VBP work_ln56cwsp7ffppl4wxeq7osqfuu 83 41 uncertain uncertain JJ work_ln56cwsp7ffppl4wxeq7osqfuu 83 42 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 84 1 A a DT work_ln56cwsp7ffppl4wxeq7osqfuu 84 2 voting voting NN work_ln56cwsp7ffppl4wxeq7osqfuu 84 3 rule rule NN work_ln56cwsp7ffppl4wxeq7osqfuu 84 4 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 84 5 characterized characterize VBN work_ln56cwsp7ffppl4wxeq7osqfuu 84 6 by by IN work_ln56cwsp7ffppl4wxeq7osqfuu 84 7 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 84 8 number number NN work_ln56cwsp7ffppl4wxeq7osqfuu 84 9 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 84 10 votes vote NNS work_ln56cwsp7ffppl4wxeq7osqfuu 84 11 needed need VBN work_ln56cwsp7ffppl4wxeq7osqfuu 84 12 to to TO work_ln56cwsp7ffppl4wxeq7osqfuu 84 13 accept accept VB work_ln56cwsp7ffppl4wxeq7osqfuu 84 14 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 84 15 second second JJ work_ln56cwsp7ffppl4wxeq7osqfuu 84 16 alternative alternative NN work_ln56cwsp7ffppl4wxeq7osqfuu 84 17 over over IN work_ln56cwsp7ffppl4wxeq7osqfuu 84 18 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 84 19 status status NN work_ln56cwsp7ffppl4wxeq7osqfuu 84 20 quo quo NN work_ln56cwsp7ffppl4wxeq7osqfuu 84 21 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 85 1 The the DT work_ln56cwsp7ffppl4wxeq7osqfuu 85 2 papers paper NNS work_ln56cwsp7ffppl4wxeq7osqfuu 85 3 that that WDT work_ln56cwsp7ffppl4wxeq7osqfuu 85 4 comprise comprise VBP work_ln56cwsp7ffppl4wxeq7osqfuu 85 5 this this DT work_ln56cwsp7ffppl4wxeq7osqfuu 85 6 literature literature NN work_ln56cwsp7ffppl4wxeq7osqfuu 85 7 examine examine VBP work_ln56cwsp7ffppl4wxeq7osqfuu 85 8 issues issue NNS work_ln56cwsp7ffppl4wxeq7osqfuu 85 9 such such JJ work_ln56cwsp7ffppl4wxeq7osqfuu 85 10 as as IN work_ln56cwsp7ffppl4wxeq7osqfuu 85 11 which which WDT work_ln56cwsp7ffppl4wxeq7osqfuu 85 12 voting voting NN work_ln56cwsp7ffppl4wxeq7osqfuu 85 13 rules rule NNS work_ln56cwsp7ffppl4wxeq7osqfuu 85 14 maximize maximize VBP work_ln56cwsp7ffppl4wxeq7osqfuu 85 15 efficiency efficiency NN work_ln56cwsp7ffppl4wxeq7osqfuu 85 16 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 85 17 which which WDT work_ln56cwsp7ffppl4wxeq7osqfuu 85 18 are be VBP work_ln56cwsp7ffppl4wxeq7osqfuu 85 19 self self NN work_ln56cwsp7ffppl4wxeq7osqfuu 85 20 - - HYPH work_ln56cwsp7ffppl4wxeq7osqfuu 85 21 stable stable JJ work_ln56cwsp7ffppl4wxeq7osqfuu 85 22 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 85 23 how how WRB work_ln56cwsp7ffppl4wxeq7osqfuu 85 24 to to TO work_ln56cwsp7ffppl4wxeq7osqfuu 85 25 weight weight VB work_ln56cwsp7ffppl4wxeq7osqfuu 85 26 votes vote NNS work_ln56cwsp7ffppl4wxeq7osqfuu 85 27 in in IN work_ln56cwsp7ffppl4wxeq7osqfuu 85 28 heterogeneous heterogeneous JJ work_ln56cwsp7ffppl4wxeq7osqfuu 85 29 contexts contexts NN work_ln56cwsp7ffppl4wxeq7osqfuu 85 30 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 85 31 self self NN work_ln56cwsp7ffppl4wxeq7osqfuu 85 32 - - HYPH work_ln56cwsp7ffppl4wxeq7osqfuu 85 33 enforcement enforcement NN work_ln56cwsp7ffppl4wxeq7osqfuu 85 34 voting voting NN work_ln56cwsp7ffppl4wxeq7osqfuu 85 35 rules rule NNS work_ln56cwsp7ffppl4wxeq7osqfuu 85 36 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 85 37 etc etc FW work_ln56cwsp7ffppl4wxeq7osqfuu 85 38 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 86 1 For for IN work_ln56cwsp7ffppl4wxeq7osqfuu 86 2 examples example NNS work_ln56cwsp7ffppl4wxeq7osqfuu 86 3 in in IN work_ln56cwsp7ffppl4wxeq7osqfuu 86 4 this this DT work_ln56cwsp7ffppl4wxeq7osqfuu 86 5 vein vein NN work_ln56cwsp7ffppl4wxeq7osqfuu 86 6 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 86 7 see see VB work_ln56cwsp7ffppl4wxeq7osqfuu 86 8 Rae Rae NNP work_ln56cwsp7ffppl4wxeq7osqfuu 86 9 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 86 10 1969 1969 CD work_ln56cwsp7ffppl4wxeq7osqfuu 86 11 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 86 12 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 86 13 Barbera Barbera NNP work_ln56cwsp7ffppl4wxeq7osqfuu 86 14 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 86 15 Jackson Jackson NNP work_ln56cwsp7ffppl4wxeq7osqfuu 86 16 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 86 17 2004 2004 CD work_ln56cwsp7ffppl4wxeq7osqfuu 86 18 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 86 19 2006 2006 CD work_ln56cwsp7ffppl4wxeq7osqfuu 86 20 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 86 21 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 86 22 Maggi Maggi NNP work_ln56cwsp7ffppl4wxeq7osqfuu 86 23 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 86 24 Morelli Morelli NNP work_ln56cwsp7ffppl4wxeq7osqfuu 86 25 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 86 26 2006 2006 CD work_ln56cwsp7ffppl4wxeq7osqfuu 86 27 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 86 28 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 86 29 papers paper NNS work_ln56cwsp7ffppl4wxeq7osqfuu 86 30 cited cite VBD work_ln56cwsp7ffppl4wxeq7osqfuu 86 31 therein therein RB work_ln56cwsp7ffppl4wxeq7osqfuu 86 32 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 87 1 Finally finally RB work_ln56cwsp7ffppl4wxeq7osqfuu 87 2 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 87 3 there there EX work_ln56cwsp7ffppl4wxeq7osqfuu 87 4 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 87 5 a a DT work_ln56cwsp7ffppl4wxeq7osqfuu 87 6 growing grow VBG work_ln56cwsp7ffppl4wxeq7osqfuu 87 7 literature literature NN work_ln56cwsp7ffppl4wxeq7osqfuu 87 8 addressing address VBG work_ln56cwsp7ffppl4wxeq7osqfuu 87 9 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 87 10 question question NN work_ln56cwsp7ffppl4wxeq7osqfuu 87 11 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 87 12 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 87 13 transmission transmission NN work_ln56cwsp7ffppl4wxeq7osqfuu 87 14 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 87 15 utility utility NN work_ln56cwsp7ffppl4wxeq7osqfuu 87 16 intensities intensity NNS work_ln56cwsp7ffppl4wxeq7osqfuu 87 17 in in IN work_ln56cwsp7ffppl4wxeq7osqfuu 87 18 collective collective JJ work_ln56cwsp7ffppl4wxeq7osqfuu 87 19 decision decision NN work_ln56cwsp7ffppl4wxeq7osqfuu 87 20 problems problem NNS work_ln56cwsp7ffppl4wxeq7osqfuu 87 21 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 87 22 see see VB work_ln56cwsp7ffppl4wxeq7osqfuu 87 23 Casella Casella NNP work_ln56cwsp7ffppl4wxeq7osqfuu 87 24 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 87 25 2005 2005 CD work_ln56cwsp7ffppl4wxeq7osqfuu 87 26 ; ; : work_ln56cwsp7ffppl4wxeq7osqfuu 87 27 Jackson Jackson NNP work_ln56cwsp7ffppl4wxeq7osqfuu 87 28 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 87 29 Sonnenschein Sonnenschein NNP work_ln56cwsp7ffppl4wxeq7osqfuu 87 30 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 87 31 2007 2007 CD work_ln56cwsp7ffppl4wxeq7osqfuu 87 32 ; ; : work_ln56cwsp7ffppl4wxeq7osqfuu 87 33 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 87 34 Hortala Hortala NNP work_ln56cwsp7ffppl4wxeq7osqfuu 87 35 - - HYPH work_ln56cwsp7ffppl4wxeq7osqfuu 87 36 Vallve Vallve NNP work_ln56cwsp7ffppl4wxeq7osqfuu 87 37 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 87 38 2007 2007 CD work_ln56cwsp7ffppl4wxeq7osqfuu 87 39 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 87 40 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 88 1 The the DT work_ln56cwsp7ffppl4wxeq7osqfuu 88 2 innovation innovation NN work_ln56cwsp7ffppl4wxeq7osqfuu 88 3 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 88 4 these these DT work_ln56cwsp7ffppl4wxeq7osqfuu 88 5 papers paper NNS work_ln56cwsp7ffppl4wxeq7osqfuu 88 6 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 88 7 to to TO work_ln56cwsp7ffppl4wxeq7osqfuu 88 8 consider consider VB work_ln56cwsp7ffppl4wxeq7osqfuu 88 9 a a DT work_ln56cwsp7ffppl4wxeq7osqfuu 88 10 collective collective JJ work_ln56cwsp7ffppl4wxeq7osqfuu 88 11 decision decision NN work_ln56cwsp7ffppl4wxeq7osqfuu 88 12 situation situation NN work_ln56cwsp7ffppl4wxeq7osqfuu 88 13 problem problem NN work_ln56cwsp7ffppl4wxeq7osqfuu 88 14 repeated repeat VBN work_ln56cwsp7ffppl4wxeq7osqfuu 88 15 over over IN work_ln56cwsp7ffppl4wxeq7osqfuu 88 16 T T NNP work_ln56cwsp7ffppl4wxeq7osqfuu 88 17 times time NNS work_ln56cwsp7ffppl4wxeq7osqfuu 88 18 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 88 19 endow endow NN work_ln56cwsp7ffppl4wxeq7osqfuu 88 20 individuals individual NNS work_ln56cwsp7ffppl4wxeq7osqfuu 88 21 with with IN work_ln56cwsp7ffppl4wxeq7osqfuu 88 22 a a DT work_ln56cwsp7ffppl4wxeq7osqfuu 88 23 maximum maximum JJ work_ln56cwsp7ffppl4wxeq7osqfuu 88 24 number number NN work_ln56cwsp7ffppl4wxeq7osqfuu 88 25 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 88 26 votes vote NNS work_ln56cwsp7ffppl4wxeq7osqfuu 88 27 to to TO work_ln56cwsp7ffppl4wxeq7osqfuu 88 28 allocate allocate VB work_ln56cwsp7ffppl4wxeq7osqfuu 88 29 over over IN work_ln56cwsp7ffppl4wxeq7osqfuu 88 30 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 88 31 T T NNP work_ln56cwsp7ffppl4wxeq7osqfuu 88 32 problems problem NNS work_ln56cwsp7ffppl4wxeq7osqfuu 88 33 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 89 1 By by IN work_ln56cwsp7ffppl4wxeq7osqfuu 89 2 so so RB work_ln56cwsp7ffppl4wxeq7osqfuu 89 3 doing do VBG work_ln56cwsp7ffppl4wxeq7osqfuu 89 4 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 89 5 individuals individual NNS work_ln56cwsp7ffppl4wxeq7osqfuu 89 6 may may MD work_ln56cwsp7ffppl4wxeq7osqfuu 89 7 transmit transmit VB work_ln56cwsp7ffppl4wxeq7osqfuu 89 8 utility utility NN work_ln56cwsp7ffppl4wxeq7osqfuu 89 9 intensities intensity NNS work_ln56cwsp7ffppl4wxeq7osqfuu 89 10 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 90 1 The the DT work_ln56cwsp7ffppl4wxeq7osqfuu 90 2 remainder remainder NN work_ln56cwsp7ffppl4wxeq7osqfuu 90 3 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 90 4 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 90 5 paper paper NN work_ln56cwsp7ffppl4wxeq7osqfuu 90 6 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 90 7 organized organize VBN work_ln56cwsp7ffppl4wxeq7osqfuu 90 8 as as IN work_ln56cwsp7ffppl4wxeq7osqfuu 90 9 follows follow VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 90 10 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 91 1 Section section NN work_ln56cwsp7ffppl4wxeq7osqfuu 91 2 2 2 CD work_ln56cwsp7ffppl4wxeq7osqfuu 91 3 introduces introduce NNS work_ln56cwsp7ffppl4wxeq7osqfuu 91 4 in in IN work_ln56cwsp7ffppl4wxeq7osqfuu 91 5 detail detail NN work_ln56cwsp7ffppl4wxeq7osqfuu 91 6 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 91 7 setting setting NN work_ln56cwsp7ffppl4wxeq7osqfuu 91 8 in in IN work_ln56cwsp7ffppl4wxeq7osqfuu 91 9 which which WDT work_ln56cwsp7ffppl4wxeq7osqfuu 91 10 we -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 91 11 will will MD work_ln56cwsp7ffppl4wxeq7osqfuu 91 12 be be VB work_ln56cwsp7ffppl4wxeq7osqfuu 91 13 working work VBG work_ln56cwsp7ffppl4wxeq7osqfuu 91 14 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 92 1 Sections section NNS work_ln56cwsp7ffppl4wxeq7osqfuu 92 2 3 3 CD work_ln56cwsp7ffppl4wxeq7osqfuu 92 3 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 92 4 4 4 CD work_ln56cwsp7ffppl4wxeq7osqfuu 92 5 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 92 6 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 92 7 5 5 CD work_ln56cwsp7ffppl4wxeq7osqfuu 92 8 study study VB work_ln56cwsp7ffppl4wxeq7osqfuu 92 9 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 92 10 cases case NNS work_ln56cwsp7ffppl4wxeq7osqfuu 92 11 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 92 12 utilitarianism utilitarianism NN work_ln56cwsp7ffppl4wxeq7osqfuu 92 13 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 92 14 maximax maximax NNP work_ln56cwsp7ffppl4wxeq7osqfuu 92 15 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 92 16 maximin maximin NNP work_ln56cwsp7ffppl4wxeq7osqfuu 92 17 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 92 18 respectively respectively RB work_ln56cwsp7ffppl4wxeq7osqfuu 92 19 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 93 1 Finally finally RB work_ln56cwsp7ffppl4wxeq7osqfuu 93 2 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 93 3 Section section NN work_ln56cwsp7ffppl4wxeq7osqfuu 93 4 6 6 CD work_ln56cwsp7ffppl4wxeq7osqfuu 93 5 presents present VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 93 6 some some DT work_ln56cwsp7ffppl4wxeq7osqfuu 93 7 conclusions conclusion NNS work_ln56cwsp7ffppl4wxeq7osqfuu 93 8 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 94 1 All all PDT work_ln56cwsp7ffppl4wxeq7osqfuu 94 2 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 94 3 proofs proof NNS work_ln56cwsp7ffppl4wxeq7osqfuu 94 4 are be VBP work_ln56cwsp7ffppl4wxeq7osqfuu 94 5 given give VBN work_ln56cwsp7ffppl4wxeq7osqfuu 94 6 in in IN work_ln56cwsp7ffppl4wxeq7osqfuu 94 7 Appendix Appendix NNP work_ln56cwsp7ffppl4wxeq7osqfuu 94 8 A. A. NNP work_ln56cwsp7ffppl4wxeq7osqfuu 95 1 2 2 LS work_ln56cwsp7ffppl4wxeq7osqfuu 95 2 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 96 1 Environment Environment NNP work_ln56cwsp7ffppl4wxeq7osqfuu 96 2 Let Let VBD work_ln56cwsp7ffppl4wxeq7osqfuu 96 3 N n CC work_ln56cwsp7ffppl4wxeq7osqfuu 96 4 be be VB work_ln56cwsp7ffppl4wxeq7osqfuu 96 5 a a DT work_ln56cwsp7ffppl4wxeq7osqfuu 96 6 finite finite JJ work_ln56cwsp7ffppl4wxeq7osqfuu 96 7 set set NN work_ln56cwsp7ffppl4wxeq7osqfuu 96 8 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 96 9 individuals individual NNS work_ln56cwsp7ffppl4wxeq7osqfuu 96 10 with with IN work_ln56cwsp7ffppl4wxeq7osqfuu 96 11 cardinality cardinality NN work_ln56cwsp7ffppl4wxeq7osqfuu 96 12 n n CC work_ln56cwsp7ffppl4wxeq7osqfuu 96 13 ≥ ≥ NN work_ln56cwsp7ffppl4wxeq7osqfuu 96 14 2 2 CD work_ln56cwsp7ffppl4wxeq7osqfuu 96 15 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 96 16 K K NNP work_ln56cwsp7ffppl4wxeq7osqfuu 96 17 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 96 18 set set NN work_ln56cwsp7ffppl4wxeq7osqfuu 96 19 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 96 20 alternatives alternative NNS work_ln56cwsp7ffppl4wxeq7osqfuu 96 21 with with IN work_ln56cwsp7ffppl4wxeq7osqfuu 96 22 cardinality cardinality NN work_ln56cwsp7ffppl4wxeq7osqfuu 96 23 k k NN work_ln56cwsp7ffppl4wxeq7osqfuu 96 24 ≥ ≥ DT work_ln56cwsp7ffppl4wxeq7osqfuu 96 25 3 3 CD work_ln56cwsp7ffppl4wxeq7osqfuu 96 26 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 97 1 Typical typical JJ work_ln56cwsp7ffppl4wxeq7osqfuu 97 2 elements element NNS work_ln56cwsp7ffppl4wxeq7osqfuu 97 3 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 97 4 N n NN work_ln56cwsp7ffppl4wxeq7osqfuu 97 5 are be VBP work_ln56cwsp7ffppl4wxeq7osqfuu 97 6 denoted denote VBN work_ln56cwsp7ffppl4wxeq7osqfuu 97 7 by by IN work_ln56cwsp7ffppl4wxeq7osqfuu 97 8 i i PRP work_ln56cwsp7ffppl4wxeq7osqfuu 97 9 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 97 10 j j NNP work_ln56cwsp7ffppl4wxeq7osqfuu 97 11 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 97 12 those those DT work_ln56cwsp7ffppl4wxeq7osqfuu 97 13 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 97 14 K K NNP work_ln56cwsp7ffppl4wxeq7osqfuu 97 15 are be VBP work_ln56cwsp7ffppl4wxeq7osqfuu 97 16 denoted denote VBN work_ln56cwsp7ffppl4wxeq7osqfuu 97 17 by by IN work_ln56cwsp7ffppl4wxeq7osqfuu 97 18 l l NN work_ln56cwsp7ffppl4wxeq7osqfuu 97 19 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 97 20 h h NNP work_ln56cwsp7ffppl4wxeq7osqfuu 97 21 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 97 22 q. q. NN work_ln56cwsp7ffppl4wxeq7osqfuu 98 1 We -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 98 2 then then RB work_ln56cwsp7ffppl4wxeq7osqfuu 98 3 say say VBP work_ln56cwsp7ffppl4wxeq7osqfuu 98 4 that that IN work_ln56cwsp7ffppl4wxeq7osqfuu 98 5 a a DT work_ln56cwsp7ffppl4wxeq7osqfuu 98 6 society society NN work_ln56cwsp7ffppl4wxeq7osqfuu 98 7 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 98 8 composed compose VBN work_ln56cwsp7ffppl4wxeq7osqfuu 98 9 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 98 10 n n JJ work_ln56cwsp7ffppl4wxeq7osqfuu 98 11 individuals individual NNS work_ln56cwsp7ffppl4wxeq7osqfuu 98 12 with with IN work_ln56cwsp7ffppl4wxeq7osqfuu 98 13 preferences preference NNS work_ln56cwsp7ffppl4wxeq7osqfuu 98 14 over over IN work_ln56cwsp7ffppl4wxeq7osqfuu 98 15 k k NNP work_ln56cwsp7ffppl4wxeq7osqfuu 98 16 alternatives alternative NNS work_ln56cwsp7ffppl4wxeq7osqfuu 98 17 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 99 1 To to TO work_ln56cwsp7ffppl4wxeq7osqfuu 99 2 address address VB work_ln56cwsp7ffppl4wxeq7osqfuu 99 3 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 99 4 question question NN work_ln56cwsp7ffppl4wxeq7osqfuu 99 5 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 99 6 finding find VBG work_ln56cwsp7ffppl4wxeq7osqfuu 99 7 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 99 8 best good JJS work_ln56cwsp7ffppl4wxeq7osqfuu 99 9 ordinal ordinal JJ work_ln56cwsp7ffppl4wxeq7osqfuu 99 10 decision decision NN work_ln56cwsp7ffppl4wxeq7osqfuu 99 11 rule rule NN work_ln56cwsp7ffppl4wxeq7osqfuu 99 12 to to TO work_ln56cwsp7ffppl4wxeq7osqfuu 99 13 approach approach VB work_ln56cwsp7ffppl4wxeq7osqfuu 99 14 each each DT work_ln56cwsp7ffppl4wxeq7osqfuu 99 15 given give VBN work_ln56cwsp7ffppl4wxeq7osqfuu 99 16 ideal ideal NN work_ln56cwsp7ffppl4wxeq7osqfuu 99 17 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 99 18 justice justice NN work_ln56cwsp7ffppl4wxeq7osqfuu 99 19 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 99 20 we -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 99 21 first first RB work_ln56cwsp7ffppl4wxeq7osqfuu 99 22 present present VBP work_ln56cwsp7ffppl4wxeq7osqfuu 99 23 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 99 24 cardinal cardinal JJ work_ln56cwsp7ffppl4wxeq7osqfuu 99 25 environment environment NN work_ln56cwsp7ffppl4wxeq7osqfuu 99 26 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 99 27 utilities utility NNS work_ln56cwsp7ffppl4wxeq7osqfuu 99 28 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 99 29 ideals ideal NNS work_ln56cwsp7ffppl4wxeq7osqfuu 99 30 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 99 31 justice justice NN work_ln56cwsp7ffppl4wxeq7osqfuu 99 32 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 99 33 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 99 34 then then RB work_ln56cwsp7ffppl4wxeq7osqfuu 99 35 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 99 36 ordinal ordinal JJ work_ln56cwsp7ffppl4wxeq7osqfuu 99 37 setting setting NN work_ln56cwsp7ffppl4wxeq7osqfuu 99 38 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 99 39 decision decision NN work_ln56cwsp7ffppl4wxeq7osqfuu 99 40 rules rule NNS work_ln56cwsp7ffppl4wxeq7osqfuu 99 41 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 99 42 ordinal ordinal JJ work_ln56cwsp7ffppl4wxeq7osqfuu 99 43 preferences preference NNS work_ln56cwsp7ffppl4wxeq7osqfuu 99 44 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 99 45 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 99 46 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 99 47 then then RB work_ln56cwsp7ffppl4wxeq7osqfuu 99 48 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 99 49 one one NN work_ln56cwsp7ffppl4wxeq7osqfuu 99 50 that that WDT work_ln56cwsp7ffppl4wxeq7osqfuu 99 51 connects connect VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 99 52 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 99 53 two two CD work_ln56cwsp7ffppl4wxeq7osqfuu 99 54 worlds world NNS work_ln56cwsp7ffppl4wxeq7osqfuu 99 55 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 99 56 indices index NNS work_ln56cwsp7ffppl4wxeq7osqfuu 99 57 evaluating evaluate VBG work_ln56cwsp7ffppl4wxeq7osqfuu 99 58 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 99 59 success success NN work_ln56cwsp7ffppl4wxeq7osqfuu 99 60 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 99 61 a a DT work_ln56cwsp7ffppl4wxeq7osqfuu 99 62 decision decision NN work_ln56cwsp7ffppl4wxeq7osqfuu 99 63 rule rule NN work_ln56cwsp7ffppl4wxeq7osqfuu 99 64 in in IN work_ln56cwsp7ffppl4wxeq7osqfuu 99 65 terms term NNS work_ln56cwsp7ffppl4wxeq7osqfuu 99 66 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 99 67 an an DT work_ln56cwsp7ffppl4wxeq7osqfuu 99 68 ideal ideal NN work_ln56cwsp7ffppl4wxeq7osqfuu 99 69 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 99 70 justice justice NN work_ln56cwsp7ffppl4wxeq7osqfuu 99 71 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 99 72 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 100 1 2.1 2.1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 100 2 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 101 1 Cardinal Cardinal NNP work_ln56cwsp7ffppl4wxeq7osqfuu 101 2 Preferences Preferences NNPS work_ln56cwsp7ffppl4wxeq7osqfuu 101 3 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 102 1 Individual individual JJ work_ln56cwsp7ffppl4wxeq7osqfuu 102 2 preferences preference NNS work_ln56cwsp7ffppl4wxeq7osqfuu 102 3 over over IN work_ln56cwsp7ffppl4wxeq7osqfuu 102 4 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 102 5 set set NN work_ln56cwsp7ffppl4wxeq7osqfuu 102 6 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 102 7 alternatives alternative NNS work_ln56cwsp7ffppl4wxeq7osqfuu 102 8 are be VBP work_ln56cwsp7ffppl4wxeq7osqfuu 102 9 cardinal cardinal JJ work_ln56cwsp7ffppl4wxeq7osqfuu 102 10 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 102 11 interpersonally interpersonally RB work_ln56cwsp7ffppl4wxeq7osqfuu 102 12 comparable comparable JJ work_ln56cwsp7ffppl4wxeq7osqfuu 102 13 utility utility NN work_ln56cwsp7ffppl4wxeq7osqfuu 102 14 random random JJ work_ln56cwsp7ffppl4wxeq7osqfuu 102 15 variables variable NNS work_ln56cwsp7ffppl4wxeq7osqfuu 102 16 in in IN work_ln56cwsp7ffppl4wxeq7osqfuu 102 17 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 102 18 [ [ -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 102 19 0 0 CD work_ln56cwsp7ffppl4wxeq7osqfuu 102 20 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 102 21 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 102 22 ] ] -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 102 23 interval interval NN work_ln56cwsp7ffppl4wxeq7osqfuu 102 24 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 103 1 Uli Uli NNP work_ln56cwsp7ffppl4wxeq7osqfuu 103 2 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 103 3 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 103 4 random random JJ work_ln56cwsp7ffppl4wxeq7osqfuu 103 5 variable variable JJ work_ln56cwsp7ffppl4wxeq7osqfuu 103 6 representing represent VBG work_ln56cwsp7ffppl4wxeq7osqfuu 103 7 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 103 8 cardinal cardinal JJ work_ln56cwsp7ffppl4wxeq7osqfuu 103 9 utility utility NN work_ln56cwsp7ffppl4wxeq7osqfuu 103 10 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 103 11 individual individual NN work_ln56cwsp7ffppl4wxeq7osqfuu 103 12 i i PRP work_ln56cwsp7ffppl4wxeq7osqfuu 103 13 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 103 14 alternative alternative NN work_ln56cwsp7ffppl4wxeq7osqfuu 103 15 5 5 CD work_ln56cwsp7ffppl4wxeq7osqfuu 103 16 l. l. NN work_ln56cwsp7ffppl4wxeq7osqfuu 103 17 We -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 103 18 adopt adopt VBP work_ln56cwsp7ffppl4wxeq7osqfuu 103 19 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 103 20 convention convention NN work_ln56cwsp7ffppl4wxeq7osqfuu 103 21 that that WDT work_ln56cwsp7ffppl4wxeq7osqfuu 103 22 subindices subindice VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 103 23 refer refer VBP work_ln56cwsp7ffppl4wxeq7osqfuu 103 24 to to IN work_ln56cwsp7ffppl4wxeq7osqfuu 103 25 individuals individual NNS work_ln56cwsp7ffppl4wxeq7osqfuu 103 26 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 103 27 superindices superindice NNS work_ln56cwsp7ffppl4wxeq7osqfuu 103 28 refer refer VBP work_ln56cwsp7ffppl4wxeq7osqfuu 103 29 to to IN work_ln56cwsp7ffppl4wxeq7osqfuu 103 30 alternatives alternative NNS work_ln56cwsp7ffppl4wxeq7osqfuu 103 31 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 104 1 Let let VB work_ln56cwsp7ffppl4wxeq7osqfuu 104 2 culture culture NN work_ln56cwsp7ffppl4wxeq7osqfuu 104 3 C c NN work_ln56cwsp7ffppl4wxeq7osqfuu 104 4 be be VB work_ln56cwsp7ffppl4wxeq7osqfuu 104 5 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 104 6 probability probability NN work_ln56cwsp7ffppl4wxeq7osqfuu 104 7 distribution distribution NN work_ln56cwsp7ffppl4wxeq7osqfuu 104 8 from from IN work_ln56cwsp7ffppl4wxeq7osqfuu 104 9 which which WDT work_ln56cwsp7ffppl4wxeq7osqfuu 104 10 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 104 11 cardinal cardinal JJ work_ln56cwsp7ffppl4wxeq7osqfuu 104 12 individual individual JJ work_ln56cwsp7ffppl4wxeq7osqfuu 104 13 utility utility NN work_ln56cwsp7ffppl4wxeq7osqfuu 104 14 values value NNS work_ln56cwsp7ffppl4wxeq7osqfuu 104 15 are be VBP work_ln56cwsp7ffppl4wxeq7osqfuu 104 16 drawn draw VBN work_ln56cwsp7ffppl4wxeq7osqfuu 104 17 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 105 1 We -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 105 2 consider consider VBP work_ln56cwsp7ffppl4wxeq7osqfuu 105 3 cultures culture NNS work_ln56cwsp7ffppl4wxeq7osqfuu 105 4 with with IN work_ln56cwsp7ffppl4wxeq7osqfuu 105 5 continuous continuous JJ work_ln56cwsp7ffppl4wxeq7osqfuu 105 6 probability probability NN work_ln56cwsp7ffppl4wxeq7osqfuu 105 7 distributions distribution NNS work_ln56cwsp7ffppl4wxeq7osqfuu 105 8 on on IN work_ln56cwsp7ffppl4wxeq7osqfuu 105 9 [ [ -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 105 10 0 0 CD work_ln56cwsp7ffppl4wxeq7osqfuu 105 11 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 105 12 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 105 13 ] ] -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 105 14 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 106 1 Hence hence RB work_ln56cwsp7ffppl4wxeq7osqfuu 106 2 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 106 3 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 106 4 probability probability NN work_ln56cwsp7ffppl4wxeq7osqfuu 106 5 that that WDT work_ln56cwsp7ffppl4wxeq7osqfuu 106 6 Uli Uli NNP work_ln56cwsp7ffppl4wxeq7osqfuu 106 7 takes take VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 106 8 a a DT work_ln56cwsp7ffppl4wxeq7osqfuu 106 9 particular particular JJ work_ln56cwsp7ffppl4wxeq7osqfuu 106 10 value value NN work_ln56cwsp7ffppl4wxeq7osqfuu 106 11 on on IN work_ln56cwsp7ffppl4wxeq7osqfuu 106 12 [ [ -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 106 13 0 0 CD work_ln56cwsp7ffppl4wxeq7osqfuu 106 14 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 106 15 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 106 16 ] ] -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 106 17 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 106 18 zero zero CD work_ln56cwsp7ffppl4wxeq7osqfuu 106 19 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 106 20 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 106 21 then then RB work_ln56cwsp7ffppl4wxeq7osqfuu 106 22 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 106 23 probability probability NN work_ln56cwsp7ffppl4wxeq7osqfuu 106 24 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 106 25 ties tie NNS work_ln56cwsp7ffppl4wxeq7osqfuu 106 26 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 106 27 i.e. i.e. FW work_ln56cwsp7ffppl4wxeq7osqfuu 106 28 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 106 29 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 106 30 individual individual NN work_ln56cwsp7ffppl4wxeq7osqfuu 106 31 i i PRP work_ln56cwsp7ffppl4wxeq7osqfuu 106 32 being be VBG work_ln56cwsp7ffppl4wxeq7osqfuu 106 33 indifferent indifferent JJ work_ln56cwsp7ffppl4wxeq7osqfuu 106 34 between between IN work_ln56cwsp7ffppl4wxeq7osqfuu 106 35 two two CD work_ln56cwsp7ffppl4wxeq7osqfuu 106 36 alternatives alternative NNS work_ln56cwsp7ffppl4wxeq7osqfuu 106 37 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 106 38 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 106 39 also also RB work_ln56cwsp7ffppl4wxeq7osqfuu 106 40 zero.2 zero.2 PRP work_ln56cwsp7ffppl4wxeq7osqfuu 106 41 Moreover moreover RB work_ln56cwsp7ffppl4wxeq7osqfuu 106 42 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 106 43 we -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 106 44 assume assume VBP work_ln56cwsp7ffppl4wxeq7osqfuu 106 45 that that IN work_ln56cwsp7ffppl4wxeq7osqfuu 106 46 variables variable NNS work_ln56cwsp7ffppl4wxeq7osqfuu 106 47 { { -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 106 48 Uli}i∈N uli}i∈n UH work_ln56cwsp7ffppl4wxeq7osqfuu 106 49 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 106 50 l∈K l∈K NNP work_ln56cwsp7ffppl4wxeq7osqfuu 106 51 are be VBP work_ln56cwsp7ffppl4wxeq7osqfuu 106 52 iid iid JJ work_ln56cwsp7ffppl4wxeq7osqfuu 106 53 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 107 1 We -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 107 2 say say VBP work_ln56cwsp7ffppl4wxeq7osqfuu 107 3 that that IN work_ln56cwsp7ffppl4wxeq7osqfuu 107 4 a a DT work_ln56cwsp7ffppl4wxeq7osqfuu 107 5 culture culture NN work_ln56cwsp7ffppl4wxeq7osqfuu 107 6 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 107 7 symmetric symmetric JJ work_ln56cwsp7ffppl4wxeq7osqfuu 107 8 whenever whenever WRB work_ln56cwsp7ffppl4wxeq7osqfuu 107 9 its -PRON- PRP$ work_ln56cwsp7ffppl4wxeq7osqfuu 107 10 density density NN work_ln56cwsp7ffppl4wxeq7osqfuu 107 11 function function NN work_ln56cwsp7ffppl4wxeq7osqfuu 107 12 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 107 13 symmetric symmetric JJ work_ln56cwsp7ffppl4wxeq7osqfuu 107 14 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 108 1 Given give VBN work_ln56cwsp7ffppl4wxeq7osqfuu 108 2 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 108 3 random random JJ work_ln56cwsp7ffppl4wxeq7osqfuu 108 4 variables variable NNS work_ln56cwsp7ffppl4wxeq7osqfuu 108 5 U1i u1i CD work_ln56cwsp7ffppl4wxeq7osqfuu 108 6 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 108 7 U u NN work_ln56cwsp7ffppl4wxeq7osqfuu 108 8 2 2 CD work_ln56cwsp7ffppl4wxeq7osqfuu 108 9 i i PRP work_ln56cwsp7ffppl4wxeq7osqfuu 108 10 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 108 11 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 109 1 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 110 1 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 111 1 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 111 2 U U NNP work_ln56cwsp7ffppl4wxeq7osqfuu 111 3 k k NNP work_ln56cwsp7ffppl4wxeq7osqfuu 111 4 i i NN work_ln56cwsp7ffppl4wxeq7osqfuu 111 5 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 111 6 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 111 7 order order NN work_ln56cwsp7ffppl4wxeq7osqfuu 111 8 statistics statistic VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 111 9 U u NN work_ln56cwsp7ffppl4wxeq7osqfuu 111 10 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 111 11 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 111 12 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 111 13 i i PRP work_ln56cwsp7ffppl4wxeq7osqfuu 111 14 ≤ ≤ VBP work_ln56cwsp7ffppl4wxeq7osqfuu 111 15 U U NNP work_ln56cwsp7ffppl4wxeq7osqfuu 111 16 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 111 17 2 2 CD work_ln56cwsp7ffppl4wxeq7osqfuu 111 18 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 111 19 i i PRP work_ln56cwsp7ffppl4wxeq7osqfuu 111 20 ≤ ≤ VBP work_ln56cwsp7ffppl4wxeq7osqfuu 111 21 · · NFP work_ln56cwsp7ffppl4wxeq7osqfuu 111 22 · · NFP work_ln56cwsp7ffppl4wxeq7osqfuu 111 23 · · NFP work_ln56cwsp7ffppl4wxeq7osqfuu 111 24 ≤ ≤ XX work_ln56cwsp7ffppl4wxeq7osqfuu 111 25 U u NN work_ln56cwsp7ffppl4wxeq7osqfuu 111 26 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 111 27 k k NNP work_ln56cwsp7ffppl4wxeq7osqfuu 111 28 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 111 29 i i PRP work_ln56cwsp7ffppl4wxeq7osqfuu 111 30 are be VBP work_ln56cwsp7ffppl4wxeq7osqfuu 111 31 also also RB work_ln56cwsp7ffppl4wxeq7osqfuu 111 32 random random JJ work_ln56cwsp7ffppl4wxeq7osqfuu 111 33 variables variable NNS work_ln56cwsp7ffppl4wxeq7osqfuu 111 34 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 111 35 defined define VBN work_ln56cwsp7ffppl4wxeq7osqfuu 111 36 by by IN work_ln56cwsp7ffppl4wxeq7osqfuu 111 37 sorting sort VBG work_ln56cwsp7ffppl4wxeq7osqfuu 111 38 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 111 39 realizations realization NNS work_ln56cwsp7ffppl4wxeq7osqfuu 111 40 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 111 41 U u NN work_ln56cwsp7ffppl4wxeq7osqfuu 111 42 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 111 43 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 111 44 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 111 45 i i PRP work_ln56cwsp7ffppl4wxeq7osqfuu 111 46 ≤ ≤ VBP work_ln56cwsp7ffppl4wxeq7osqfuu 111 47 U U NNP work_ln56cwsp7ffppl4wxeq7osqfuu 111 48 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 111 49 2 2 CD work_ln56cwsp7ffppl4wxeq7osqfuu 111 50 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 111 51 i i PRP work_ln56cwsp7ffppl4wxeq7osqfuu 111 52 ≤ ≤ VBP work_ln56cwsp7ffppl4wxeq7osqfuu 111 53 · · NFP work_ln56cwsp7ffppl4wxeq7osqfuu 111 54 · · NFP work_ln56cwsp7ffppl4wxeq7osqfuu 111 55 · · NFP work_ln56cwsp7ffppl4wxeq7osqfuu 111 56 ≤ ≤ NNP work_ln56cwsp7ffppl4wxeq7osqfuu 111 57 U(k)i U(k)i NNP work_ln56cwsp7ffppl4wxeq7osqfuu 111 58 in in IN work_ln56cwsp7ffppl4wxeq7osqfuu 111 59 increasing increase VBG work_ln56cwsp7ffppl4wxeq7osqfuu 111 60 order order NN work_ln56cwsp7ffppl4wxeq7osqfuu 111 61 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 111 62 magnitude magnitude NN work_ln56cwsp7ffppl4wxeq7osqfuu 111 63 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 112 1 U U NNP work_ln56cwsp7ffppl4wxeq7osqfuu 112 2 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 112 3 l l NN work_ln56cwsp7ffppl4wxeq7osqfuu 112 4 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 112 5 i i PRP work_ln56cwsp7ffppl4wxeq7osqfuu 112 6 denotes denote VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 112 7 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 112 8 l l NN work_ln56cwsp7ffppl4wxeq7osqfuu 112 9 - - HYPH work_ln56cwsp7ffppl4wxeq7osqfuu 112 10 th th NNP work_ln56cwsp7ffppl4wxeq7osqfuu 112 11 order order NN work_ln56cwsp7ffppl4wxeq7osqfuu 112 12 statistic statistic NN work_ln56cwsp7ffppl4wxeq7osqfuu 112 13 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 112 14 individual individual NN work_ln56cwsp7ffppl4wxeq7osqfuu 112 15 i i PRP work_ln56cwsp7ffppl4wxeq7osqfuu 112 16 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 112 17 representing represent VBG work_ln56cwsp7ffppl4wxeq7osqfuu 112 18 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 112 19 utility utility NN work_ln56cwsp7ffppl4wxeq7osqfuu 112 20 value value NN work_ln56cwsp7ffppl4wxeq7osqfuu 112 21 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 112 22 individual individual JJ work_ln56cwsp7ffppl4wxeq7osqfuu 112 23 i i PRP work_ln56cwsp7ffppl4wxeq7osqfuu 112 24 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 112 25 that that DT work_ln56cwsp7ffppl4wxeq7osqfuu 112 26 alternative alternative NN work_ln56cwsp7ffppl4wxeq7osqfuu 112 27 having have VBG work_ln56cwsp7ffppl4wxeq7osqfuu 112 28 l− l− NNS work_ln56cwsp7ffppl4wxeq7osqfuu 112 29 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 112 30 alternatives alternative NNS work_ln56cwsp7ffppl4wxeq7osqfuu 112 31 with with IN work_ln56cwsp7ffppl4wxeq7osqfuu 112 32 lower low JJR work_ln56cwsp7ffppl4wxeq7osqfuu 112 33 utility utility NN work_ln56cwsp7ffppl4wxeq7osqfuu 112 34 values value NNS work_ln56cwsp7ffppl4wxeq7osqfuu 112 35 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 113 1 Analogously analogously RB work_ln56cwsp7ffppl4wxeq7osqfuu 113 2 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 113 3 we -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 113 4 will will MD work_ln56cwsp7ffppl4wxeq7osqfuu 113 5 be be VB work_ln56cwsp7ffppl4wxeq7osqfuu 113 6 using use VBG work_ln56cwsp7ffppl4wxeq7osqfuu 113 7 order order NN work_ln56cwsp7ffppl4wxeq7osqfuu 113 8 statistics statistic NNS work_ln56cwsp7ffppl4wxeq7osqfuu 113 9 given give VBN work_ln56cwsp7ffppl4wxeq7osqfuu 113 10 an an DT work_ln56cwsp7ffppl4wxeq7osqfuu 113 11 alternative alternative NN work_ln56cwsp7ffppl4wxeq7osqfuu 113 12 l. l. NN work_ln56cwsp7ffppl4wxeq7osqfuu 113 13 Consider consider VB work_ln56cwsp7ffppl4wxeq7osqfuu 113 14 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 113 15 collection collection NN work_ln56cwsp7ffppl4wxeq7osqfuu 113 16 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 113 17 random random JJ work_ln56cwsp7ffppl4wxeq7osqfuu 113 18 variables variable NNS work_ln56cwsp7ffppl4wxeq7osqfuu 113 19 Ul1,U Ul1,U NNP work_ln56cwsp7ffppl4wxeq7osqfuu 113 20 l l NNP work_ln56cwsp7ffppl4wxeq7osqfuu 113 21 2 2 CD work_ln56cwsp7ffppl4wxeq7osqfuu 113 22 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 113 23 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 114 1 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 115 1 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 116 1 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 116 2 U U NNP work_ln56cwsp7ffppl4wxeq7osqfuu 116 3 l l NN work_ln56cwsp7ffppl4wxeq7osqfuu 116 4 n n NN work_ln56cwsp7ffppl4wxeq7osqfuu 116 5 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 116 6 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 116 7 arrange arrange VB work_ln56cwsp7ffppl4wxeq7osqfuu 116 8 them -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 116 9 in in IN work_ln56cwsp7ffppl4wxeq7osqfuu 116 10 order order NN work_ln56cwsp7ffppl4wxeq7osqfuu 116 11 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 116 12 magnitude magnitude NN work_ln56cwsp7ffppl4wxeq7osqfuu 116 13 by by IN work_ln56cwsp7ffppl4wxeq7osqfuu 116 14 denoting denote VBG work_ln56cwsp7ffppl4wxeq7osqfuu 116 15 Ul(1 ul(1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 116 16 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 116 17 ≤ ≤ NN work_ln56cwsp7ffppl4wxeq7osqfuu 116 18 U U NNP work_ln56cwsp7ffppl4wxeq7osqfuu 116 19 l l NN work_ln56cwsp7ffppl4wxeq7osqfuu 116 20 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 116 21 2 2 LS work_ln56cwsp7ffppl4wxeq7osqfuu 116 22 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 116 23 ≤ ≤ NN work_ln56cwsp7ffppl4wxeq7osqfuu 116 24 · · NFP work_ln56cwsp7ffppl4wxeq7osqfuu 116 25 · · NFP work_ln56cwsp7ffppl4wxeq7osqfuu 116 26 · · NFP work_ln56cwsp7ffppl4wxeq7osqfuu 116 27 ≤ ≤ XX work_ln56cwsp7ffppl4wxeq7osqfuu 116 28 U U NNP work_ln56cwsp7ffppl4wxeq7osqfuu 116 29 l l NN work_ln56cwsp7ffppl4wxeq7osqfuu 116 30 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 116 31 n n NNP work_ln56cwsp7ffppl4wxeq7osqfuu 116 32 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 116 33 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 117 1 Here here RB work_ln56cwsp7ffppl4wxeq7osqfuu 117 2 U u PRP work_ln56cwsp7ffppl4wxeq7osqfuu 117 3 l l NN work_ln56cwsp7ffppl4wxeq7osqfuu 117 4 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 117 5 i i NN work_ln56cwsp7ffppl4wxeq7osqfuu 117 6 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 117 7 denotes denote VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 117 8 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 117 9 utility utility NN work_ln56cwsp7ffppl4wxeq7osqfuu 117 10 value value NN work_ln56cwsp7ffppl4wxeq7osqfuu 117 11 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 117 12 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 117 13 i i NNP work_ln56cwsp7ffppl4wxeq7osqfuu 117 14 - - HYPH work_ln56cwsp7ffppl4wxeq7osqfuu 117 15 th th NNP work_ln56cwsp7ffppl4wxeq7osqfuu 117 16 order order NN work_ln56cwsp7ffppl4wxeq7osqfuu 117 17 statistic statistic NN work_ln56cwsp7ffppl4wxeq7osqfuu 117 18 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 117 19 alternative alternative JJ work_ln56cwsp7ffppl4wxeq7osqfuu 117 20 l l NNP work_ln56cwsp7ffppl4wxeq7osqfuu 117 21 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 117 22 representing represent VBG work_ln56cwsp7ffppl4wxeq7osqfuu 117 23 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 117 24 utility utility NN work_ln56cwsp7ffppl4wxeq7osqfuu 117 25 value value NN work_ln56cwsp7ffppl4wxeq7osqfuu 117 26 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 117 27 l l NN work_ln56cwsp7ffppl4wxeq7osqfuu 117 28 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 117 29 that that DT work_ln56cwsp7ffppl4wxeq7osqfuu 117 30 individual individual NN work_ln56cwsp7ffppl4wxeq7osqfuu 117 31 who who WP work_ln56cwsp7ffppl4wxeq7osqfuu 117 32 ranks rank VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 117 33 l l NN work_ln56cwsp7ffppl4wxeq7osqfuu 117 34 higher high JJR work_ln56cwsp7ffppl4wxeq7osqfuu 117 35 than than IN work_ln56cwsp7ffppl4wxeq7osqfuu 117 36 exactly exactly RB work_ln56cwsp7ffppl4wxeq7osqfuu 117 37 i−1 i−1 JJ work_ln56cwsp7ffppl4wxeq7osqfuu 117 38 individuals individual NNS work_ln56cwsp7ffppl4wxeq7osqfuu 117 39 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 118 1 A a DT work_ln56cwsp7ffppl4wxeq7osqfuu 118 2 Social Social NNP work_ln56cwsp7ffppl4wxeq7osqfuu 118 3 Welfare Welfare NNP work_ln56cwsp7ffppl4wxeq7osqfuu 118 4 Function Function NNP work_ln56cwsp7ffppl4wxeq7osqfuu 118 5 SWF SWF NNP work_ln56cwsp7ffppl4wxeq7osqfuu 118 6 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 118 7 a a DT work_ln56cwsp7ffppl4wxeq7osqfuu 118 8 mapping mapping NN work_ln56cwsp7ffppl4wxeq7osqfuu 118 9 W w NN work_ln56cwsp7ffppl4wxeq7osqfuu 118 10 from from IN work_ln56cwsp7ffppl4wxeq7osqfuu 118 11 [ [ -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 118 12 0 0 CD work_ln56cwsp7ffppl4wxeq7osqfuu 118 13 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 118 14 1]n×k 1]n×k CD work_ln56cwsp7ffppl4wxeq7osqfuu 118 15 to to IN work_ln56cwsp7ffppl4wxeq7osqfuu 118 16 [ [ -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 118 17 0 0 CD work_ln56cwsp7ffppl4wxeq7osqfuu 118 18 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 118 19 1]k 1]k CD work_ln56cwsp7ffppl4wxeq7osqfuu 118 20 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 118 21 where where WRB work_ln56cwsp7ffppl4wxeq7osqfuu 118 22 W w NN work_ln56cwsp7ffppl4wxeq7osqfuu 118 23 l(Ul l(Ul NNP work_ln56cwsp7ffppl4wxeq7osqfuu 118 24 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 118 25 ∈ ∈ NNP work_ln56cwsp7ffppl4wxeq7osqfuu 118 26 [ [ -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 118 27 0 0 CD work_ln56cwsp7ffppl4wxeq7osqfuu 118 28 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 118 29 1 1 LS work_ln56cwsp7ffppl4wxeq7osqfuu 118 30 ] ] -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 118 31 denotes denote VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 118 32 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 118 33 social social JJ work_ln56cwsp7ffppl4wxeq7osqfuu 118 34 value value NN work_ln56cwsp7ffppl4wxeq7osqfuu 118 35 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 118 36 alternative alternative JJ work_ln56cwsp7ffppl4wxeq7osqfuu 118 37 l l NN work_ln56cwsp7ffppl4wxeq7osqfuu 118 38 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 118 39 given give VBN work_ln56cwsp7ffppl4wxeq7osqfuu 118 40 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 118 41 realization realization NN work_ln56cwsp7ffppl4wxeq7osqfuu 118 42 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 118 43 random random JJ work_ln56cwsp7ffppl4wxeq7osqfuu 118 44 variables variable NNS work_ln56cwsp7ffppl4wxeq7osqfuu 118 45 Ul Ul NNP work_ln56cwsp7ffppl4wxeq7osqfuu 118 46 = = FW work_ln56cwsp7ffppl4wxeq7osqfuu 118 47 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 118 48 Ul1 Ul1 NNP work_ln56cwsp7ffppl4wxeq7osqfuu 118 49 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 118 50 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 119 1 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 120 1 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 121 1 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 121 2 U U NNP work_ln56cwsp7ffppl4wxeq7osqfuu 121 3 l l NNP work_ln56cwsp7ffppl4wxeq7osqfuu 121 4 n n NN work_ln56cwsp7ffppl4wxeq7osqfuu 121 5 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 121 6 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 122 1 3 3 CD work_ln56cwsp7ffppl4wxeq7osqfuu 122 2 The the DT work_ln56cwsp7ffppl4wxeq7osqfuu 122 3 three three CD work_ln56cwsp7ffppl4wxeq7osqfuu 122 4 SWFs swf NNS work_ln56cwsp7ffppl4wxeq7osqfuu 122 5 we -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 122 6 consider consider VBP work_ln56cwsp7ffppl4wxeq7osqfuu 122 7 here here RB work_ln56cwsp7ffppl4wxeq7osqfuu 122 8 are be VBP work_ln56cwsp7ffppl4wxeq7osqfuu 122 9 utilitarianism utilitarianism NN work_ln56cwsp7ffppl4wxeq7osqfuu 122 10 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 122 11 maximin maximin NN work_ln56cwsp7ffppl4wxeq7osqfuu 122 12 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 122 13 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 122 14 maximax maximax NNP work_ln56cwsp7ffppl4wxeq7osqfuu 122 15 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 123 1 Utilitarianism Utilitarianism NNP work_ln56cwsp7ffppl4wxeq7osqfuu 123 2 evaluates evaluate VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 123 3 an an DT work_ln56cwsp7ffppl4wxeq7osqfuu 123 4 alternative alternative NN work_ln56cwsp7ffppl4wxeq7osqfuu 123 5 by by IN work_ln56cwsp7ffppl4wxeq7osqfuu 123 6 taking take VBG work_ln56cwsp7ffppl4wxeq7osqfuu 123 7 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 123 8 average average NN work_ln56cwsp7ffppl4wxeq7osqfuu 123 9 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 123 10 individual individual JJ work_ln56cwsp7ffppl4wxeq7osqfuu 123 11 cardinal cardinal JJ work_ln56cwsp7ffppl4wxeq7osqfuu 123 12 utilities utility NNS work_ln56cwsp7ffppl4wxeq7osqfuu 123 13 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 124 1 Formally formally RB work_ln56cwsp7ffppl4wxeq7osqfuu 124 2 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 124 3 a a DT work_ln56cwsp7ffppl4wxeq7osqfuu 124 4 SWF SWF NNP work_ln56cwsp7ffppl4wxeq7osqfuu 124 5 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 124 6 utilitarian utilitarian JJ work_ln56cwsp7ffppl4wxeq7osqfuu 124 7 if if IN work_ln56cwsp7ffppl4wxeq7osqfuu 124 8 W W NNP work_ln56cwsp7ffppl4wxeq7osqfuu 124 9 = = SYM work_ln56cwsp7ffppl4wxeq7osqfuu 124 10 WUT WUT NNP work_ln56cwsp7ffppl4wxeq7osqfuu 124 11 with with IN work_ln56cwsp7ffppl4wxeq7osqfuu 124 12 W w NN work_ln56cwsp7ffppl4wxeq7osqfuu 124 13 lUT lUT NNS work_ln56cwsp7ffppl4wxeq7osqfuu 124 14 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 124 15 U U NNP work_ln56cwsp7ffppl4wxeq7osqfuu 124 16 l l NN work_ln56cwsp7ffppl4wxeq7osqfuu 124 17 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 124 18 = = NFP work_ln56cwsp7ffppl4wxeq7osqfuu 124 19 ∑n ∑n NFP work_ln56cwsp7ffppl4wxeq7osqfuu 124 20 i=1 i=1 UH work_ln56cwsp7ffppl4wxeq7osqfuu 124 21 U U NNP work_ln56cwsp7ffppl4wxeq7osqfuu 124 22 l l NNP work_ln56cwsp7ffppl4wxeq7osqfuu 124 23 i i NNP work_ln56cwsp7ffppl4wxeq7osqfuu 124 24 / / SYM work_ln56cwsp7ffppl4wxeq7osqfuu 124 25 n n NN work_ln56cwsp7ffppl4wxeq7osqfuu 124 26 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 125 1 The the DT work_ln56cwsp7ffppl4wxeq7osqfuu 125 2 maximin maximin NN work_ln56cwsp7ffppl4wxeq7osqfuu 125 3 principle principle NN work_ln56cwsp7ffppl4wxeq7osqfuu 125 4 evaluates evaluate VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 125 5 an an DT work_ln56cwsp7ffppl4wxeq7osqfuu 125 6 alternative alternative NN work_ln56cwsp7ffppl4wxeq7osqfuu 125 7 on on IN work_ln56cwsp7ffppl4wxeq7osqfuu 125 8 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 125 9 basis basis NN work_ln56cwsp7ffppl4wxeq7osqfuu 125 10 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 125 11 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 125 12 utility utility NN work_ln56cwsp7ffppl4wxeq7osqfuu 125 13 value value NN work_ln56cwsp7ffppl4wxeq7osqfuu 125 14 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 125 15 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 125 16 worst worst RBS work_ln56cwsp7ffppl4wxeq7osqfuu 125 17 - - HYPH work_ln56cwsp7ffppl4wxeq7osqfuu 125 18 off off RP work_ln56cwsp7ffppl4wxeq7osqfuu 125 19 agent agent NN work_ln56cwsp7ffppl4wxeq7osqfuu 125 20 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 125 21 disregarding disregard VBG work_ln56cwsp7ffppl4wxeq7osqfuu 125 22 any any DT work_ln56cwsp7ffppl4wxeq7osqfuu 125 23 other other JJ work_ln56cwsp7ffppl4wxeq7osqfuu 125 24 utility utility NN work_ln56cwsp7ffppl4wxeq7osqfuu 125 25 value value NN work_ln56cwsp7ffppl4wxeq7osqfuu 125 26 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 126 1 In in IN work_ln56cwsp7ffppl4wxeq7osqfuu 126 2 other other JJ work_ln56cwsp7ffppl4wxeq7osqfuu 126 3 words word NNS work_ln56cwsp7ffppl4wxeq7osqfuu 126 4 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 126 5 a a DT work_ln56cwsp7ffppl4wxeq7osqfuu 126 6 SWF SWF NNP work_ln56cwsp7ffppl4wxeq7osqfuu 126 7 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 126 8 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 126 9 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 126 10 maximin maximin NN work_ln56cwsp7ffppl4wxeq7osqfuu 126 11 type type NN work_ln56cwsp7ffppl4wxeq7osqfuu 126 12 if if IN work_ln56cwsp7ffppl4wxeq7osqfuu 126 13 W W NNP work_ln56cwsp7ffppl4wxeq7osqfuu 126 14 = = SYM work_ln56cwsp7ffppl4wxeq7osqfuu 126 15 WMN WMN NNP work_ln56cwsp7ffppl4wxeq7osqfuu 126 16 with with IN work_ln56cwsp7ffppl4wxeq7osqfuu 126 17 W W NNP work_ln56cwsp7ffppl4wxeq7osqfuu 126 18 l l NN work_ln56cwsp7ffppl4wxeq7osqfuu 126 19 MN MN NNP work_ln56cwsp7ffppl4wxeq7osqfuu 126 20 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 126 21 U U NNP work_ln56cwsp7ffppl4wxeq7osqfuu 126 22 l l NN work_ln56cwsp7ffppl4wxeq7osqfuu 126 23 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 126 24 = = NFP work_ln56cwsp7ffppl4wxeq7osqfuu 126 25 Ul(1 ul(1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 126 26 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 126 27 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 127 1 Consider consider VB work_ln56cwsp7ffppl4wxeq7osqfuu 127 2 also also RB work_ln56cwsp7ffppl4wxeq7osqfuu 127 3 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 127 4 maximax maximax NNP work_ln56cwsp7ffppl4wxeq7osqfuu 127 5 rule rule NN work_ln56cwsp7ffppl4wxeq7osqfuu 127 6 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 128 1 In in IN work_ln56cwsp7ffppl4wxeq7osqfuu 128 2 contrast contrast NN work_ln56cwsp7ffppl4wxeq7osqfuu 128 3 to to IN work_ln56cwsp7ffppl4wxeq7osqfuu 128 4 maximin maximin NNP work_ln56cwsp7ffppl4wxeq7osqfuu 128 5 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 128 6 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 128 7 maximax maximax NNP work_ln56cwsp7ffppl4wxeq7osqfuu 128 8 rule rule NN work_ln56cwsp7ffppl4wxeq7osqfuu 128 9 focuses focus VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 128 10 on on IN work_ln56cwsp7ffppl4wxeq7osqfuu 128 11 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 128 12 best well RBS work_ln56cwsp7ffppl4wxeq7osqfuu 128 13 - - HYPH work_ln56cwsp7ffppl4wxeq7osqfuu 128 14 off off RP work_ln56cwsp7ffppl4wxeq7osqfuu 128 15 individuals individual NNS work_ln56cwsp7ffppl4wxeq7osqfuu 128 16 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 129 1 That that RB work_ln56cwsp7ffppl4wxeq7osqfuu 129 2 is is RB work_ln56cwsp7ffppl4wxeq7osqfuu 129 3 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 129 4 a a DT work_ln56cwsp7ffppl4wxeq7osqfuu 129 5 SWF SWF NNP work_ln56cwsp7ffppl4wxeq7osqfuu 129 6 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 129 7 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 129 8 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 129 9 maximax maximax NNP work_ln56cwsp7ffppl4wxeq7osqfuu 129 10 type type NN work_ln56cwsp7ffppl4wxeq7osqfuu 129 11 if if IN work_ln56cwsp7ffppl4wxeq7osqfuu 129 12 W W NNP work_ln56cwsp7ffppl4wxeq7osqfuu 129 13 = = SYM work_ln56cwsp7ffppl4wxeq7osqfuu 129 14 WMX WMX NNP work_ln56cwsp7ffppl4wxeq7osqfuu 129 15 with with IN work_ln56cwsp7ffppl4wxeq7osqfuu 129 16 W w NN work_ln56cwsp7ffppl4wxeq7osqfuu 129 17 lMX(U lMX(U NNP work_ln56cwsp7ffppl4wxeq7osqfuu 129 18 l l NN work_ln56cwsp7ffppl4wxeq7osqfuu 129 19 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 129 20 = = NFP work_ln56cwsp7ffppl4wxeq7osqfuu 129 21 Ul(n Ul(n NNP work_ln56cwsp7ffppl4wxeq7osqfuu 129 22 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 129 23 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 130 1 2.2 2.2 CD work_ln56cwsp7ffppl4wxeq7osqfuu 130 2 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 131 1 Ordinal Ordinal NNP work_ln56cwsp7ffppl4wxeq7osqfuu 131 2 Preferences Preferences NNPS work_ln56cwsp7ffppl4wxeq7osqfuu 131 3 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 132 1 The the DT work_ln56cwsp7ffppl4wxeq7osqfuu 132 2 following follow VBG work_ln56cwsp7ffppl4wxeq7osqfuu 132 3 describes describe VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 132 4 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 132 5 ordinal ordinal JJ work_ln56cwsp7ffppl4wxeq7osqfuu 132 6 rankings ranking NNS work_ln56cwsp7ffppl4wxeq7osqfuu 132 7 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 132 8 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 132 9 in- in- JJ work_ln56cwsp7ffppl4wxeq7osqfuu 132 10 dividuals dividual NNS work_ln56cwsp7ffppl4wxeq7osqfuu 132 11 over over IN work_ln56cwsp7ffppl4wxeq7osqfuu 132 12 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 132 13 set set NN work_ln56cwsp7ffppl4wxeq7osqfuu 132 14 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 132 15 alternatives alternative NNS work_ln56cwsp7ffppl4wxeq7osqfuu 132 16 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 133 1 M M NNP work_ln56cwsp7ffppl4wxeq7osqfuu 133 2 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 133 3 an an DT work_ln56cwsp7ffppl4wxeq7osqfuu 133 4 n n NNP work_ln56cwsp7ffppl4wxeq7osqfuu 133 5 × × NN work_ln56cwsp7ffppl4wxeq7osqfuu 133 6 k k NN work_ln56cwsp7ffppl4wxeq7osqfuu 133 7 matrix matrix NN work_ln56cwsp7ffppl4wxeq7osqfuu 133 8 with with IN work_ln56cwsp7ffppl4wxeq7osqfuu 133 9 properties property NNS work_ln56cwsp7ffppl4wxeq7osqfuu 133 10 : : : work_ln56cwsp7ffppl4wxeq7osqfuu 133 11 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 133 12 1 1 LS work_ln56cwsp7ffppl4wxeq7osqfuu 133 13 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 133 14 mli mli NNP work_ln56cwsp7ffppl4wxeq7osqfuu 133 15 ∈ ∈ NNP work_ln56cwsp7ffppl4wxeq7osqfuu 133 16 { { -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 133 17 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 133 18 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 133 19 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 134 1 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 135 1 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 136 1 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 136 2 k k NNP work_ln56cwsp7ffppl4wxeq7osqfuu 136 3 } } -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 136 4 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 136 5 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 136 6 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 136 7 2 2 LS work_ln56cwsp7ffppl4wxeq7osqfuu 136 8 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 136 9 mli mli NNP work_ln56cwsp7ffppl4wxeq7osqfuu 136 10 6= 6= CD work_ln56cwsp7ffppl4wxeq7osqfuu 136 11 mhi mhi NN work_ln56cwsp7ffppl4wxeq7osqfuu 136 12 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 136 13 all all DT work_ln56cwsp7ffppl4wxeq7osqfuu 136 14 i i NN work_ln56cwsp7ffppl4wxeq7osqfuu 136 15 ∈ ∈ NNP work_ln56cwsp7ffppl4wxeq7osqfuu 136 16 N n NN work_ln56cwsp7ffppl4wxeq7osqfuu 136 17 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 136 18 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 136 19 all all DT work_ln56cwsp7ffppl4wxeq7osqfuu 136 20 l l NN work_ln56cwsp7ffppl4wxeq7osqfuu 136 21 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 136 22 h h NNP work_ln56cwsp7ffppl4wxeq7osqfuu 136 23 ∈ ∈ NNP work_ln56cwsp7ffppl4wxeq7osqfuu 136 24 K K NNP work_ln56cwsp7ffppl4wxeq7osqfuu 136 25 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 136 26 l l NNP work_ln56cwsp7ffppl4wxeq7osqfuu 136 27 6= 6= CD work_ln56cwsp7ffppl4wxeq7osqfuu 136 28 h. h. NN work_ln56cwsp7ffppl4wxeq7osqfuu 136 29 Entry Entry NNP work_ln56cwsp7ffppl4wxeq7osqfuu 136 30 mli mli NNP work_ln56cwsp7ffppl4wxeq7osqfuu 136 31 denotes denote VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 136 32 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 136 33 position position NN work_ln56cwsp7ffppl4wxeq7osqfuu 136 34 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 136 35 alternative alternative JJ work_ln56cwsp7ffppl4wxeq7osqfuu 136 36 l l NN work_ln56cwsp7ffppl4wxeq7osqfuu 136 37 in in IN work_ln56cwsp7ffppl4wxeq7osqfuu 136 38 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 136 39 preferences preference NNS work_ln56cwsp7ffppl4wxeq7osqfuu 136 40 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 136 41 individual individual NN work_ln56cwsp7ffppl4wxeq7osqfuu 136 42 i i PRP work_ln56cwsp7ffppl4wxeq7osqfuu 136 43 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 136 44 where where WRB work_ln56cwsp7ffppl4wxeq7osqfuu 136 45 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 136 46 higher high JJR work_ln56cwsp7ffppl4wxeq7osqfuu 136 47 mli mli NNP work_ln56cwsp7ffppl4wxeq7osqfuu 136 48 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 136 49 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 136 50 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 136 51 higher high JJR work_ln56cwsp7ffppl4wxeq7osqfuu 136 52 alternative alternative JJ work_ln56cwsp7ffppl4wxeq7osqfuu 136 53 l l NN work_ln56cwsp7ffppl4wxeq7osqfuu 136 54 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 136 55 ranked rank VBN work_ln56cwsp7ffppl4wxeq7osqfuu 136 56 by by IN work_ln56cwsp7ffppl4wxeq7osqfuu 136 57 individual individual NN work_ln56cwsp7ffppl4wxeq7osqfuu 136 58 i. i. NN work_ln56cwsp7ffppl4wxeq7osqfuu 137 1 4 4 LS work_ln56cwsp7ffppl4wxeq7osqfuu 137 2 Mi Mi NNP work_ln56cwsp7ffppl4wxeq7osqfuu 137 3 denotes denote VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 137 4 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 137 5 i- i- XX work_ln56cwsp7ffppl4wxeq7osqfuu 137 6 th th XX work_ln56cwsp7ffppl4wxeq7osqfuu 137 7 row row NN work_ln56cwsp7ffppl4wxeq7osqfuu 137 8 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 137 9 matrix matrix NN work_ln56cwsp7ffppl4wxeq7osqfuu 137 10 M. M. NNP work_ln56cwsp7ffppl4wxeq7osqfuu 137 11 That That NNP work_ln56cwsp7ffppl4wxeq7osqfuu 137 12 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 137 13 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 137 14 Mi Mi NNP work_ln56cwsp7ffppl4wxeq7osqfuu 137 15 represents represent VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 137 16 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 137 17 ordinal ordinal JJ work_ln56cwsp7ffppl4wxeq7osqfuu 137 18 preferences preference NNS work_ln56cwsp7ffppl4wxeq7osqfuu 137 19 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 137 20 individual individual JJ work_ln56cwsp7ffppl4wxeq7osqfuu 137 21 i. i. NNP work_ln56cwsp7ffppl4wxeq7osqfuu 137 22 Ml Ml NNP work_ln56cwsp7ffppl4wxeq7osqfuu 137 23 denotes denote VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 137 24 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 137 25 l l NN work_ln56cwsp7ffppl4wxeq7osqfuu 137 26 - - HYPH work_ln56cwsp7ffppl4wxeq7osqfuu 137 27 th th NNP work_ln56cwsp7ffppl4wxeq7osqfuu 137 28 column column NN work_ln56cwsp7ffppl4wxeq7osqfuu 137 29 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 137 30 matrix matrix NN work_ln56cwsp7ffppl4wxeq7osqfuu 137 31 M M NNP work_ln56cwsp7ffppl4wxeq7osqfuu 137 32 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 137 33 representing represent VBG work_ln56cwsp7ffppl4wxeq7osqfuu 137 34 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 137 35 ordinal ordinal JJ work_ln56cwsp7ffppl4wxeq7osqfuu 137 36 preferences preference NNS work_ln56cwsp7ffppl4wxeq7osqfuu 137 37 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 137 38 all all DT work_ln56cwsp7ffppl4wxeq7osqfuu 137 39 2Given 2given CD work_ln56cwsp7ffppl4wxeq7osqfuu 137 40 our -PRON- PRP$ work_ln56cwsp7ffppl4wxeq7osqfuu 137 41 assumption assumption NN work_ln56cwsp7ffppl4wxeq7osqfuu 137 42 that that IN work_ln56cwsp7ffppl4wxeq7osqfuu 137 43 cultures culture NNS work_ln56cwsp7ffppl4wxeq7osqfuu 137 44 are be VBP work_ln56cwsp7ffppl4wxeq7osqfuu 137 45 continuous continuous JJ work_ln56cwsp7ffppl4wxeq7osqfuu 137 46 probability probability NN work_ln56cwsp7ffppl4wxeq7osqfuu 137 47 distributions distribution NNS work_ln56cwsp7ffppl4wxeq7osqfuu 137 48 on on IN work_ln56cwsp7ffppl4wxeq7osqfuu 137 49 [ [ -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 137 50 0 0 CD work_ln56cwsp7ffppl4wxeq7osqfuu 137 51 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 137 52 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 137 53 ] ] -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 137 54 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 137 55 all all PDT work_ln56cwsp7ffppl4wxeq7osqfuu 137 56 our -PRON- PRP$ work_ln56cwsp7ffppl4wxeq7osqfuu 137 57 results result NNS work_ln56cwsp7ffppl4wxeq7osqfuu 137 58 naturally naturally RB work_ln56cwsp7ffppl4wxeq7osqfuu 137 59 extend extend VBP work_ln56cwsp7ffppl4wxeq7osqfuu 137 60 to to IN work_ln56cwsp7ffppl4wxeq7osqfuu 137 61 other other JJ work_ln56cwsp7ffppl4wxeq7osqfuu 137 62 ranges range NNS work_ln56cwsp7ffppl4wxeq7osqfuu 137 63 such such JJ work_ln56cwsp7ffppl4wxeq7osqfuu 137 64 as as IN work_ln56cwsp7ffppl4wxeq7osqfuu 137 65 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 137 66 0 0 CD work_ln56cwsp7ffppl4wxeq7osqfuu 137 67 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 137 68 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 137 69 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 137 70 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 137 71 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 137 72 −∞,∞ −∞,∞ NNP work_ln56cwsp7ffppl4wxeq7osqfuu 137 73 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 137 74 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 137 75 or or CC work_ln56cwsp7ffppl4wxeq7osqfuu 137 76 [ [ -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 137 77 0,∞ 0,∞ NNP work_ln56cwsp7ffppl4wxeq7osqfuu 137 78 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 137 79 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 138 1 3Throughout 3throughout RB work_ln56cwsp7ffppl4wxeq7osqfuu 138 2 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 138 3 paper paper NN work_ln56cwsp7ffppl4wxeq7osqfuu 138 4 we -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 138 5 use use VBP work_ln56cwsp7ffppl4wxeq7osqfuu 138 6 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 138 7 terms term NNS work_ln56cwsp7ffppl4wxeq7osqfuu 138 8 “ " `` work_ln56cwsp7ffppl4wxeq7osqfuu 138 9 social social JJ work_ln56cwsp7ffppl4wxeq7osqfuu 138 10 welfare welfare NN work_ln56cwsp7ffppl4wxeq7osqfuu 138 11 function function NN work_ln56cwsp7ffppl4wxeq7osqfuu 138 12 ” " '' work_ln56cwsp7ffppl4wxeq7osqfuu 138 13 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 138 14 “ " `` work_ln56cwsp7ffppl4wxeq7osqfuu 138 15 ideal ideal NN work_ln56cwsp7ffppl4wxeq7osqfuu 138 16 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 138 17 justice justice NN work_ln56cwsp7ffppl4wxeq7osqfuu 138 18 ” " '' work_ln56cwsp7ffppl4wxeq7osqfuu 138 19 indistinctly indistinctly RB work_ln56cwsp7ffppl4wxeq7osqfuu 138 20 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 139 1 4Note 4note CD work_ln56cwsp7ffppl4wxeq7osqfuu 139 2 that that IN work_ln56cwsp7ffppl4wxeq7osqfuu 139 3 given give VBN work_ln56cwsp7ffppl4wxeq7osqfuu 139 4 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 139 5 assumptions assumption NNS work_ln56cwsp7ffppl4wxeq7osqfuu 139 6 on on IN work_ln56cwsp7ffppl4wxeq7osqfuu 139 7 continuous continuous JJ work_ln56cwsp7ffppl4wxeq7osqfuu 139 8 probability probability NN work_ln56cwsp7ffppl4wxeq7osqfuu 139 9 distributions distribution NNS work_ln56cwsp7ffppl4wxeq7osqfuu 139 10 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 139 11 there there EX work_ln56cwsp7ffppl4wxeq7osqfuu 139 12 are be VBP work_ln56cwsp7ffppl4wxeq7osqfuu 139 13 no no DT work_ln56cwsp7ffppl4wxeq7osqfuu 139 14 ties tie NNS work_ln56cwsp7ffppl4wxeq7osqfuu 139 15 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 139 16 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 139 17 hence hence RB work_ln56cwsp7ffppl4wxeq7osqfuu 139 18 property property NN work_ln56cwsp7ffppl4wxeq7osqfuu 139 19 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 139 20 2 2 CD work_ln56cwsp7ffppl4wxeq7osqfuu 139 21 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 139 22 above above RB work_ln56cwsp7ffppl4wxeq7osqfuu 139 23 follows follow VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 139 24 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 140 1 6 6 CD work_ln56cwsp7ffppl4wxeq7osqfuu 140 2 individuals individual NNS work_ln56cwsp7ffppl4wxeq7osqfuu 140 3 with with IN work_ln56cwsp7ffppl4wxeq7osqfuu 140 4 respect respect NN work_ln56cwsp7ffppl4wxeq7osqfuu 140 5 to to IN work_ln56cwsp7ffppl4wxeq7osqfuu 140 6 alternative alternative JJ work_ln56cwsp7ffppl4wxeq7osqfuu 140 7 l. l. NNP work_ln56cwsp7ffppl4wxeq7osqfuu 140 8 The the DT work_ln56cwsp7ffppl4wxeq7osqfuu 140 9 collection collection NN work_ln56cwsp7ffppl4wxeq7osqfuu 140 10 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 140 11 all all DT work_ln56cwsp7ffppl4wxeq7osqfuu 140 12 possible possible JJ work_ln56cwsp7ffppl4wxeq7osqfuu 140 13 matrices matrix NNS work_ln56cwsp7ffppl4wxeq7osqfuu 140 14 M M NNP work_ln56cwsp7ffppl4wxeq7osqfuu 140 15 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 140 16 denoted denote VBN work_ln56cwsp7ffppl4wxeq7osqfuu 140 17 by by IN work_ln56cwsp7ffppl4wxeq7osqfuu 140 18 M. M. NNP work_ln56cwsp7ffppl4wxeq7osqfuu 140 19 Finally Finally NNP work_ln56cwsp7ffppl4wxeq7osqfuu 140 20 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 140 21 by by IN work_ln56cwsp7ffppl4wxeq7osqfuu 140 22 l(h l(h NNP work_ln56cwsp7ffppl4wxeq7osqfuu 140 23 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 140 24 we -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 140 25 refer refer VBP work_ln56cwsp7ffppl4wxeq7osqfuu 140 26 to to IN work_ln56cwsp7ffppl4wxeq7osqfuu 140 27 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 140 28 number number NN work_ln56cwsp7ffppl4wxeq7osqfuu 140 29 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 140 30 individuals individual NNS work_ln56cwsp7ffppl4wxeq7osqfuu 140 31 that that WDT work_ln56cwsp7ffppl4wxeq7osqfuu 140 32 place place VBP work_ln56cwsp7ffppl4wxeq7osqfuu 140 33 alternative alternative NN work_ln56cwsp7ffppl4wxeq7osqfuu 140 34 l l NN work_ln56cwsp7ffppl4wxeq7osqfuu 140 35 exactly exactly RB work_ln56cwsp7ffppl4wxeq7osqfuu 140 36 above above IN work_ln56cwsp7ffppl4wxeq7osqfuu 140 37 h− h− NNP work_ln56cwsp7ffppl4wxeq7osqfuu 140 38 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 140 39 alternatives alternative NNS work_ln56cwsp7ffppl4wxeq7osqfuu 140 40 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 141 1 That that RB work_ln56cwsp7ffppl4wxeq7osqfuu 141 2 is is RB work_ln56cwsp7ffppl4wxeq7osqfuu 141 3 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 141 4 l(h l(h NNP work_ln56cwsp7ffppl4wxeq7osqfuu 141 5 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 141 6 = = NFP work_ln56cwsp7ffppl4wxeq7osqfuu 141 7 |{i |{i CD work_ln56cwsp7ffppl4wxeq7osqfuu 141 8 ∈ ∈ NNP work_ln56cwsp7ffppl4wxeq7osqfuu 141 9 N n NN work_ln56cwsp7ffppl4wxeq7osqfuu 141 10 : : : work_ln56cwsp7ffppl4wxeq7osqfuu 141 11 mli mli NNP work_ln56cwsp7ffppl4wxeq7osqfuu 141 12 = = SYM work_ln56cwsp7ffppl4wxeq7osqfuu 141 13 h}| h}| NNP work_ln56cwsp7ffppl4wxeq7osqfuu 141 14 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 142 1 A a DT work_ln56cwsp7ffppl4wxeq7osqfuu 142 2 multi multi JJ work_ln56cwsp7ffppl4wxeq7osqfuu 142 3 - - JJ work_ln56cwsp7ffppl4wxeq7osqfuu 142 4 valued value VBN work_ln56cwsp7ffppl4wxeq7osqfuu 142 5 decision decision NN work_ln56cwsp7ffppl4wxeq7osqfuu 142 6 rule rule NN work_ln56cwsp7ffppl4wxeq7osqfuu 142 7 f f NNP work_ln56cwsp7ffppl4wxeq7osqfuu 142 8 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 142 9 a a DT work_ln56cwsp7ffppl4wxeq7osqfuu 142 10 correspondence correspondence NN work_ln56cwsp7ffppl4wxeq7osqfuu 142 11 from from IN work_ln56cwsp7ffppl4wxeq7osqfuu 142 12 M M NNP work_ln56cwsp7ffppl4wxeq7osqfuu 142 13 to to IN work_ln56cwsp7ffppl4wxeq7osqfuu 142 14 K. K. NNP work_ln56cwsp7ffppl4wxeq7osqfuu 142 15 Denote Denote NNP work_ln56cwsp7ffppl4wxeq7osqfuu 142 16 by by IN work_ln56cwsp7ffppl4wxeq7osqfuu 142 17 F F NNP work_ln56cwsp7ffppl4wxeq7osqfuu 142 18 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 142 19 set set NN work_ln56cwsp7ffppl4wxeq7osqfuu 142 20 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 142 21 all all DT work_ln56cwsp7ffppl4wxeq7osqfuu 142 22 decision decision NN work_ln56cwsp7ffppl4wxeq7osqfuu 142 23 rules rule NNS work_ln56cwsp7ffppl4wxeq7osqfuu 142 24 f. f. . work_ln56cwsp7ffppl4wxeq7osqfuu 142 25 That that DT work_ln56cwsp7ffppl4wxeq7osqfuu 142 26 is is RB work_ln56cwsp7ffppl4wxeq7osqfuu 142 27 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 142 28 a a DT work_ln56cwsp7ffppl4wxeq7osqfuu 142 29 decision decision NN work_ln56cwsp7ffppl4wxeq7osqfuu 142 30 rule rule NN work_ln56cwsp7ffppl4wxeq7osqfuu 142 31 takes take VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 142 32 ordinal ordinal JJ work_ln56cwsp7ffppl4wxeq7osqfuu 142 33 information information NN work_ln56cwsp7ffppl4wxeq7osqfuu 142 34 on on IN work_ln56cwsp7ffppl4wxeq7osqfuu 142 35 preferences preference NNS work_ln56cwsp7ffppl4wxeq7osqfuu 142 36 as as IN work_ln56cwsp7ffppl4wxeq7osqfuu 142 37 input input NN work_ln56cwsp7ffppl4wxeq7osqfuu 142 38 to to TO work_ln56cwsp7ffppl4wxeq7osqfuu 142 39 determine determine VB work_ln56cwsp7ffppl4wxeq7osqfuu 142 40 a a DT work_ln56cwsp7ffppl4wxeq7osqfuu 142 41 set set NN work_ln56cwsp7ffppl4wxeq7osqfuu 142 42 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 142 43 alternatives alternative NNS work_ln56cwsp7ffppl4wxeq7osqfuu 142 44 as as IN work_ln56cwsp7ffppl4wxeq7osqfuu 142 45 social social JJ work_ln56cwsp7ffppl4wxeq7osqfuu 142 46 choice choice NN work_ln56cwsp7ffppl4wxeq7osqfuu 142 47 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 143 1 We -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 143 2 assume assume VBP work_ln56cwsp7ffppl4wxeq7osqfuu 143 3 that that IN work_ln56cwsp7ffppl4wxeq7osqfuu 143 4 f f NNP work_ln56cwsp7ffppl4wxeq7osqfuu 143 5 uses use VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 143 6 true true JJ work_ln56cwsp7ffppl4wxeq7osqfuu 143 7 information information NN work_ln56cwsp7ffppl4wxeq7osqfuu 143 8 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 144 1 That that RB work_ln56cwsp7ffppl4wxeq7osqfuu 144 2 is is RB work_ln56cwsp7ffppl4wxeq7osqfuu 144 3 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 144 4 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 144 5 particular particular JJ work_ln56cwsp7ffppl4wxeq7osqfuu 144 6 matrix matrix NN work_ln56cwsp7ffppl4wxeq7osqfuu 144 7 M M NNP work_ln56cwsp7ffppl4wxeq7osqfuu 144 8 over over IN work_ln56cwsp7ffppl4wxeq7osqfuu 144 9 which which WDT work_ln56cwsp7ffppl4wxeq7osqfuu 144 10 f f NNP work_ln56cwsp7ffppl4wxeq7osqfuu 144 11 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 144 12 applied apply VBN work_ln56cwsp7ffppl4wxeq7osqfuu 144 13 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 144 14 assumed assume VBN work_ln56cwsp7ffppl4wxeq7osqfuu 144 15 to to TO work_ln56cwsp7ffppl4wxeq7osqfuu 144 16 be be VB work_ln56cwsp7ffppl4wxeq7osqfuu 144 17 known know VBN work_ln56cwsp7ffppl4wxeq7osqfuu 144 18 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 145 1 Scoring score VBG work_ln56cwsp7ffppl4wxeq7osqfuu 145 2 rules rule NNS work_ln56cwsp7ffppl4wxeq7osqfuu 145 3 are be VBP work_ln56cwsp7ffppl4wxeq7osqfuu 145 4 a a DT work_ln56cwsp7ffppl4wxeq7osqfuu 145 5 particularly particularly RB work_ln56cwsp7ffppl4wxeq7osqfuu 145 6 interesting interesting JJ work_ln56cwsp7ffppl4wxeq7osqfuu 145 7 class class NN work_ln56cwsp7ffppl4wxeq7osqfuu 145 8 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 145 9 decision decision NN work_ln56cwsp7ffppl4wxeq7osqfuu 145 10 rules rule NNS work_ln56cwsp7ffppl4wxeq7osqfuu 145 11 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 146 1 They -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 146 2 are be VBP work_ln56cwsp7ffppl4wxeq7osqfuu 146 3 typically typically RB work_ln56cwsp7ffppl4wxeq7osqfuu 146 4 simple simple JJ work_ln56cwsp7ffppl4wxeq7osqfuu 146 5 to to TO work_ln56cwsp7ffppl4wxeq7osqfuu 146 6 implement implement VB work_ln56cwsp7ffppl4wxeq7osqfuu 146 7 in in IN work_ln56cwsp7ffppl4wxeq7osqfuu 146 8 practice practice NN work_ln56cwsp7ffppl4wxeq7osqfuu 146 9 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 146 10 they -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 146 11 encompass encompass VBP work_ln56cwsp7ffppl4wxeq7osqfuu 146 12 a a DT work_ln56cwsp7ffppl4wxeq7osqfuu 146 13 number number NN work_ln56cwsp7ffppl4wxeq7osqfuu 146 14 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 146 15 widely widely RB work_ln56cwsp7ffppl4wxeq7osqfuu 146 16 - - HYPH work_ln56cwsp7ffppl4wxeq7osqfuu 146 17 used use VBN work_ln56cwsp7ffppl4wxeq7osqfuu 146 18 decision decision NN work_ln56cwsp7ffppl4wxeq7osqfuu 146 19 rules rule NNS work_ln56cwsp7ffppl4wxeq7osqfuu 146 20 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 147 1 Formally formally RB work_ln56cwsp7ffppl4wxeq7osqfuu 147 2 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 147 3 a a DT work_ln56cwsp7ffppl4wxeq7osqfuu 147 4 scoring score VBG work_ln56cwsp7ffppl4wxeq7osqfuu 147 5 rule rule NN work_ln56cwsp7ffppl4wxeq7osqfuu 147 6 S S NNP work_ln56cwsp7ffppl4wxeq7osqfuu 147 7 can can MD work_ln56cwsp7ffppl4wxeq7osqfuu 147 8 be be VB work_ln56cwsp7ffppl4wxeq7osqfuu 147 9 represented represent VBN work_ln56cwsp7ffppl4wxeq7osqfuu 147 10 by by IN work_ln56cwsp7ffppl4wxeq7osqfuu 147 11 a a DT work_ln56cwsp7ffppl4wxeq7osqfuu 147 12 vector vector NN work_ln56cwsp7ffppl4wxeq7osqfuu 147 13 S S NNP work_ln56cwsp7ffppl4wxeq7osqfuu 147 14 ∈ ∈ IN work_ln56cwsp7ffppl4wxeq7osqfuu 147 15 [ [ -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 147 16 0 0 CD work_ln56cwsp7ffppl4wxeq7osqfuu 147 17 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 147 18 1]k 1]k CD work_ln56cwsp7ffppl4wxeq7osqfuu 147 19 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 147 20 with with IN work_ln56cwsp7ffppl4wxeq7osqfuu 147 21 Sl Sl NNP work_ln56cwsp7ffppl4wxeq7osqfuu 147 22 denoting denote VBG work_ln56cwsp7ffppl4wxeq7osqfuu 147 23 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 147 24 strength strength NN work_ln56cwsp7ffppl4wxeq7osqfuu 147 25 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 147 26 an an DT work_ln56cwsp7ffppl4wxeq7osqfuu 147 27 individual individual NN work_ln56cwsp7ffppl4wxeq7osqfuu 147 28 ’s ’s POS work_ln56cwsp7ffppl4wxeq7osqfuu 147 29 vote vote NN work_ln56cwsp7ffppl4wxeq7osqfuu 147 30 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 147 31 whichever whichever WDT work_ln56cwsp7ffppl4wxeq7osqfuu 147 32 alternative alternative NN work_ln56cwsp7ffppl4wxeq7osqfuu 147 33 she -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 147 34 ranks rank VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 147 35 higher high JJR work_ln56cwsp7ffppl4wxeq7osqfuu 147 36 than than IN work_ln56cwsp7ffppl4wxeq7osqfuu 147 37 exactly exactly RB work_ln56cwsp7ffppl4wxeq7osqfuu 147 38 l l NN work_ln56cwsp7ffppl4wxeq7osqfuu 147 39 − − NNP work_ln56cwsp7ffppl4wxeq7osqfuu 147 40 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 147 41 alternatives alternative NNS work_ln56cwsp7ffppl4wxeq7osqfuu 147 42 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 148 1 We -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 148 2 normalize normalize VBP work_ln56cwsp7ffppl4wxeq7osqfuu 148 3 strength strength NN work_ln56cwsp7ffppl4wxeq7osqfuu 148 4 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 148 5 vote vote NN work_ln56cwsp7ffppl4wxeq7osqfuu 148 6 by by IN work_ln56cwsp7ffppl4wxeq7osqfuu 148 7 assigning assign VBG work_ln56cwsp7ffppl4wxeq7osqfuu 148 8 a a DT work_ln56cwsp7ffppl4wxeq7osqfuu 148 9 value value NN work_ln56cwsp7ffppl4wxeq7osqfuu 148 10 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 148 11 to to IN work_ln56cwsp7ffppl4wxeq7osqfuu 148 12 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 148 13 best good JJS work_ln56cwsp7ffppl4wxeq7osqfuu 148 14 alternative alternative NN work_ln56cwsp7ffppl4wxeq7osqfuu 148 15 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 148 16 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 148 17 a a DT work_ln56cwsp7ffppl4wxeq7osqfuu 148 18 value value NN work_ln56cwsp7ffppl4wxeq7osqfuu 148 19 0 0 CD work_ln56cwsp7ffppl4wxeq7osqfuu 148 20 to to IN work_ln56cwsp7ffppl4wxeq7osqfuu 148 21 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 148 22 worst bad JJS work_ln56cwsp7ffppl4wxeq7osqfuu 148 23 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 149 1 That that RB work_ln56cwsp7ffppl4wxeq7osqfuu 149 2 is is RB work_ln56cwsp7ffppl4wxeq7osqfuu 149 3 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 149 4 we -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 149 5 set set VBP work_ln56cwsp7ffppl4wxeq7osqfuu 149 6 Sk Sk NNP work_ln56cwsp7ffppl4wxeq7osqfuu 149 7 = = SYM work_ln56cwsp7ffppl4wxeq7osqfuu 149 8 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 149 9 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 149 10 S1 S1 NNS work_ln56cwsp7ffppl4wxeq7osqfuu 149 11 = = SYM work_ln56cwsp7ffppl4wxeq7osqfuu 149 12 0 0 NFP work_ln56cwsp7ffppl4wxeq7osqfuu 149 13 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 150 1 Note note VB work_ln56cwsp7ffppl4wxeq7osqfuu 150 2 that that IN work_ln56cwsp7ffppl4wxeq7osqfuu 150 3 this this DT work_ln56cwsp7ffppl4wxeq7osqfuu 150 4 normalization normalization NN work_ln56cwsp7ffppl4wxeq7osqfuu 150 5 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 150 6 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 150 7 extreme extreme JJ work_ln56cwsp7ffppl4wxeq7osqfuu 150 8 values value NNS work_ln56cwsp7ffppl4wxeq7osqfuu 150 9 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 150 10 without without IN work_ln56cwsp7ffppl4wxeq7osqfuu 150 11 loss loss NN work_ln56cwsp7ffppl4wxeq7osqfuu 150 12 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 150 13 generality generality NN work_ln56cwsp7ffppl4wxeq7osqfuu 150 14 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 151 1 We -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 151 2 denote denote VBP work_ln56cwsp7ffppl4wxeq7osqfuu 151 3 by by IN work_ln56cwsp7ffppl4wxeq7osqfuu 151 4 S(M S(M NNP work_ln56cwsp7ffppl4wxeq7osqfuu 151 5 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 151 6 ⊆ ⊆ . work_ln56cwsp7ffppl4wxeq7osqfuu 151 7 K k VB work_ln56cwsp7ffppl4wxeq7osqfuu 151 8 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 151 9 set set NN work_ln56cwsp7ffppl4wxeq7osqfuu 151 10 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 151 11 alternatives alternative NNS work_ln56cwsp7ffppl4wxeq7osqfuu 151 12 selected select VBN work_ln56cwsp7ffppl4wxeq7osqfuu 151 13 by by IN work_ln56cwsp7ffppl4wxeq7osqfuu 151 14 scoring score VBG work_ln56cwsp7ffppl4wxeq7osqfuu 151 15 rule rule NN work_ln56cwsp7ffppl4wxeq7osqfuu 151 16 S S NNP work_ln56cwsp7ffppl4wxeq7osqfuu 151 17 with with IN work_ln56cwsp7ffppl4wxeq7osqfuu 151 18 preferences preference NNS work_ln56cwsp7ffppl4wxeq7osqfuu 151 19 M. M. NNP work_ln56cwsp7ffppl4wxeq7osqfuu 151 20 An An NNP work_ln56cwsp7ffppl4wxeq7osqfuu 151 21 alternative alternative JJ work_ln56cwsp7ffppl4wxeq7osqfuu 151 22 l l NN work_ln56cwsp7ffppl4wxeq7osqfuu 151 23 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 151 24 selected select VBN work_ln56cwsp7ffppl4wxeq7osqfuu 151 25 by by IN work_ln56cwsp7ffppl4wxeq7osqfuu 151 26 scoring score VBG work_ln56cwsp7ffppl4wxeq7osqfuu 151 27 rule rule NN work_ln56cwsp7ffppl4wxeq7osqfuu 151 28 S S NNP work_ln56cwsp7ffppl4wxeq7osqfuu 151 29 when when WRB work_ln56cwsp7ffppl4wxeq7osqfuu 151 30 M M NNP work_ln56cwsp7ffppl4wxeq7osqfuu 151 31 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 151 32 if if IN work_ln56cwsp7ffppl4wxeq7osqfuu 151 33 l l NN work_ln56cwsp7ffppl4wxeq7osqfuu 151 34 gets get VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 151 35 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 151 36 highest high JJS work_ln56cwsp7ffppl4wxeq7osqfuu 151 37 number number NN work_ln56cwsp7ffppl4wxeq7osqfuu 151 38 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 151 39 points point NNS work_ln56cwsp7ffppl4wxeq7osqfuu 151 40 across across IN work_ln56cwsp7ffppl4wxeq7osqfuu 151 41 individuals individual NNS work_ln56cwsp7ffppl4wxeq7osqfuu 151 42 when when WRB work_ln56cwsp7ffppl4wxeq7osqfuu 151 43 ordinal ordinal JJ work_ln56cwsp7ffppl4wxeq7osqfuu 151 44 preferences preference NNS work_ln56cwsp7ffppl4wxeq7osqfuu 151 45 are be VBP work_ln56cwsp7ffppl4wxeq7osqfuu 151 46 M. M. NNP work_ln56cwsp7ffppl4wxeq7osqfuu 151 47 The the DT work_ln56cwsp7ffppl4wxeq7osqfuu 151 48 especially especially RB work_ln56cwsp7ffppl4wxeq7osqfuu 151 49 salient salient NN work_ln56cwsp7ffppl4wxeq7osqfuu 151 50 scoring score VBG work_ln56cwsp7ffppl4wxeq7osqfuu 151 51 rules rule NNS work_ln56cwsp7ffppl4wxeq7osqfuu 151 52 are be VBP work_ln56cwsp7ffppl4wxeq7osqfuu 151 53 plurality plurality NN work_ln56cwsp7ffppl4wxeq7osqfuu 151 54 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 151 55 Borda Borda NNP work_ln56cwsp7ffppl4wxeq7osqfuu 151 56 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 151 57 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 151 58 negative negative JJ work_ln56cwsp7ffppl4wxeq7osqfuu 151 59 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 152 1 A a DT work_ln56cwsp7ffppl4wxeq7osqfuu 152 2 scoring score VBG work_ln56cwsp7ffppl4wxeq7osqfuu 152 3 rule rule NN work_ln56cwsp7ffppl4wxeq7osqfuu 152 4 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 152 5 plurality plurality NN work_ln56cwsp7ffppl4wxeq7osqfuu 152 6 if if IN work_ln56cwsp7ffppl4wxeq7osqfuu 152 7 S S NNP work_ln56cwsp7ffppl4wxeq7osqfuu 152 8 = = SYM work_ln56cwsp7ffppl4wxeq7osqfuu 152 9 SPl SPl NNP work_ln56cwsp7ffppl4wxeq7osqfuu 152 10 with with IN work_ln56cwsp7ffppl4wxeq7osqfuu 152 11 S S NNP work_ln56cwsp7ffppl4wxeq7osqfuu 152 12 l l NNP work_ln56cwsp7ffppl4wxeq7osqfuu 152 13 Pl Pl NNP work_ln56cwsp7ffppl4wxeq7osqfuu 152 14 = = NFP work_ln56cwsp7ffppl4wxeq7osqfuu 152 15 0 0 CD work_ln56cwsp7ffppl4wxeq7osqfuu 152 16 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 152 17 every every DT work_ln56cwsp7ffppl4wxeq7osqfuu 152 18 l l NN work_ln56cwsp7ffppl4wxeq7osqfuu 152 19 < < XX work_ln56cwsp7ffppl4wxeq7osqfuu 152 20 k. k. NN work_ln56cwsp7ffppl4wxeq7osqfuu 152 21 It -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 152 22 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 152 23 negative negative JJ work_ln56cwsp7ffppl4wxeq7osqfuu 152 24 if if IN work_ln56cwsp7ffppl4wxeq7osqfuu 152 25 S s NN work_ln56cwsp7ffppl4wxeq7osqfuu 152 26 = = SYM work_ln56cwsp7ffppl4wxeq7osqfuu 152 27 SNg SNg NNS work_ln56cwsp7ffppl4wxeq7osqfuu 152 28 with with IN work_ln56cwsp7ffppl4wxeq7osqfuu 152 29 SlNg SlNg NNP work_ln56cwsp7ffppl4wxeq7osqfuu 152 30 = = SYM work_ln56cwsp7ffppl4wxeq7osqfuu 152 31 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 152 32 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 152 33 every every DT work_ln56cwsp7ffppl4wxeq7osqfuu 152 34 l l NN work_ln56cwsp7ffppl4wxeq7osqfuu 152 35 > > NN work_ln56cwsp7ffppl4wxeq7osqfuu 152 36 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 152 37 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 152 38 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 152 39 it -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 152 40 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 152 41 Borda Borda NNP work_ln56cwsp7ffppl4wxeq7osqfuu 152 42 if if IN work_ln56cwsp7ffppl4wxeq7osqfuu 152 43 S s NN work_ln56cwsp7ffppl4wxeq7osqfuu 152 44 = = SYM work_ln56cwsp7ffppl4wxeq7osqfuu 152 45 SBd SBd NNS work_ln56cwsp7ffppl4wxeq7osqfuu 152 46 with with IN work_ln56cwsp7ffppl4wxeq7osqfuu 152 47 S S NNP work_ln56cwsp7ffppl4wxeq7osqfuu 152 48 l l NN work_ln56cwsp7ffppl4wxeq7osqfuu 152 49 Bd Bd NNP work_ln56cwsp7ffppl4wxeq7osqfuu 152 50 = = SYM work_ln56cwsp7ffppl4wxeq7osqfuu 152 51 l−1 l−1 NNP work_ln56cwsp7ffppl4wxeq7osqfuu 152 52 k−1 k−1 NNP work_ln56cwsp7ffppl4wxeq7osqfuu 152 53 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 152 54 every every DT work_ln56cwsp7ffppl4wxeq7osqfuu 152 55 l. l. NN work_ln56cwsp7ffppl4wxeq7osqfuu 152 56 2.3 2.3 CD work_ln56cwsp7ffppl4wxeq7osqfuu 152 57 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 153 1 Cardinal Cardinal NNP work_ln56cwsp7ffppl4wxeq7osqfuu 153 2 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 153 3 Ordinal Ordinal NNP work_ln56cwsp7ffppl4wxeq7osqfuu 153 4 Preferences Preferences NNPS work_ln56cwsp7ffppl4wxeq7osqfuu 153 5 : : : work_ln56cwsp7ffppl4wxeq7osqfuu 153 6 Evaluating evaluate VBG work_ln56cwsp7ffppl4wxeq7osqfuu 153 7 Decision Decision NNP work_ln56cwsp7ffppl4wxeq7osqfuu 153 8 Rules Rules NNPS work_ln56cwsp7ffppl4wxeq7osqfuu 153 9 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 154 1 We -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 154 2 will will MD work_ln56cwsp7ffppl4wxeq7osqfuu 154 3 be be VB work_ln56cwsp7ffppl4wxeq7osqfuu 154 4 using use VBG work_ln56cwsp7ffppl4wxeq7osqfuu 154 5 three three CD work_ln56cwsp7ffppl4wxeq7osqfuu 154 6 different different JJ work_ln56cwsp7ffppl4wxeq7osqfuu 154 7 indices index NNS work_ln56cwsp7ffppl4wxeq7osqfuu 154 8 to to TO work_ln56cwsp7ffppl4wxeq7osqfuu 154 9 evaluate evaluate VB work_ln56cwsp7ffppl4wxeq7osqfuu 154 10 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 154 11 performance performance NN work_ln56cwsp7ffppl4wxeq7osqfuu 154 12 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 154 13 alternatives alternative NNS work_ln56cwsp7ffppl4wxeq7osqfuu 154 14 in in IN work_ln56cwsp7ffppl4wxeq7osqfuu 154 15 terms term NNS work_ln56cwsp7ffppl4wxeq7osqfuu 154 16 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 154 17 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 154 18 ideals ideal NNS work_ln56cwsp7ffppl4wxeq7osqfuu 154 19 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 154 20 justice justice NN work_ln56cwsp7ffppl4wxeq7osqfuu 154 21 under under IN work_ln56cwsp7ffppl4wxeq7osqfuu 154 22 consideration consideration NN work_ln56cwsp7ffppl4wxeq7osqfuu 154 23 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 155 1 The the DT work_ln56cwsp7ffppl4wxeq7osqfuu 155 2 first first JJ work_ln56cwsp7ffppl4wxeq7osqfuu 155 3 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 155 4 which which WDT work_ln56cwsp7ffppl4wxeq7osqfuu 155 5 we -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 155 6 denote denote VBP work_ln56cwsp7ffppl4wxeq7osqfuu 155 7 by by IN work_ln56cwsp7ffppl4wxeq7osqfuu 155 8 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 155 9 α α NNP work_ln56cwsp7ffppl4wxeq7osqfuu 155 10 - - HYPH work_ln56cwsp7ffppl4wxeq7osqfuu 155 11 index index NN work_ln56cwsp7ffppl4wxeq7osqfuu 155 12 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 155 13 judges judge VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 155 14 an an DT work_ln56cwsp7ffppl4wxeq7osqfuu 155 15 alternative alternative JJ work_ln56cwsp7ffppl4wxeq7osqfuu 155 16 l l NN work_ln56cwsp7ffppl4wxeq7osqfuu 155 17 on on IN work_ln56cwsp7ffppl4wxeq7osqfuu 155 18 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 155 19 basis basis NN work_ln56cwsp7ffppl4wxeq7osqfuu 155 20 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 155 21 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 155 22 expected expect VBN work_ln56cwsp7ffppl4wxeq7osqfuu 155 23 value value NN work_ln56cwsp7ffppl4wxeq7osqfuu 155 24 that that WDT work_ln56cwsp7ffppl4wxeq7osqfuu 155 25 l l NN work_ln56cwsp7ffppl4wxeq7osqfuu 155 26 provides provide VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 155 27 in in IN work_ln56cwsp7ffppl4wxeq7osqfuu 155 28 terms term NNS work_ln56cwsp7ffppl4wxeq7osqfuu 155 29 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 155 30 an an DT work_ln56cwsp7ffppl4wxeq7osqfuu 155 31 ideal ideal NN work_ln56cwsp7ffppl4wxeq7osqfuu 155 32 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 155 33 justice justice NN work_ln56cwsp7ffppl4wxeq7osqfuu 155 34 W. W. NNP work_ln56cwsp7ffppl4wxeq7osqfuu 155 35 That that RB work_ln56cwsp7ffppl4wxeq7osqfuu 155 36 is is RB work_ln56cwsp7ffppl4wxeq7osqfuu 155 37 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 155 38 αlW αlW NNP work_ln56cwsp7ffppl4wxeq7osqfuu 155 39 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 155 40 M m NN work_ln56cwsp7ffppl4wxeq7osqfuu 155 41 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 155 42 = = NFP work_ln56cwsp7ffppl4wxeq7osqfuu 155 43 E[W E[W NNP work_ln56cwsp7ffppl4wxeq7osqfuu 155 44 l(Ul l(Ul NNP work_ln56cwsp7ffppl4wxeq7osqfuu 155 45 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 155 46 | | NNP work_ln56cwsp7ffppl4wxeq7osqfuu 155 47 M M NNP work_ln56cwsp7ffppl4wxeq7osqfuu 155 48 ] ] -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 155 49 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 156 1 Recall recall VB work_ln56cwsp7ffppl4wxeq7osqfuu 156 2 that that IN work_ln56cwsp7ffppl4wxeq7osqfuu 156 3 W w NN work_ln56cwsp7ffppl4wxeq7osqfuu 156 4 lUT lut NN work_ln56cwsp7ffppl4wxeq7osqfuu 156 5 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 156 6 U U NNP work_ln56cwsp7ffppl4wxeq7osqfuu 156 7 l l NN work_ln56cwsp7ffppl4wxeq7osqfuu 156 8 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 156 9 = = NFP work_ln56cwsp7ffppl4wxeq7osqfuu 156 10 ∑n ∑n NFP work_ln56cwsp7ffppl4wxeq7osqfuu 156 11 i=1 i=1 UH work_ln56cwsp7ffppl4wxeq7osqfuu 156 12 U U NNP work_ln56cwsp7ffppl4wxeq7osqfuu 156 13 l l NN work_ln56cwsp7ffppl4wxeq7osqfuu 156 14 i i NN work_ln56cwsp7ffppl4wxeq7osqfuu 156 15 n n NN work_ln56cwsp7ffppl4wxeq7osqfuu 156 16 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 156 17 W w NN work_ln56cwsp7ffppl4wxeq7osqfuu 156 18 lMN lmn NN work_ln56cwsp7ffppl4wxeq7osqfuu 156 19 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 156 20 U U NNP work_ln56cwsp7ffppl4wxeq7osqfuu 156 21 l l NN work_ln56cwsp7ffppl4wxeq7osqfuu 156 22 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 156 23 = = NFP work_ln56cwsp7ffppl4wxeq7osqfuu 156 24 Ul(1 ul(1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 156 25 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 156 26 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 156 27 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 156 28 W W NNP work_ln56cwsp7ffppl4wxeq7osqfuu 156 29 l l NNP work_ln56cwsp7ffppl4wxeq7osqfuu 156 30 MX(U MX(U NNP work_ln56cwsp7ffppl4wxeq7osqfuu 156 31 l l NN work_ln56cwsp7ffppl4wxeq7osqfuu 156 32 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 156 33 = = NFP work_ln56cwsp7ffppl4wxeq7osqfuu 156 34 Ul(n Ul(n NNP work_ln56cwsp7ffppl4wxeq7osqfuu 156 35 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 156 36 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 157 1 For for IN work_ln56cwsp7ffppl4wxeq7osqfuu 157 2 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 157 3 case case NN work_ln56cwsp7ffppl4wxeq7osqfuu 157 4 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 157 5 utilitarianism utilitarianism NN work_ln56cwsp7ffppl4wxeq7osqfuu 157 6 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 157 7 given give VBN work_ln56cwsp7ffppl4wxeq7osqfuu 157 8 ordinal ordinal JJ work_ln56cwsp7ffppl4wxeq7osqfuu 157 9 preferences preference NNS work_ln56cwsp7ffppl4wxeq7osqfuu 157 10 M M NNP work_ln56cwsp7ffppl4wxeq7osqfuu 157 11 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 157 12 alternative alternative JJ work_ln56cwsp7ffppl4wxeq7osqfuu 157 13 l l NN work_ln56cwsp7ffppl4wxeq7osqfuu 157 14 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 157 15 better well JJR work_ln56cwsp7ffppl4wxeq7osqfuu 157 16 than than IN work_ln56cwsp7ffppl4wxeq7osqfuu 157 17 alternative alternative JJ work_ln56cwsp7ffppl4wxeq7osqfuu 157 18 q q NNP work_ln56cwsp7ffppl4wxeq7osqfuu 157 19 in in IN work_ln56cwsp7ffppl4wxeq7osqfuu 157 20 terms term NNS work_ln56cwsp7ffppl4wxeq7osqfuu 157 21 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 157 22 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 157 23 α α NNP work_ln56cwsp7ffppl4wxeq7osqfuu 157 24 - - HYPH work_ln56cwsp7ffppl4wxeq7osqfuu 157 25 index index NN work_ln56cwsp7ffppl4wxeq7osqfuu 157 26 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 157 27 if if IN work_ln56cwsp7ffppl4wxeq7osqfuu 157 28 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 157 29 expected expect VBN work_ln56cwsp7ffppl4wxeq7osqfuu 157 30 average average JJ work_ln56cwsp7ffppl4wxeq7osqfuu 157 31 utility utility NN work_ln56cwsp7ffppl4wxeq7osqfuu 157 32 value value NN work_ln56cwsp7ffppl4wxeq7osqfuu 157 33 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 157 34 l l NN work_ln56cwsp7ffppl4wxeq7osqfuu 157 35 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 157 36 larger large JJR work_ln56cwsp7ffppl4wxeq7osqfuu 157 37 than than IN work_ln56cwsp7ffppl4wxeq7osqfuu 157 38 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 157 39 expected expect VBN work_ln56cwsp7ffppl4wxeq7osqfuu 157 40 average average JJ work_ln56cwsp7ffppl4wxeq7osqfuu 157 41 value value NN work_ln56cwsp7ffppl4wxeq7osqfuu 157 42 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 157 43 q. q. NN work_ln56cwsp7ffppl4wxeq7osqfuu 158 1 Therefore therefore RB work_ln56cwsp7ffppl4wxeq7osqfuu 158 2 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 158 3 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 158 4 aim aim NN work_ln56cwsp7ffppl4wxeq7osqfuu 158 5 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 158 6 to to TO work_ln56cwsp7ffppl4wxeq7osqfuu 158 7 find find VB work_ln56cwsp7ffppl4wxeq7osqfuu 158 8 decision decision NN work_ln56cwsp7ffppl4wxeq7osqfuu 158 9 rules rule NNS work_ln56cwsp7ffppl4wxeq7osqfuu 158 10 that that WDT work_ln56cwsp7ffppl4wxeq7osqfuu 158 11 select select VBP work_ln56cwsp7ffppl4wxeq7osqfuu 158 12 alternatives alternative NNS work_ln56cwsp7ffppl4wxeq7osqfuu 158 13 with with IN work_ln56cwsp7ffppl4wxeq7osqfuu 158 14 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 158 15 highest high JJS work_ln56cwsp7ffppl4wxeq7osqfuu 158 16 expected expect VBN work_ln56cwsp7ffppl4wxeq7osqfuu 158 17 average average JJ work_ln56cwsp7ffppl4wxeq7osqfuu 158 18 utility utility NN work_ln56cwsp7ffppl4wxeq7osqfuu 158 19 value value NN work_ln56cwsp7ffppl4wxeq7osqfuu 158 20 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 159 1 Now now RB work_ln56cwsp7ffppl4wxeq7osqfuu 159 2 consider consider VB work_ln56cwsp7ffppl4wxeq7osqfuu 159 3 maximin maximin NN work_ln56cwsp7ffppl4wxeq7osqfuu 159 4 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 160 1 Then then RB work_ln56cwsp7ffppl4wxeq7osqfuu 160 2 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 160 3 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 160 4 a a DT work_ln56cwsp7ffppl4wxeq7osqfuu 160 5 given give VBN work_ln56cwsp7ffppl4wxeq7osqfuu 160 6 M M NNP work_ln56cwsp7ffppl4wxeq7osqfuu 160 7 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 160 8 alternative alternative JJ work_ln56cwsp7ffppl4wxeq7osqfuu 160 9 l l NN work_ln56cwsp7ffppl4wxeq7osqfuu 160 10 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 160 11 better well JJR work_ln56cwsp7ffppl4wxeq7osqfuu 160 12 than than IN work_ln56cwsp7ffppl4wxeq7osqfuu 160 13 alternative alternative JJ work_ln56cwsp7ffppl4wxeq7osqfuu 160 14 q q NNP work_ln56cwsp7ffppl4wxeq7osqfuu 160 15 in in IN work_ln56cwsp7ffppl4wxeq7osqfuu 160 16 terms term NNS work_ln56cwsp7ffppl4wxeq7osqfuu 160 17 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 160 18 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 160 19 α α NNP work_ln56cwsp7ffppl4wxeq7osqfuu 160 20 - - HYPH work_ln56cwsp7ffppl4wxeq7osqfuu 160 21 index index NN work_ln56cwsp7ffppl4wxeq7osqfuu 160 22 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 160 23 if if IN work_ln56cwsp7ffppl4wxeq7osqfuu 160 24 l l NN work_ln56cwsp7ffppl4wxeq7osqfuu 160 25 provides provide VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 160 26 a a DT work_ln56cwsp7ffppl4wxeq7osqfuu 160 27 higher high JJR work_ln56cwsp7ffppl4wxeq7osqfuu 160 28 expected expect VBN work_ln56cwsp7ffppl4wxeq7osqfuu 160 29 value value NN work_ln56cwsp7ffppl4wxeq7osqfuu 160 30 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 160 31 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 160 32 lowest low JJS work_ln56cwsp7ffppl4wxeq7osqfuu 160 33 order order NN work_ln56cwsp7ffppl4wxeq7osqfuu 160 34 statistic statistic NN work_ln56cwsp7ffppl4wxeq7osqfuu 160 35 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 160 36 than than IN work_ln56cwsp7ffppl4wxeq7osqfuu 160 37 q. q. NNP work_ln56cwsp7ffppl4wxeq7osqfuu 161 1 Finally finally RB work_ln56cwsp7ffppl4wxeq7osqfuu 161 2 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 161 3 l l NN work_ln56cwsp7ffppl4wxeq7osqfuu 161 4 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 161 5 better well JJR work_ln56cwsp7ffppl4wxeq7osqfuu 161 6 than than IN work_ln56cwsp7ffppl4wxeq7osqfuu 161 7 q q NNP work_ln56cwsp7ffppl4wxeq7osqfuu 161 8 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 161 9 maximax maximax NNP work_ln56cwsp7ffppl4wxeq7osqfuu 161 10 in in IN work_ln56cwsp7ffppl4wxeq7osqfuu 161 11 terms term NNS work_ln56cwsp7ffppl4wxeq7osqfuu 161 12 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 161 13 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 161 14 α α NNP work_ln56cwsp7ffppl4wxeq7osqfuu 161 15 - - HYPH work_ln56cwsp7ffppl4wxeq7osqfuu 161 16 index index NN work_ln56cwsp7ffppl4wxeq7osqfuu 161 17 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 161 18 if if IN work_ln56cwsp7ffppl4wxeq7osqfuu 161 19 l l NN work_ln56cwsp7ffppl4wxeq7osqfuu 161 20 provides provide VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 161 21 a a DT work_ln56cwsp7ffppl4wxeq7osqfuu 161 22 higher high JJR work_ln56cwsp7ffppl4wxeq7osqfuu 161 23 expected expect VBN work_ln56cwsp7ffppl4wxeq7osqfuu 161 24 value value NN work_ln56cwsp7ffppl4wxeq7osqfuu 161 25 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 161 26 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 161 27 highest high JJS work_ln56cwsp7ffppl4wxeq7osqfuu 161 28 order order NN work_ln56cwsp7ffppl4wxeq7osqfuu 161 29 statistic statistic NN work_ln56cwsp7ffppl4wxeq7osqfuu 161 30 than than IN work_ln56cwsp7ffppl4wxeq7osqfuu 161 31 q q NNP work_ln56cwsp7ffppl4wxeq7osqfuu 161 32 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 161 33 given give VBN work_ln56cwsp7ffppl4wxeq7osqfuu 161 34 ordinal ordinal JJ work_ln56cwsp7ffppl4wxeq7osqfuu 161 35 preferences preference NNS work_ln56cwsp7ffppl4wxeq7osqfuu 161 36 M. M. NNP work_ln56cwsp7ffppl4wxeq7osqfuu 161 37 7 7 CD work_ln56cwsp7ffppl4wxeq7osqfuu 161 38 The the DT work_ln56cwsp7ffppl4wxeq7osqfuu 161 39 β β NNP work_ln56cwsp7ffppl4wxeq7osqfuu 161 40 - - HYPH work_ln56cwsp7ffppl4wxeq7osqfuu 161 41 index index NN work_ln56cwsp7ffppl4wxeq7osqfuu 161 42 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 161 43 on on IN work_ln56cwsp7ffppl4wxeq7osqfuu 161 44 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 161 45 other other JJ work_ln56cwsp7ffppl4wxeq7osqfuu 161 46 hand hand NN work_ln56cwsp7ffppl4wxeq7osqfuu 161 47 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 161 48 measures measure NNS work_ln56cwsp7ffppl4wxeq7osqfuu 161 49 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 161 50 a a DT work_ln56cwsp7ffppl4wxeq7osqfuu 161 51 given give VBN work_ln56cwsp7ffppl4wxeq7osqfuu 161 52 SWF SWF NNP work_ln56cwsp7ffppl4wxeq7osqfuu 161 53 W W NNP work_ln56cwsp7ffppl4wxeq7osqfuu 161 54 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 161 55 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 161 56 probability probability NN work_ln56cwsp7ffppl4wxeq7osqfuu 161 57 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 161 58 an an DT work_ln56cwsp7ffppl4wxeq7osqfuu 161 59 alternative alternative JJ work_ln56cwsp7ffppl4wxeq7osqfuu 161 60 l l NN work_ln56cwsp7ffppl4wxeq7osqfuu 161 61 being be VBG work_ln56cwsp7ffppl4wxeq7osqfuu 161 62 optimal optimal JJ work_ln56cwsp7ffppl4wxeq7osqfuu 161 63 : : : work_ln56cwsp7ffppl4wxeq7osqfuu 161 64 βlW βlW NNP work_ln56cwsp7ffppl4wxeq7osqfuu 161 65 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 161 66 M m NN work_ln56cwsp7ffppl4wxeq7osqfuu 161 67 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 161 68 = = NFP work_ln56cwsp7ffppl4wxeq7osqfuu 161 69 P(W P(W NNP work_ln56cwsp7ffppl4wxeq7osqfuu 161 70 l(Ul l(Ul NNP work_ln56cwsp7ffppl4wxeq7osqfuu 161 71 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 161 72 ≥ ≥ UH work_ln56cwsp7ffppl4wxeq7osqfuu 161 73 Wh(Uh Wh(Uh NNP work_ln56cwsp7ffppl4wxeq7osqfuu 161 74 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 161 75 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 161 76 all all DT work_ln56cwsp7ffppl4wxeq7osqfuu 161 77 h h NN work_ln56cwsp7ffppl4wxeq7osqfuu 161 78 ∈ ∈ NNP work_ln56cwsp7ffppl4wxeq7osqfuu 161 79 K K NNP work_ln56cwsp7ffppl4wxeq7osqfuu 161 80 \{l \{l NNP work_ln56cwsp7ffppl4wxeq7osqfuu 161 81 } } -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 161 82 | | NNP work_ln56cwsp7ffppl4wxeq7osqfuu 161 83 M M NNP work_ln56cwsp7ffppl4wxeq7osqfuu 161 84 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 161 85 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 162 1 Instead instead RB work_ln56cwsp7ffppl4wxeq7osqfuu 162 2 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 162 3 looking look VBG work_ln56cwsp7ffppl4wxeq7osqfuu 162 4 to to IN work_ln56cwsp7ffppl4wxeq7osqfuu 162 5 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 162 6 expected expect VBN work_ln56cwsp7ffppl4wxeq7osqfuu 162 7 value value NN work_ln56cwsp7ffppl4wxeq7osqfuu 162 8 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 162 9 an an DT work_ln56cwsp7ffppl4wxeq7osqfuu 162 10 alternative alternative NN work_ln56cwsp7ffppl4wxeq7osqfuu 162 11 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 162 12 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 162 13 β β NNP work_ln56cwsp7ffppl4wxeq7osqfuu 162 14 - - HYPH work_ln56cwsp7ffppl4wxeq7osqfuu 162 15 index index NN work_ln56cwsp7ffppl4wxeq7osqfuu 162 16 considers consider VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 162 17 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 162 18 probability probability NN work_ln56cwsp7ffppl4wxeq7osqfuu 162 19 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 162 20 that that DT work_ln56cwsp7ffppl4wxeq7osqfuu 162 21 alternative alternative NN work_ln56cwsp7ffppl4wxeq7osqfuu 162 22 providing provide VBG work_ln56cwsp7ffppl4wxeq7osqfuu 162 23 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 162 24 highest high JJS work_ln56cwsp7ffppl4wxeq7osqfuu 162 25 social social JJ work_ln56cwsp7ffppl4wxeq7osqfuu 162 26 welfare welfare NN work_ln56cwsp7ffppl4wxeq7osqfuu 162 27 value value NN work_ln56cwsp7ffppl4wxeq7osqfuu 162 28 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 162 29 given give VBN work_ln56cwsp7ffppl4wxeq7osqfuu 162 30 ordinal ordinal JJ work_ln56cwsp7ffppl4wxeq7osqfuu 162 31 preferences preference NNS work_ln56cwsp7ffppl4wxeq7osqfuu 162 32 M. M. NNP work_ln56cwsp7ffppl4wxeq7osqfuu 162 33 Under Under NNP work_ln56cwsp7ffppl4wxeq7osqfuu 162 34 utilitarianism utilitarianism NN work_ln56cwsp7ffppl4wxeq7osqfuu 162 35 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 162 36 maximin maximin NN work_ln56cwsp7ffppl4wxeq7osqfuu 162 37 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 162 38 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 162 39 maximax maximax NNP work_ln56cwsp7ffppl4wxeq7osqfuu 162 40 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 162 41 we -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 162 42 will will MD work_ln56cwsp7ffppl4wxeq7osqfuu 162 43 be be VB work_ln56cwsp7ffppl4wxeq7osqfuu 162 44 talking talk VBG work_ln56cwsp7ffppl4wxeq7osqfuu 162 45 about about IN work_ln56cwsp7ffppl4wxeq7osqfuu 162 46 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 162 47 probability probability NN work_ln56cwsp7ffppl4wxeq7osqfuu 162 48 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 162 49 selecting select VBG work_ln56cwsp7ffppl4wxeq7osqfuu 162 50 those those DT work_ln56cwsp7ffppl4wxeq7osqfuu 162 51 alternatives alternative NNS work_ln56cwsp7ffppl4wxeq7osqfuu 162 52 that that WDT work_ln56cwsp7ffppl4wxeq7osqfuu 162 53 give give VBP work_ln56cwsp7ffppl4wxeq7osqfuu 162 54 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 162 55 highest high JJS work_ln56cwsp7ffppl4wxeq7osqfuu 162 56 average average JJ work_ln56cwsp7ffppl4wxeq7osqfuu 162 57 utility utility NN work_ln56cwsp7ffppl4wxeq7osqfuu 162 58 value value NN work_ln56cwsp7ffppl4wxeq7osqfuu 162 59 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 162 60 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 162 61 highest high JJS work_ln56cwsp7ffppl4wxeq7osqfuu 162 62 value value NN work_ln56cwsp7ffppl4wxeq7osqfuu 162 63 among among IN work_ln56cwsp7ffppl4wxeq7osqfuu 162 64 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 162 65 first first JJ work_ln56cwsp7ffppl4wxeq7osqfuu 162 66 order order NN work_ln56cwsp7ffppl4wxeq7osqfuu 162 67 statistics statistic NNS work_ln56cwsp7ffppl4wxeq7osqfuu 162 68 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 162 69 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 162 70 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 162 71 highest high JJS work_ln56cwsp7ffppl4wxeq7osqfuu 162 72 value value NN work_ln56cwsp7ffppl4wxeq7osqfuu 162 73 among among IN work_ln56cwsp7ffppl4wxeq7osqfuu 162 74 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 162 75 highest high JJS work_ln56cwsp7ffppl4wxeq7osqfuu 162 76 order order NN work_ln56cwsp7ffppl4wxeq7osqfuu 162 77 statistics statistic NNS work_ln56cwsp7ffppl4wxeq7osqfuu 162 78 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 162 79 respectively respectively RB work_ln56cwsp7ffppl4wxeq7osqfuu 162 80 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 163 1 Finally finally RB work_ln56cwsp7ffppl4wxeq7osqfuu 163 2 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 163 3 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 163 4 a a DT work_ln56cwsp7ffppl4wxeq7osqfuu 163 5 given give VBN work_ln56cwsp7ffppl4wxeq7osqfuu 163 6 SWF SWF NNP work_ln56cwsp7ffppl4wxeq7osqfuu 163 7 W W NNP work_ln56cwsp7ffppl4wxeq7osqfuu 163 8 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 163 9 γ γ NN work_ln56cwsp7ffppl4wxeq7osqfuu 163 10 - - HYPH work_ln56cwsp7ffppl4wxeq7osqfuu 163 11 index index NN work_ln56cwsp7ffppl4wxeq7osqfuu 163 12 evaluates evaluate VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 163 13 alternatives alternative NNS work_ln56cwsp7ffppl4wxeq7osqfuu 163 14 in in IN work_ln56cwsp7ffppl4wxeq7osqfuu 163 15 terms term NNS work_ln56cwsp7ffppl4wxeq7osqfuu 163 16 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 163 17 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 163 18 probability probability NN work_ln56cwsp7ffppl4wxeq7osqfuu 163 19 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 163 20 not not RB work_ln56cwsp7ffppl4wxeq7osqfuu 163 21 choosing choose VBG work_ln56cwsp7ffppl4wxeq7osqfuu 163 22 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 163 23 worst bad JJS work_ln56cwsp7ffppl4wxeq7osqfuu 163 24 alternative alternative NN work_ln56cwsp7ffppl4wxeq7osqfuu 163 25 : : : work_ln56cwsp7ffppl4wxeq7osqfuu 163 26 γlW γlW NNP work_ln56cwsp7ffppl4wxeq7osqfuu 163 27 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 163 28 M m NN work_ln56cwsp7ffppl4wxeq7osqfuu 163 29 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 163 30 = = NFP work_ln56cwsp7ffppl4wxeq7osqfuu 163 31 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 163 32 −P(W −p(w SYM work_ln56cwsp7ffppl4wxeq7osqfuu 163 33 l(Ul l(Ul NNP work_ln56cwsp7ffppl4wxeq7osqfuu 163 34 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 163 35 < < XX work_ln56cwsp7ffppl4wxeq7osqfuu 163 36 Wh(Uh wh(uh XX work_ln56cwsp7ffppl4wxeq7osqfuu 163 37 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 163 38 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 163 39 all all DT work_ln56cwsp7ffppl4wxeq7osqfuu 163 40 h h NN work_ln56cwsp7ffppl4wxeq7osqfuu 163 41 ∈ ∈ NNP work_ln56cwsp7ffppl4wxeq7osqfuu 163 42 K K NNP work_ln56cwsp7ffppl4wxeq7osqfuu 163 43 \{l \{l NNP work_ln56cwsp7ffppl4wxeq7osqfuu 163 44 } } -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 163 45 | | NNP work_ln56cwsp7ffppl4wxeq7osqfuu 163 46 M M NNP work_ln56cwsp7ffppl4wxeq7osqfuu 163 47 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 163 48 = = NFP work_ln56cwsp7ffppl4wxeq7osqfuu 163 49 P(W P(W NNP work_ln56cwsp7ffppl4wxeq7osqfuu 163 50 l(Ul l(Ul NNP work_ln56cwsp7ffppl4wxeq7osqfuu 163 51 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 163 52 ≥ ≥ UH work_ln56cwsp7ffppl4wxeq7osqfuu 163 53 Wh(Uh Wh(Uh NNP work_ln56cwsp7ffppl4wxeq7osqfuu 163 54 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 163 55 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 163 56 some some DT work_ln56cwsp7ffppl4wxeq7osqfuu 163 57 h h NN work_ln56cwsp7ffppl4wxeq7osqfuu 163 58 ∈ ∈ NN work_ln56cwsp7ffppl4wxeq7osqfuu 163 59 K K NNP work_ln56cwsp7ffppl4wxeq7osqfuu 163 60 \{l \{l NNP work_ln56cwsp7ffppl4wxeq7osqfuu 163 61 } } -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 163 62 | | NNP work_ln56cwsp7ffppl4wxeq7osqfuu 163 63 M M NNP work_ln56cwsp7ffppl4wxeq7osqfuu 163 64 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 163 65 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 164 1 The the DT work_ln56cwsp7ffppl4wxeq7osqfuu 164 2 three three CD work_ln56cwsp7ffppl4wxeq7osqfuu 164 3 indices index NNS work_ln56cwsp7ffppl4wxeq7osqfuu 164 4 are be VBP work_ln56cwsp7ffppl4wxeq7osqfuu 164 5 different different JJ work_ln56cwsp7ffppl4wxeq7osqfuu 164 6 in in IN work_ln56cwsp7ffppl4wxeq7osqfuu 164 7 nature nature NN work_ln56cwsp7ffppl4wxeq7osqfuu 164 8 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 165 1 It -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 165 2 could could MD work_ln56cwsp7ffppl4wxeq7osqfuu 165 3 be be VB work_ln56cwsp7ffppl4wxeq7osqfuu 165 4 argued argue VBN work_ln56cwsp7ffppl4wxeq7osqfuu 165 5 that that IN work_ln56cwsp7ffppl4wxeq7osqfuu 165 6 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 165 7 α α NNP work_ln56cwsp7ffppl4wxeq7osqfuu 165 8 - - HYPH work_ln56cwsp7ffppl4wxeq7osqfuu 165 9 index index NN work_ln56cwsp7ffppl4wxeq7osqfuu 165 10 adopts adopt VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 165 11 a a DT work_ln56cwsp7ffppl4wxeq7osqfuu 165 12 risk risk NN work_ln56cwsp7ffppl4wxeq7osqfuu 165 13 neutral neutral JJ work_ln56cwsp7ffppl4wxeq7osqfuu 165 14 approach approach NN work_ln56cwsp7ffppl4wxeq7osqfuu 165 15 to to TO work_ln56cwsp7ffppl4wxeq7osqfuu 165 16 measure measure VB work_ln56cwsp7ffppl4wxeq7osqfuu 165 17 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 165 18 success success NN work_ln56cwsp7ffppl4wxeq7osqfuu 165 19 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 165 20 decision decision NN work_ln56cwsp7ffppl4wxeq7osqfuu 165 21 rules rule NNS work_ln56cwsp7ffppl4wxeq7osqfuu 165 22 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 166 1 Indices Indices NNP work_ln56cwsp7ffppl4wxeq7osqfuu 166 2 β β NNP work_ln56cwsp7ffppl4wxeq7osqfuu 166 3 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 166 4 γ γ NNP work_ln56cwsp7ffppl4wxeq7osqfuu 166 5 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 166 6 however however RB work_ln56cwsp7ffppl4wxeq7osqfuu 166 7 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 166 8 could could MD work_ln56cwsp7ffppl4wxeq7osqfuu 166 9 be be VB work_ln56cwsp7ffppl4wxeq7osqfuu 166 10 understood understand VBN work_ln56cwsp7ffppl4wxeq7osqfuu 166 11 as as IN work_ln56cwsp7ffppl4wxeq7osqfuu 166 12 adopting adopt VBG work_ln56cwsp7ffppl4wxeq7osqfuu 166 13 risk risk NN work_ln56cwsp7ffppl4wxeq7osqfuu 166 14 - - HYPH work_ln56cwsp7ffppl4wxeq7osqfuu 166 15 loving loving NN work_ln56cwsp7ffppl4wxeq7osqfuu 166 16 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 166 17 risk risk NN work_ln56cwsp7ffppl4wxeq7osqfuu 166 18 - - HYPH work_ln56cwsp7ffppl4wxeq7osqfuu 166 19 averse averse JJ work_ln56cwsp7ffppl4wxeq7osqfuu 166 20 positions position NNS work_ln56cwsp7ffppl4wxeq7osqfuu 166 21 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 166 22 respectively respectively RB work_ln56cwsp7ffppl4wxeq7osqfuu 166 23 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 167 1 Indices index NNS work_ln56cwsp7ffppl4wxeq7osqfuu 167 2 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 167 3 ideals ideal NNS work_ln56cwsp7ffppl4wxeq7osqfuu 167 4 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 167 5 justice justice NN work_ln56cwsp7ffppl4wxeq7osqfuu 167 6 are be VBP work_ln56cwsp7ffppl4wxeq7osqfuu 167 7 intimately intimately RB work_ln56cwsp7ffppl4wxeq7osqfuu 167 8 linked link VBN work_ln56cwsp7ffppl4wxeq7osqfuu 167 9 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 168 1 There there EX work_ln56cwsp7ffppl4wxeq7osqfuu 168 2 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 168 3 a a DT work_ln56cwsp7ffppl4wxeq7osqfuu 168 4 natural natural JJ work_ln56cwsp7ffppl4wxeq7osqfuu 168 5 link link NN work_ln56cwsp7ffppl4wxeq7osqfuu 168 6 between between IN work_ln56cwsp7ffppl4wxeq7osqfuu 168 7 utilitarianism utilitarianism NN work_ln56cwsp7ffppl4wxeq7osqfuu 168 8 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 168 9 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 168 10 α α NNP work_ln56cwsp7ffppl4wxeq7osqfuu 168 11 - - HYPH work_ln56cwsp7ffppl4wxeq7osqfuu 168 12 index index NN work_ln56cwsp7ffppl4wxeq7osqfuu 168 13 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 168 14 between between IN work_ln56cwsp7ffppl4wxeq7osqfuu 168 15 maximax maximax NNP work_ln56cwsp7ffppl4wxeq7osqfuu 168 16 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 168 17 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 168 18 β β NNP work_ln56cwsp7ffppl4wxeq7osqfuu 168 19 - - HYPH work_ln56cwsp7ffppl4wxeq7osqfuu 168 20 index index NN work_ln56cwsp7ffppl4wxeq7osqfuu 168 21 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 168 22 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 168 23 between between IN work_ln56cwsp7ffppl4wxeq7osqfuu 168 24 max- max- NNP work_ln56cwsp7ffppl4wxeq7osqfuu 168 25 imin imin NNP work_ln56cwsp7ffppl4wxeq7osqfuu 168 26 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 168 27 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 168 28 γ γ NNP work_ln56cwsp7ffppl4wxeq7osqfuu 168 29 - - HYPH work_ln56cwsp7ffppl4wxeq7osqfuu 168 30 index index NN work_ln56cwsp7ffppl4wxeq7osqfuu 168 31 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 169 1 It -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 169 2 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 169 3 in in IN work_ln56cwsp7ffppl4wxeq7osqfuu 169 4 fact fact NN work_ln56cwsp7ffppl4wxeq7osqfuu 169 5 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 169 6 case case NN work_ln56cwsp7ffppl4wxeq7osqfuu 169 7 that that IN work_ln56cwsp7ffppl4wxeq7osqfuu 169 8 these these DT work_ln56cwsp7ffppl4wxeq7osqfuu 169 9 natural natural JJ work_ln56cwsp7ffppl4wxeq7osqfuu 169 10 links link NNS work_ln56cwsp7ffppl4wxeq7osqfuu 169 11 translate translate VBP work_ln56cwsp7ffppl4wxeq7osqfuu 169 12 into into IN work_ln56cwsp7ffppl4wxeq7osqfuu 169 13 ana- ana- DT work_ln56cwsp7ffppl4wxeq7osqfuu 169 14 lytical lytical JJ work_ln56cwsp7ffppl4wxeq7osqfuu 169 15 tractability tractability NN work_ln56cwsp7ffppl4wxeq7osqfuu 169 16 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 170 1 We -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 170 2 will will MD work_ln56cwsp7ffppl4wxeq7osqfuu 170 3 see see VB work_ln56cwsp7ffppl4wxeq7osqfuu 170 4 that that DT work_ln56cwsp7ffppl4wxeq7osqfuu 170 5 utilitarianism utilitarianism NN work_ln56cwsp7ffppl4wxeq7osqfuu 170 6 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 170 7 best well RBS work_ln56cwsp7ffppl4wxeq7osqfuu 170 8 approached approach VBN work_ln56cwsp7ffppl4wxeq7osqfuu 170 9 analytically analytically RB work_ln56cwsp7ffppl4wxeq7osqfuu 170 10 by by IN work_ln56cwsp7ffppl4wxeq7osqfuu 170 11 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 170 12 α α NNP work_ln56cwsp7ffppl4wxeq7osqfuu 170 13 - - HYPH work_ln56cwsp7ffppl4wxeq7osqfuu 170 14 index index NN work_ln56cwsp7ffppl4wxeq7osqfuu 170 15 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 170 16 while while IN work_ln56cwsp7ffppl4wxeq7osqfuu 170 17 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 170 18 β β NNP work_ln56cwsp7ffppl4wxeq7osqfuu 170 19 - - HYPH work_ln56cwsp7ffppl4wxeq7osqfuu 170 20 index index NN work_ln56cwsp7ffppl4wxeq7osqfuu 170 21 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 170 22 poorly poorly RB work_ln56cwsp7ffppl4wxeq7osqfuu 170 23 suited suit VBN work_ln56cwsp7ffppl4wxeq7osqfuu 170 24 to to IN work_ln56cwsp7ffppl4wxeq7osqfuu 170 25 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 170 26 formal formal JJ work_ln56cwsp7ffppl4wxeq7osqfuu 170 27 study study NN work_ln56cwsp7ffppl4wxeq7osqfuu 170 28 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 170 29 utilitarianism utilitarianism NN work_ln56cwsp7ffppl4wxeq7osqfuu 170 30 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 171 1 With with IN work_ln56cwsp7ffppl4wxeq7osqfuu 171 2 respect respect NN work_ln56cwsp7ffppl4wxeq7osqfuu 171 3 to to IN work_ln56cwsp7ffppl4wxeq7osqfuu 171 4 maximax maximax NNP work_ln56cwsp7ffppl4wxeq7osqfuu 171 5 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 171 6 in in IN work_ln56cwsp7ffppl4wxeq7osqfuu 171 7 contrast contrast NN work_ln56cwsp7ffppl4wxeq7osqfuu 171 8 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 171 9 great great JJ work_ln56cwsp7ffppl4wxeq7osqfuu 171 10 analytical analytical JJ work_ln56cwsp7ffppl4wxeq7osqfuu 171 11 progress progress NN work_ln56cwsp7ffppl4wxeq7osqfuu 171 12 can can MD work_ln56cwsp7ffppl4wxeq7osqfuu 171 13 be be VB work_ln56cwsp7ffppl4wxeq7osqfuu 171 14 made make VBN work_ln56cwsp7ffppl4wxeq7osqfuu 171 15 with with IN work_ln56cwsp7ffppl4wxeq7osqfuu 171 16 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 171 17 β β NNP work_ln56cwsp7ffppl4wxeq7osqfuu 171 18 - - HYPH work_ln56cwsp7ffppl4wxeq7osqfuu 171 19 index index NN work_ln56cwsp7ffppl4wxeq7osqfuu 171 20 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 171 21 but but CC work_ln56cwsp7ffppl4wxeq7osqfuu 171 22 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 171 23 tractability tractability NN work_ln56cwsp7ffppl4wxeq7osqfuu 171 24 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 171 25 maximax maximax NNP work_ln56cwsp7ffppl4wxeq7osqfuu 171 26 with with IN work_ln56cwsp7ffppl4wxeq7osqfuu 171 27 regard regard NN work_ln56cwsp7ffppl4wxeq7osqfuu 171 28 to to IN work_ln56cwsp7ffppl4wxeq7osqfuu 171 29 α α NNP work_ln56cwsp7ffppl4wxeq7osqfuu 171 30 becomes become VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 171 31 complex complex JJ work_ln56cwsp7ffppl4wxeq7osqfuu 171 32 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 172 1 For for IN work_ln56cwsp7ffppl4wxeq7osqfuu 172 2 intuition intuition NN work_ln56cwsp7ffppl4wxeq7osqfuu 172 3 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 172 4 consider consider VB work_ln56cwsp7ffppl4wxeq7osqfuu 172 5 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 172 6 instance instance NN work_ln56cwsp7ffppl4wxeq7osqfuu 172 7 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 172 8 α α NNP work_ln56cwsp7ffppl4wxeq7osqfuu 172 9 - - NN work_ln56cwsp7ffppl4wxeq7osqfuu 172 10 index index NN work_ln56cwsp7ffppl4wxeq7osqfuu 172 11 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 172 12 an an DT work_ln56cwsp7ffppl4wxeq7osqfuu 172 13 alternative alternative JJ work_ln56cwsp7ffppl4wxeq7osqfuu 172 14 l l NN work_ln56cwsp7ffppl4wxeq7osqfuu 172 15 in in IN work_ln56cwsp7ffppl4wxeq7osqfuu 172 16 utilitarian utilitarian JJ work_ln56cwsp7ffppl4wxeq7osqfuu 172 17 terms term NNS work_ln56cwsp7ffppl4wxeq7osqfuu 172 18 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 173 1 The the DT work_ln56cwsp7ffppl4wxeq7osqfuu 173 2 value value NN work_ln56cwsp7ffppl4wxeq7osqfuu 173 3 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 173 4 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 173 5 α α NNP work_ln56cwsp7ffppl4wxeq7osqfuu 173 6 - - HYPH work_ln56cwsp7ffppl4wxeq7osqfuu 173 7 index index NN work_ln56cwsp7ffppl4wxeq7osqfuu 173 8 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 173 9 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 173 10 average average NN work_ln56cwsp7ffppl4wxeq7osqfuu 173 11 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 173 12 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 173 13 expected expect VBN work_ln56cwsp7ffppl4wxeq7osqfuu 173 14 value value NN work_ln56cwsp7ffppl4wxeq7osqfuu 173 15 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 173 16 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 173 17 different different JJ work_ln56cwsp7ffppl4wxeq7osqfuu 173 18 order order NN work_ln56cwsp7ffppl4wxeq7osqfuu 173 19 statistics statistic NNS work_ln56cwsp7ffppl4wxeq7osqfuu 173 20 that that WDT work_ln56cwsp7ffppl4wxeq7osqfuu 173 21 make make VBP work_ln56cwsp7ffppl4wxeq7osqfuu 173 22 up up RP work_ln56cwsp7ffppl4wxeq7osqfuu 173 23 alternative alternative JJ work_ln56cwsp7ffppl4wxeq7osqfuu 173 24 l. l. NN work_ln56cwsp7ffppl4wxeq7osqfuu 173 25 In in IN work_ln56cwsp7ffppl4wxeq7osqfuu 173 26 terms term NNS work_ln56cwsp7ffppl4wxeq7osqfuu 173 27 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 173 28 maximax maximax NNP work_ln56cwsp7ffppl4wxeq7osqfuu 173 29 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 173 30 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 173 31 similarly similarly RB work_ln56cwsp7ffppl4wxeq7osqfuu 173 32 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 173 33 max- max- NNP work_ln56cwsp7ffppl4wxeq7osqfuu 173 34 imin imin NNP work_ln56cwsp7ffppl4wxeq7osqfuu 173 35 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 173 36 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 173 37 one one PRP work_ln56cwsp7ffppl4wxeq7osqfuu 173 38 has have VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 173 39 to to TO work_ln56cwsp7ffppl4wxeq7osqfuu 173 40 obtain obtain VB work_ln56cwsp7ffppl4wxeq7osqfuu 173 41 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 173 42 expected expect VBN work_ln56cwsp7ffppl4wxeq7osqfuu 173 43 value value NN work_ln56cwsp7ffppl4wxeq7osqfuu 173 44 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 173 45 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 173 46 highest high JJS work_ln56cwsp7ffppl4wxeq7osqfuu 173 47 order order NN work_ln56cwsp7ffppl4wxeq7osqfuu 173 48 statistic statistic NN work_ln56cwsp7ffppl4wxeq7osqfuu 173 49 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 173 50 l. l. NN work_ln56cwsp7ffppl4wxeq7osqfuu 173 51 This this DT work_ln56cwsp7ffppl4wxeq7osqfuu 173 52 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 173 53 a a DT work_ln56cwsp7ffppl4wxeq7osqfuu 173 54 challenge challenge NN work_ln56cwsp7ffppl4wxeq7osqfuu 173 55 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 174 1 If if IN work_ln56cwsp7ffppl4wxeq7osqfuu 174 2 there there EX work_ln56cwsp7ffppl4wxeq7osqfuu 174 3 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 174 4 an an DT work_ln56cwsp7ffppl4wxeq7osqfuu 174 5 individual individual NN work_ln56cwsp7ffppl4wxeq7osqfuu 174 6 who who WP work_ln56cwsp7ffppl4wxeq7osqfuu 174 7 ranks rank VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 174 8 l l NN work_ln56cwsp7ffppl4wxeq7osqfuu 174 9 as as IN work_ln56cwsp7ffppl4wxeq7osqfuu 174 10 her -PRON- PRP$ work_ln56cwsp7ffppl4wxeq7osqfuu 174 11 best good JJS work_ln56cwsp7ffppl4wxeq7osqfuu 174 12 alternative alternative NN work_ln56cwsp7ffppl4wxeq7osqfuu 174 13 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 174 14 then then RB work_ln56cwsp7ffppl4wxeq7osqfuu 174 15 this this DT work_ln56cwsp7ffppl4wxeq7osqfuu 174 16 individual individual NN work_ln56cwsp7ffppl4wxeq7osqfuu 174 17 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 174 18 a a DT work_ln56cwsp7ffppl4wxeq7osqfuu 174 19 good good JJ work_ln56cwsp7ffppl4wxeq7osqfuu 174 20 candidate candidate NN work_ln56cwsp7ffppl4wxeq7osqfuu 174 21 to to TO work_ln56cwsp7ffppl4wxeq7osqfuu 174 22 represent represent VB work_ln56cwsp7ffppl4wxeq7osqfuu 174 23 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 174 24 highest high JJS work_ln56cwsp7ffppl4wxeq7osqfuu 174 25 order order NN work_ln56cwsp7ffppl4wxeq7osqfuu 174 26 statistic statistic NN work_ln56cwsp7ffppl4wxeq7osqfuu 174 27 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 174 28 l. l. NNP work_ln56cwsp7ffppl4wxeq7osqfuu 174 29 However however RB work_ln56cwsp7ffppl4wxeq7osqfuu 174 30 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 174 31 if if IN work_ln56cwsp7ffppl4wxeq7osqfuu 174 32 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 174 33 example example NN work_ln56cwsp7ffppl4wxeq7osqfuu 174 34 there there EX work_ln56cwsp7ffppl4wxeq7osqfuu 174 35 are be VBP work_ln56cwsp7ffppl4wxeq7osqfuu 174 36 many many JJ work_ln56cwsp7ffppl4wxeq7osqfuu 174 37 individuals individual NNS work_ln56cwsp7ffppl4wxeq7osqfuu 174 38 who who WP work_ln56cwsp7ffppl4wxeq7osqfuu 174 39 ranks rank VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 174 40 l l NN work_ln56cwsp7ffppl4wxeq7osqfuu 174 41 as as IN work_ln56cwsp7ffppl4wxeq7osqfuu 174 42 their -PRON- PRP$ work_ln56cwsp7ffppl4wxeq7osqfuu 174 43 second second JJ work_ln56cwsp7ffppl4wxeq7osqfuu 174 44 best good JJS work_ln56cwsp7ffppl4wxeq7osqfuu 174 45 alterna- alterna- NN work_ln56cwsp7ffppl4wxeq7osqfuu 174 46 tive tive JJ work_ln56cwsp7ffppl4wxeq7osqfuu 174 47 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 174 48 then then RB work_ln56cwsp7ffppl4wxeq7osqfuu 174 49 it -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 174 50 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 174 51 likely likely JJ work_ln56cwsp7ffppl4wxeq7osqfuu 174 52 that that IN work_ln56cwsp7ffppl4wxeq7osqfuu 174 53 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 174 54 highest high JJS work_ln56cwsp7ffppl4wxeq7osqfuu 174 55 order order NN work_ln56cwsp7ffppl4wxeq7osqfuu 174 56 statistic statistic NN work_ln56cwsp7ffppl4wxeq7osqfuu 174 57 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 174 58 l l NN work_ln56cwsp7ffppl4wxeq7osqfuu 174 59 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 174 60 among among IN work_ln56cwsp7ffppl4wxeq7osqfuu 174 61 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 174 62 latter latter JJ work_ln56cwsp7ffppl4wxeq7osqfuu 174 63 group group NN work_ln56cwsp7ffppl4wxeq7osqfuu 174 64 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 174 65 individuals individual NNS work_ln56cwsp7ffppl4wxeq7osqfuu 174 66 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 175 1 Thus thus RB work_ln56cwsp7ffppl4wxeq7osqfuu 175 2 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 175 3 there there EX work_ln56cwsp7ffppl4wxeq7osqfuu 175 4 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 175 5 a a DT work_ln56cwsp7ffppl4wxeq7osqfuu 175 6 complex complex JJ work_ln56cwsp7ffppl4wxeq7osqfuu 175 7 dependent dependent JJ work_ln56cwsp7ffppl4wxeq7osqfuu 175 8 structure structure NN work_ln56cwsp7ffppl4wxeq7osqfuu 175 9 that that WDT work_ln56cwsp7ffppl4wxeq7osqfuu 175 10 forces force VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 175 11 consideration consideration NN work_ln56cwsp7ffppl4wxeq7osqfuu 175 12 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 175 13 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 175 14 interrelation interrelation NN work_ln56cwsp7ffppl4wxeq7osqfuu 175 15 between between IN work_ln56cwsp7ffppl4wxeq7osqfuu 175 16 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 175 17 random random JJ work_ln56cwsp7ffppl4wxeq7osqfuu 175 18 utility utility NN work_ln56cwsp7ffppl4wxeq7osqfuu 175 19 variables variable NNS work_ln56cwsp7ffppl4wxeq7osqfuu 175 20 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 175 21 all all PDT work_ln56cwsp7ffppl4wxeq7osqfuu 175 22 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 175 23 individuals individual NNS work_ln56cwsp7ffppl4wxeq7osqfuu 175 24 in in IN work_ln56cwsp7ffppl4wxeq7osqfuu 175 25 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 175 26 society society NN work_ln56cwsp7ffppl4wxeq7osqfuu 175 27 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 175 28 all all PDT work_ln56cwsp7ffppl4wxeq7osqfuu 175 29 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 175 30 alternatives alternative NNS work_ln56cwsp7ffppl4wxeq7osqfuu 175 31 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 176 1 An an DT work_ln56cwsp7ffppl4wxeq7osqfuu 176 2 XW xw JJ work_ln56cwsp7ffppl4wxeq7osqfuu 176 3 -optimal -optimal JJ work_ln56cwsp7ffppl4wxeq7osqfuu 176 4 decision decision NN work_ln56cwsp7ffppl4wxeq7osqfuu 176 5 rule rule NN work_ln56cwsp7ffppl4wxeq7osqfuu 176 6 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 176 7 with with IN work_ln56cwsp7ffppl4wxeq7osqfuu 176 8 XW XW NNP work_ln56cwsp7ffppl4wxeq7osqfuu 176 9 = = NFP work_ln56cwsp7ffppl4wxeq7osqfuu 176 10 { { -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 176 11 αW αW NNP work_ln56cwsp7ffppl4wxeq7osqfuu 176 12 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 176 13 βW βW NNP work_ln56cwsp7ffppl4wxeq7osqfuu 176 14 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 176 15 γW γW NNP work_ln56cwsp7ffppl4wxeq7osqfuu 176 16 } } -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 176 17 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 176 18 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 176 19 a a DT work_ln56cwsp7ffppl4wxeq7osqfuu 176 20 decision decision NN work_ln56cwsp7ffppl4wxeq7osqfuu 176 21 rule rule NN work_ln56cwsp7ffppl4wxeq7osqfuu 176 22 f f NNP work_ln56cwsp7ffppl4wxeq7osqfuu 176 23 that that WDT work_ln56cwsp7ffppl4wxeq7osqfuu 176 24 always always RB work_ln56cwsp7ffppl4wxeq7osqfuu 176 25 selects select VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 176 26 alternatives alternative NNS work_ln56cwsp7ffppl4wxeq7osqfuu 176 27 with with IN work_ln56cwsp7ffppl4wxeq7osqfuu 176 28 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 176 29 largest large JJS work_ln56cwsp7ffppl4wxeq7osqfuu 176 30 X x NN work_ln56cwsp7ffppl4wxeq7osqfuu 176 31 - - NN work_ln56cwsp7ffppl4wxeq7osqfuu 176 32 index index NN work_ln56cwsp7ffppl4wxeq7osqfuu 176 33 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 176 34 ideal ideal NN work_ln56cwsp7ffppl4wxeq7osqfuu 176 35 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 176 36 justice justice NN work_ln56cwsp7ffppl4wxeq7osqfuu 176 37 W. W. NNP work_ln56cwsp7ffppl4wxeq7osqfuu 176 38 That That NNP work_ln56cwsp7ffppl4wxeq7osqfuu 176 39 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 176 40 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 176 41 8 8 CD work_ln56cwsp7ffppl4wxeq7osqfuu 176 42 f f NN work_ln56cwsp7ffppl4wxeq7osqfuu 176 43 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 176 44 XW XW NNP work_ln56cwsp7ffppl4wxeq7osqfuu 176 45 -optimal -optimal JJ work_ln56cwsp7ffppl4wxeq7osqfuu 176 46 decision decision NN work_ln56cwsp7ffppl4wxeq7osqfuu 176 47 rule rule NN work_ln56cwsp7ffppl4wxeq7osqfuu 176 48 if if IN work_ln56cwsp7ffppl4wxeq7osqfuu 176 49 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 176 50 all all DT work_ln56cwsp7ffppl4wxeq7osqfuu 176 51 M M NNP work_ln56cwsp7ffppl4wxeq7osqfuu 176 52 ∈M ∈m NN work_ln56cwsp7ffppl4wxeq7osqfuu 176 53 : : : work_ln56cwsp7ffppl4wxeq7osqfuu 176 54 l l LS work_ln56cwsp7ffppl4wxeq7osqfuu 176 55 ∈ ∈ NNP work_ln56cwsp7ffppl4wxeq7osqfuu 176 56 f(M f(m NN work_ln56cwsp7ffppl4wxeq7osqfuu 176 57 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 176 58 ⇒ ⇒ CD work_ln56cwsp7ffppl4wxeq7osqfuu 176 59 XlW XlW NNP work_ln56cwsp7ffppl4wxeq7osqfuu 176 60 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 176 61 M M NNP work_ln56cwsp7ffppl4wxeq7osqfuu 176 62 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 176 63 ≥ ≥ NN work_ln56cwsp7ffppl4wxeq7osqfuu 176 64 X x NN work_ln56cwsp7ffppl4wxeq7osqfuu 176 65 h h NNP work_ln56cwsp7ffppl4wxeq7osqfuu 176 66 W w NN work_ln56cwsp7ffppl4wxeq7osqfuu 176 67 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 176 68 M m NN work_ln56cwsp7ffppl4wxeq7osqfuu 176 69 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 176 70 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 176 71 all all DT work_ln56cwsp7ffppl4wxeq7osqfuu 176 72 h h NN work_ln56cwsp7ffppl4wxeq7osqfuu 176 73 ∈ ∈ NNP work_ln56cwsp7ffppl4wxeq7osqfuu 176 74 K. K. NNP work_ln56cwsp7ffppl4wxeq7osqfuu 176 75 It -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 176 76 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 176 77 straightforward straightforward JJ work_ln56cwsp7ffppl4wxeq7osqfuu 176 78 to to TO work_ln56cwsp7ffppl4wxeq7osqfuu 176 79 see see VB work_ln56cwsp7ffppl4wxeq7osqfuu 176 80 that that IN work_ln56cwsp7ffppl4wxeq7osqfuu 176 81 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 176 82 given give VBN work_ln56cwsp7ffppl4wxeq7osqfuu 176 83 an an DT work_ln56cwsp7ffppl4wxeq7osqfuu 176 84 XW xw JJ work_ln56cwsp7ffppl4wxeq7osqfuu 176 85 -optimal -optimal JJ work_ln56cwsp7ffppl4wxeq7osqfuu 176 86 decision decision NN work_ln56cwsp7ffppl4wxeq7osqfuu 176 87 rule rule NN work_ln56cwsp7ffppl4wxeq7osqfuu 176 88 f f NNP work_ln56cwsp7ffppl4wxeq7osqfuu 176 89 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 176 90 any any DT work_ln56cwsp7ffppl4wxeq7osqfuu 176 91 other other JJ work_ln56cwsp7ffppl4wxeq7osqfuu 176 92 decision decision NN work_ln56cwsp7ffppl4wxeq7osqfuu 176 93 rule rule NN work_ln56cwsp7ffppl4wxeq7osqfuu 176 94 in in IN work_ln56cwsp7ffppl4wxeq7osqfuu 176 95 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 176 96 family family NN work_ln56cwsp7ffppl4wxeq7osqfuu 176 97 δ(f δ(f ADD work_ln56cwsp7ffppl4wxeq7osqfuu 176 98 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 176 99 = = NFP work_ln56cwsp7ffppl4wxeq7osqfuu 176 100 { { -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 176 101 g g NNP work_ln56cwsp7ffppl4wxeq7osqfuu 176 102 ∈F ∈f NN work_ln56cwsp7ffppl4wxeq7osqfuu 176 103 : : : work_ln56cwsp7ffppl4wxeq7osqfuu 176 104 ∅ ∅ NNP work_ln56cwsp7ffppl4wxeq7osqfuu 176 105 6= 6= CD work_ln56cwsp7ffppl4wxeq7osqfuu 176 106 g(M g(m NN work_ln56cwsp7ffppl4wxeq7osqfuu 176 107 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 176 108 ⊆ ⊆ ADD work_ln56cwsp7ffppl4wxeq7osqfuu 176 109 f(M f(m LS work_ln56cwsp7ffppl4wxeq7osqfuu 176 110 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 176 111 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 176 112 all all DT work_ln56cwsp7ffppl4wxeq7osqfuu 176 113 M M NNP work_ln56cwsp7ffppl4wxeq7osqfuu 176 114 ∈M ∈m NN work_ln56cwsp7ffppl4wxeq7osqfuu 176 115 } } -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 176 116 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 176 117 also also RB work_ln56cwsp7ffppl4wxeq7osqfuu 176 118 an an DT work_ln56cwsp7ffppl4wxeq7osqfuu 176 119 XW xw JJ work_ln56cwsp7ffppl4wxeq7osqfuu 176 120 -optimal -optimal JJ work_ln56cwsp7ffppl4wxeq7osqfuu 176 121 decision decision NN work_ln56cwsp7ffppl4wxeq7osqfuu 176 122 rule rule NN work_ln56cwsp7ffppl4wxeq7osqfuu 176 123 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 177 1 In in IN work_ln56cwsp7ffppl4wxeq7osqfuu 177 2 order order NN work_ln56cwsp7ffppl4wxeq7osqfuu 177 3 to to TO work_ln56cwsp7ffppl4wxeq7osqfuu 177 4 characterize characterize VB work_ln56cwsp7ffppl4wxeq7osqfuu 177 5 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 177 6 set set NN work_ln56cwsp7ffppl4wxeq7osqfuu 177 7 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 177 8 XW xw JJ work_ln56cwsp7ffppl4wxeq7osqfuu 177 9 -optimal -optimal JJ work_ln56cwsp7ffppl4wxeq7osqfuu 177 10 decision decision NN work_ln56cwsp7ffppl4wxeq7osqfuu 177 11 rules rule NNS work_ln56cwsp7ffppl4wxeq7osqfuu 177 12 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 177 13 it -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 177 14 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 177 15 sufficient sufficient JJ work_ln56cwsp7ffppl4wxeq7osqfuu 177 16 to to TO work_ln56cwsp7ffppl4wxeq7osqfuu 177 17 identify identify VB work_ln56cwsp7ffppl4wxeq7osqfuu 177 18 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 177 19 maximum maximum JJ work_ln56cwsp7ffppl4wxeq7osqfuu 177 20 XW XW NNP work_ln56cwsp7ffppl4wxeq7osqfuu 177 21 -optimal -optimal NNP work_ln56cwsp7ffppl4wxeq7osqfuu 177 22 f. f. FW work_ln56cwsp7ffppl4wxeq7osqfuu 177 23 We -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 177 24 will will MD work_ln56cwsp7ffppl4wxeq7osqfuu 177 25 say say VB work_ln56cwsp7ffppl4wxeq7osqfuu 177 26 that that IN work_ln56cwsp7ffppl4wxeq7osqfuu 177 27 f f NNP work_ln56cwsp7ffppl4wxeq7osqfuu 177 28 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 177 29 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 177 30 maximum maximum JJ work_ln56cwsp7ffppl4wxeq7osqfuu 177 31 XW xw JJ work_ln56cwsp7ffppl4wxeq7osqfuu 177 32 -optimal -optimal JJ work_ln56cwsp7ffppl4wxeq7osqfuu 177 33 decision decision NN work_ln56cwsp7ffppl4wxeq7osqfuu 177 34 rule rule NN work_ln56cwsp7ffppl4wxeq7osqfuu 177 35 if if IN work_ln56cwsp7ffppl4wxeq7osqfuu 177 36 whenever whenever WRB work_ln56cwsp7ffppl4wxeq7osqfuu 177 37 f f NNP work_ln56cwsp7ffppl4wxeq7osqfuu 177 38 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 177 39 g g NNP work_ln56cwsp7ffppl4wxeq7osqfuu 177 40 are be VBP work_ln56cwsp7ffppl4wxeq7osqfuu 177 41 XW XW NNP work_ln56cwsp7ffppl4wxeq7osqfuu 177 42 -optimal -optimal NNP work_ln56cwsp7ffppl4wxeq7osqfuu 177 43 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 177 44 then then RB work_ln56cwsp7ffppl4wxeq7osqfuu 177 45 it -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 177 46 must must MD work_ln56cwsp7ffppl4wxeq7osqfuu 177 47 be be VB work_ln56cwsp7ffppl4wxeq7osqfuu 177 48 that that IN work_ln56cwsp7ffppl4wxeq7osqfuu 177 49 g g NN work_ln56cwsp7ffppl4wxeq7osqfuu 177 50 ∈ ∈ JJ work_ln56cwsp7ffppl4wxeq7osqfuu 177 51 δ(f δ(f NNP work_ln56cwsp7ffppl4wxeq7osqfuu 177 52 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 177 53 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 178 1 3 3 LS work_ln56cwsp7ffppl4wxeq7osqfuu 178 2 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 179 1 Utilitarianism Utilitarianism NNP work_ln56cwsp7ffppl4wxeq7osqfuu 179 2 We -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 179 3 first first RB work_ln56cwsp7ffppl4wxeq7osqfuu 179 4 show show VBP work_ln56cwsp7ffppl4wxeq7osqfuu 179 5 that that IN work_ln56cwsp7ffppl4wxeq7osqfuu 179 6 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 179 7 every every DT work_ln56cwsp7ffppl4wxeq7osqfuu 179 8 n×k n×k NNP work_ln56cwsp7ffppl4wxeq7osqfuu 179 9 society society NN work_ln56cwsp7ffppl4wxeq7osqfuu 179 10 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 179 11 every every DT work_ln56cwsp7ffppl4wxeq7osqfuu 179 12 culture culture NN work_ln56cwsp7ffppl4wxeq7osqfuu 179 13 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 179 14 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 179 15 optimal optimal JJ work_ln56cwsp7ffppl4wxeq7osqfuu 179 16 decision decision NN work_ln56cwsp7ffppl4wxeq7osqfuu 179 17 rule rule NN work_ln56cwsp7ffppl4wxeq7osqfuu 179 18 to to TO work_ln56cwsp7ffppl4wxeq7osqfuu 179 19 maximize maximize VB work_ln56cwsp7ffppl4wxeq7osqfuu 179 20 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 179 21 utilitarian utilitarian JJ work_ln56cwsp7ffppl4wxeq7osqfuu 179 22 expected expect VBN work_ln56cwsp7ffppl4wxeq7osqfuu 179 23 value value NN work_ln56cwsp7ffppl4wxeq7osqfuu 179 24 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 179 25 a a DT work_ln56cwsp7ffppl4wxeq7osqfuu 179 26 scoring score VBG work_ln56cwsp7ffppl4wxeq7osqfuu 179 27 rule rule NN work_ln56cwsp7ffppl4wxeq7osqfuu 179 28 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 180 1 This this DT work_ln56cwsp7ffppl4wxeq7osqfuu 180 2 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 180 3 good good JJ work_ln56cwsp7ffppl4wxeq7osqfuu 180 4 news news NN work_ln56cwsp7ffppl4wxeq7osqfuu 180 5 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 181 1 It -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 181 2 implies imply VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 181 3 that that IN work_ln56cwsp7ffppl4wxeq7osqfuu 181 4 if if IN work_ln56cwsp7ffppl4wxeq7osqfuu 181 5 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 181 6 interest interest NN work_ln56cwsp7ffppl4wxeq7osqfuu 181 7 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 181 8 to to TO work_ln56cwsp7ffppl4wxeq7osqfuu 181 9 maximize maximize VB work_ln56cwsp7ffppl4wxeq7osqfuu 181 10 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 181 11 expected expect VBN work_ln56cwsp7ffppl4wxeq7osqfuu 181 12 value value NN work_ln56cwsp7ffppl4wxeq7osqfuu 181 13 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 181 14 utilitarianism utilitarianism NN work_ln56cwsp7ffppl4wxeq7osqfuu 181 15 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 181 16 it -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 181 17 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 181 18 advisable advisable JJ work_ln56cwsp7ffppl4wxeq7osqfuu 181 19 to to TO work_ln56cwsp7ffppl4wxeq7osqfuu 181 20 implement implement VB work_ln56cwsp7ffppl4wxeq7osqfuu 181 21 a a DT work_ln56cwsp7ffppl4wxeq7osqfuu 181 22 scoring score VBG work_ln56cwsp7ffppl4wxeq7osqfuu 181 23 rule rule NN work_ln56cwsp7ffppl4wxeq7osqfuu 181 24 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 181 25 which which WDT work_ln56cwsp7ffppl4wxeq7osqfuu 181 26 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 181 27 a a DT work_ln56cwsp7ffppl4wxeq7osqfuu 181 28 relatively relatively RB work_ln56cwsp7ffppl4wxeq7osqfuu 181 29 simple simple JJ work_ln56cwsp7ffppl4wxeq7osqfuu 181 30 decision decision NN work_ln56cwsp7ffppl4wxeq7osqfuu 181 31 rule rule NN work_ln56cwsp7ffppl4wxeq7osqfuu 181 32 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 182 1 Furthermore furthermore RB work_ln56cwsp7ffppl4wxeq7osqfuu 182 2 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 182 3 we -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 182 4 provide provide VBP work_ln56cwsp7ffppl4wxeq7osqfuu 182 5 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 182 6 exact exact JJ work_ln56cwsp7ffppl4wxeq7osqfuu 182 7 form form NN work_ln56cwsp7ffppl4wxeq7osqfuu 182 8 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 182 9 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 182 10 optimal optimal JJ work_ln56cwsp7ffppl4wxeq7osqfuu 182 11 scoring score VBG work_ln56cwsp7ffppl4wxeq7osqfuu 182 12 rule rule NN work_ln56cwsp7ffppl4wxeq7osqfuu 182 13 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 182 14 conditional conditional JJ work_ln56cwsp7ffppl4wxeq7osqfuu 182 15 on on IN work_ln56cwsp7ffppl4wxeq7osqfuu 182 16 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 182 17 culture culture NN work_ln56cwsp7ffppl4wxeq7osqfuu 182 18 under under IN work_ln56cwsp7ffppl4wxeq7osqfuu 182 19 consideration consideration NN work_ln56cwsp7ffppl4wxeq7osqfuu 182 20 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 183 1 More more RBR work_ln56cwsp7ffppl4wxeq7osqfuu 183 2 specifically specifically RB work_ln56cwsp7ffppl4wxeq7osqfuu 183 3 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 183 4 a a DT work_ln56cwsp7ffppl4wxeq7osqfuu 183 5 culture culture NN work_ln56cwsp7ffppl4wxeq7osqfuu 183 6 determines determine VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 183 7 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 183 8 expected expect VBN work_ln56cwsp7ffppl4wxeq7osqfuu 183 9 value value NN work_ln56cwsp7ffppl4wxeq7osqfuu 183 10 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 183 11 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 183 12 order order NN work_ln56cwsp7ffppl4wxeq7osqfuu 183 13 statistics statistic NNS work_ln56cwsp7ffppl4wxeq7osqfuu 183 14 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 183 15 which which WDT work_ln56cwsp7ffppl4wxeq7osqfuu 183 16 in in IN work_ln56cwsp7ffppl4wxeq7osqfuu 183 17 turn turn NN work_ln56cwsp7ffppl4wxeq7osqfuu 183 18 determines determine VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 183 19 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 183 20 optimal optimal JJ work_ln56cwsp7ffppl4wxeq7osqfuu 183 21 value value NN work_ln56cwsp7ffppl4wxeq7osqfuu 183 22 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 183 23 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 183 24 scoring score VBG work_ln56cwsp7ffppl4wxeq7osqfuu 183 25 rule rule NN work_ln56cwsp7ffppl4wxeq7osqfuu 183 26 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 184 1 Knowledge knowledge NN work_ln56cwsp7ffppl4wxeq7osqfuu 184 2 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 184 3 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 184 4 culture culture NN work_ln56cwsp7ffppl4wxeq7osqfuu 184 5 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 184 6 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 184 7 society society NN work_ln56cwsp7ffppl4wxeq7osqfuu 184 8 provides provide VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 184 9 information information NN work_ln56cwsp7ffppl4wxeq7osqfuu 184 10 on on IN work_ln56cwsp7ffppl4wxeq7osqfuu 184 11 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 184 12 expected expect VBN work_ln56cwsp7ffppl4wxeq7osqfuu 184 13 value value NN work_ln56cwsp7ffppl4wxeq7osqfuu 184 14 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 184 15 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 184 16 order order NN work_ln56cwsp7ffppl4wxeq7osqfuu 184 17 statistics statistic NNS work_ln56cwsp7ffppl4wxeq7osqfuu 184 18 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 184 19 which which WDT work_ln56cwsp7ffppl4wxeq7osqfuu 184 20 can can MD work_ln56cwsp7ffppl4wxeq7osqfuu 184 21 be be VB work_ln56cwsp7ffppl4wxeq7osqfuu 184 22 used use VBN work_ln56cwsp7ffppl4wxeq7osqfuu 184 23 to to TO work_ln56cwsp7ffppl4wxeq7osqfuu 184 24 design design VB work_ln56cwsp7ffppl4wxeq7osqfuu 184 25 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 184 26 optimal optimal JJ work_ln56cwsp7ffppl4wxeq7osqfuu 184 27 scoring score VBG work_ln56cwsp7ffppl4wxeq7osqfuu 184 28 rule rule NN work_ln56cwsp7ffppl4wxeq7osqfuu 184 29 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 185 1 In in IN work_ln56cwsp7ffppl4wxeq7osqfuu 185 2 particular particular JJ work_ln56cwsp7ffppl4wxeq7osqfuu 185 3 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 185 4 we -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 185 5 show show VBP work_ln56cwsp7ffppl4wxeq7osqfuu 185 6 that that IN work_ln56cwsp7ffppl4wxeq7osqfuu 185 7 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 185 8 a a DT work_ln56cwsp7ffppl4wxeq7osqfuu 185 9 range range NN work_ln56cwsp7ffppl4wxeq7osqfuu 185 10 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 185 11 cultures culture NNS work_ln56cwsp7ffppl4wxeq7osqfuu 185 12 with with IN work_ln56cwsp7ffppl4wxeq7osqfuu 185 13 symmetric symmetric JJ work_ln56cwsp7ffppl4wxeq7osqfuu 185 14 density density NN work_ln56cwsp7ffppl4wxeq7osqfuu 185 15 functions function NNS work_ln56cwsp7ffppl4wxeq7osqfuu 185 16 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 185 17 a a DT work_ln56cwsp7ffppl4wxeq7osqfuu 185 18 prominent prominent JJ work_ln56cwsp7ffppl4wxeq7osqfuu 185 19 scoring score VBG work_ln56cwsp7ffppl4wxeq7osqfuu 185 20 rule rule NN work_ln56cwsp7ffppl4wxeq7osqfuu 185 21 emerges emerge VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 185 22 as as IN work_ln56cwsp7ffppl4wxeq7osqfuu 185 23 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 185 24 maximum maximum JJ work_ln56cwsp7ffppl4wxeq7osqfuu 185 25 optimal optimal NN work_ln56cwsp7ffppl4wxeq7osqfuu 185 26 : : : work_ln56cwsp7ffppl4wxeq7osqfuu 185 27 Borda Borda NNP work_ln56cwsp7ffppl4wxeq7osqfuu 185 28 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 186 1 The the DT work_ln56cwsp7ffppl4wxeq7osqfuu 186 2 intuition intuition NN work_ln56cwsp7ffppl4wxeq7osqfuu 186 3 goes go VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 186 4 as as IN work_ln56cwsp7ffppl4wxeq7osqfuu 186 5 follows follow VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 186 6 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 187 1 The the DT work_ln56cwsp7ffppl4wxeq7osqfuu 187 2 jumps jump NNS work_ln56cwsp7ffppl4wxeq7osqfuu 187 3 in in IN work_ln56cwsp7ffppl4wxeq7osqfuu 187 4 strength strength NN work_ln56cwsp7ffppl4wxeq7osqfuu 187 5 that that WDT work_ln56cwsp7ffppl4wxeq7osqfuu 187 6 Borda Borda NNP work_ln56cwsp7ffppl4wxeq7osqfuu 187 7 assigns assign VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 187 8 to to IN work_ln56cwsp7ffppl4wxeq7osqfuu 187 9 consecutive consecutive JJ work_ln56cwsp7ffppl4wxeq7osqfuu 187 10 order order NN work_ln56cwsp7ffppl4wxeq7osqfuu 187 11 statistics statistic NNS work_ln56cwsp7ffppl4wxeq7osqfuu 187 12 are be VBP work_ln56cwsp7ffppl4wxeq7osqfuu 187 13 constant constant JJ work_ln56cwsp7ffppl4wxeq7osqfuu 187 14 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 188 1 Hence hence RB work_ln56cwsp7ffppl4wxeq7osqfuu 188 2 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 188 3 cultures culture NNS work_ln56cwsp7ffppl4wxeq7osqfuu 188 4 in in IN work_ln56cwsp7ffppl4wxeq7osqfuu 188 5 which which WDT work_ln56cwsp7ffppl4wxeq7osqfuu 188 6 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 188 7 expected expect VBN work_ln56cwsp7ffppl4wxeq7osqfuu 188 8 value value NN work_ln56cwsp7ffppl4wxeq7osqfuu 188 9 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 188 10 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 188 11 order order NN work_ln56cwsp7ffppl4wxeq7osqfuu 188 12 statistics statistic NNS work_ln56cwsp7ffppl4wxeq7osqfuu 188 13 has have VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 188 14 this this DT work_ln56cwsp7ffppl4wxeq7osqfuu 188 15 property property NN work_ln56cwsp7ffppl4wxeq7osqfuu 188 16 are be VBP work_ln56cwsp7ffppl4wxeq7osqfuu 188 17 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 188 18 most most RBS work_ln56cwsp7ffppl4wxeq7osqfuu 188 19 closely closely RB work_ln56cwsp7ffppl4wxeq7osqfuu 188 20 linked link VBN work_ln56cwsp7ffppl4wxeq7osqfuu 188 21 to to IN work_ln56cwsp7ffppl4wxeq7osqfuu 188 22 Borda Borda NNP work_ln56cwsp7ffppl4wxeq7osqfuu 188 23 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 189 1 Also also RB work_ln56cwsp7ffppl4wxeq7osqfuu 189 2 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 189 3 when when WRB work_ln56cwsp7ffppl4wxeq7osqfuu 189 4 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 189 5 culture culture NN work_ln56cwsp7ffppl4wxeq7osqfuu 189 6 follows follow VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 189 7 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 189 8 normal normal JJ work_ln56cwsp7ffppl4wxeq7osqfuu 189 9 distribution distribution NN work_ln56cwsp7ffppl4wxeq7osqfuu 189 10 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 189 11 we -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 189 12 show show VBP work_ln56cwsp7ffppl4wxeq7osqfuu 189 13 that that IN work_ln56cwsp7ffppl4wxeq7osqfuu 189 14 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 189 15 optimal optimal JJ work_ln56cwsp7ffppl4wxeq7osqfuu 189 16 decision decision NN work_ln56cwsp7ffppl4wxeq7osqfuu 189 17 rule rule NN work_ln56cwsp7ffppl4wxeq7osqfuu 189 18 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 189 19 a a DT work_ln56cwsp7ffppl4wxeq7osqfuu 189 20 scoring score VBG work_ln56cwsp7ffppl4wxeq7osqfuu 189 21 rule rule NN work_ln56cwsp7ffppl4wxeq7osqfuu 189 22 where where WRB work_ln56cwsp7ffppl4wxeq7osqfuu 189 23 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 189 24 differences difference NNS work_ln56cwsp7ffppl4wxeq7osqfuu 189 25 in in IN work_ln56cwsp7ffppl4wxeq7osqfuu 189 26 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 189 27 values value NNS work_ln56cwsp7ffppl4wxeq7osqfuu 189 28 given give VBN work_ln56cwsp7ffppl4wxeq7osqfuu 189 29 to to IN work_ln56cwsp7ffppl4wxeq7osqfuu 189 30 consecutive consecutive JJ work_ln56cwsp7ffppl4wxeq7osqfuu 189 31 alternatives alternative NNS work_ln56cwsp7ffppl4wxeq7osqfuu 189 32 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 189 33 a a DT work_ln56cwsp7ffppl4wxeq7osqfuu 189 34 symmetric symmetric JJ work_ln56cwsp7ffppl4wxeq7osqfuu 189 35 convex convex NNP work_ln56cwsp7ffppl4wxeq7osqfuu 189 36 func- func- NNP work_ln56cwsp7ffppl4wxeq7osqfuu 189 37 tion tion NNP work_ln56cwsp7ffppl4wxeq7osqfuu 189 38 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 190 1 That that RB work_ln56cwsp7ffppl4wxeq7osqfuu 190 2 is is RB work_ln56cwsp7ffppl4wxeq7osqfuu 190 3 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 190 4 under under IN work_ln56cwsp7ffppl4wxeq7osqfuu 190 5 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 190 6 normal normal JJ work_ln56cwsp7ffppl4wxeq7osqfuu 190 7 distribution distribution NN work_ln56cwsp7ffppl4wxeq7osqfuu 190 8 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 190 9 it -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 190 10 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 190 11 optimal optimal JJ work_ln56cwsp7ffppl4wxeq7osqfuu 190 12 to to TO work_ln56cwsp7ffppl4wxeq7osqfuu 190 13 discriminate discriminate VB work_ln56cwsp7ffppl4wxeq7osqfuu 190 14 between between IN work_ln56cwsp7ffppl4wxeq7osqfuu 190 15 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 190 16 very very RB work_ln56cwsp7ffppl4wxeq7osqfuu 190 17 best good JJS work_ln56cwsp7ffppl4wxeq7osqfuu 190 18 alternatives alternative NNS work_ln56cwsp7ffppl4wxeq7osqfuu 190 19 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 190 20 also also RB work_ln56cwsp7ffppl4wxeq7osqfuu 190 21 between between IN work_ln56cwsp7ffppl4wxeq7osqfuu 190 22 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 190 23 very very RB work_ln56cwsp7ffppl4wxeq7osqfuu 190 24 worst bad JJS work_ln56cwsp7ffppl4wxeq7osqfuu 190 25 alternatives alternative NNS work_ln56cwsp7ffppl4wxeq7osqfuu 190 26 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 190 27 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 190 28 less less RBR work_ln56cwsp7ffppl4wxeq7osqfuu 190 29 impor- impor- JJ work_ln56cwsp7ffppl4wxeq7osqfuu 190 30 tant tant NN work_ln56cwsp7ffppl4wxeq7osqfuu 190 31 to to TO work_ln56cwsp7ffppl4wxeq7osqfuu 190 32 discriminate discriminate VB work_ln56cwsp7ffppl4wxeq7osqfuu 190 33 between between IN work_ln56cwsp7ffppl4wxeq7osqfuu 190 34 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 190 35 intermediate intermediate JJ work_ln56cwsp7ffppl4wxeq7osqfuu 190 36 alternatives alternative NNS work_ln56cwsp7ffppl4wxeq7osqfuu 190 37 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 191 1 Interestingly interestingly RB work_ln56cwsp7ffppl4wxeq7osqfuu 191 2 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 191 3 when when WRB work_ln56cwsp7ffppl4wxeq7osqfuu 191 4 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 191 5 culture culture NN work_ln56cwsp7ffppl4wxeq7osqfuu 191 6 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 191 7 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 191 8 society society NN work_ln56cwsp7ffppl4wxeq7osqfuu 191 9 follows follow VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 191 10 a a DT work_ln56cwsp7ffppl4wxeq7osqfuu 191 11 Cauchy Cauchy NNP work_ln56cwsp7ffppl4wxeq7osqfuu 191 12 distribution distribution NN work_ln56cwsp7ffppl4wxeq7osqfuu 191 13 then then RB work_ln56cwsp7ffppl4wxeq7osqfuu 191 14 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 191 15 pattern pattern NN work_ln56cwsp7ffppl4wxeq7osqfuu 191 16 becomes become VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 191 17 even even RB work_ln56cwsp7ffppl4wxeq7osqfuu 191 18 more more RBR work_ln56cwsp7ffppl4wxeq7osqfuu 191 19 pronounced pronounced JJ work_ln56cwsp7ffppl4wxeq7osqfuu 191 20 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 192 1 In in IN work_ln56cwsp7ffppl4wxeq7osqfuu 192 2 this this DT work_ln56cwsp7ffppl4wxeq7osqfuu 192 3 case case NN work_ln56cwsp7ffppl4wxeq7osqfuu 192 4 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 192 5 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 192 6 optimal optimal JJ work_ln56cwsp7ffppl4wxeq7osqfuu 192 7 scoring score VBG work_ln56cwsp7ffppl4wxeq7osqfuu 192 8 rule rule NN work_ln56cwsp7ffppl4wxeq7osqfuu 192 9 tends tend VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 192 10 to to TO work_ln56cwsp7ffppl4wxeq7osqfuu 192 11 discriminate discriminate VB work_ln56cwsp7ffppl4wxeq7osqfuu 192 12 be- be- XX work_ln56cwsp7ffppl4wxeq7osqfuu 192 13 tween tween NN work_ln56cwsp7ffppl4wxeq7osqfuu 192 14 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 192 15 very very RB work_ln56cwsp7ffppl4wxeq7osqfuu 192 16 best good JJS work_ln56cwsp7ffppl4wxeq7osqfuu 192 17 alternative alternative NN work_ln56cwsp7ffppl4wxeq7osqfuu 192 18 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 192 19 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 192 20 very very RB work_ln56cwsp7ffppl4wxeq7osqfuu 192 21 worst bad JJS work_ln56cwsp7ffppl4wxeq7osqfuu 192 22 alternative alternative NN work_ln56cwsp7ffppl4wxeq7osqfuu 192 23 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 192 24 treating treat VBG work_ln56cwsp7ffppl4wxeq7osqfuu 192 25 all all DT work_ln56cwsp7ffppl4wxeq7osqfuu 192 26 remaining remain VBG work_ln56cwsp7ffppl4wxeq7osqfuu 192 27 alternatives alternative NNS work_ln56cwsp7ffppl4wxeq7osqfuu 192 28 in in IN work_ln56cwsp7ffppl4wxeq7osqfuu 192 29 almost almost RB work_ln56cwsp7ffppl4wxeq7osqfuu 192 30 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 192 31 same same JJ work_ln56cwsp7ffppl4wxeq7osqfuu 192 32 manner manner NN work_ln56cwsp7ffppl4wxeq7osqfuu 192 33 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 193 1 We -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 193 2 then then RB work_ln56cwsp7ffppl4wxeq7osqfuu 193 3 turn turn VBP work_ln56cwsp7ffppl4wxeq7osqfuu 193 4 to to IN work_ln56cwsp7ffppl4wxeq7osqfuu 193 5 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 193 6 analysis analysis NN work_ln56cwsp7ffppl4wxeq7osqfuu 193 7 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 193 8 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 193 9 β- β- XX work_ln56cwsp7ffppl4wxeq7osqfuu 193 10 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 193 11 γ γ NNPS work_ln56cwsp7ffppl4wxeq7osqfuu 193 12 - - HYPH work_ln56cwsp7ffppl4wxeq7osqfuu 193 13 indices index NNS work_ln56cwsp7ffppl4wxeq7osqfuu 193 14 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 194 1 The the DT work_ln56cwsp7ffppl4wxeq7osqfuu 194 2 β β NNP work_ln56cwsp7ffppl4wxeq7osqfuu 194 3 - - HYPH work_ln56cwsp7ffppl4wxeq7osqfuu 194 4 index index NNP work_ln56cwsp7ffppl4wxeq7osqfuu 194 5 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 194 6 as as RB work_ln56cwsp7ffppl4wxeq7osqfuu 194 7 well well RB work_ln56cwsp7ffppl4wxeq7osqfuu 194 8 as as IN work_ln56cwsp7ffppl4wxeq7osqfuu 194 9 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 194 10 γ γ NN work_ln56cwsp7ffppl4wxeq7osqfuu 194 11 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 194 12 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 194 13 less less RBR work_ln56cwsp7ffppl4wxeq7osqfuu 194 14 well well RB work_ln56cwsp7ffppl4wxeq7osqfuu 194 15 suited suited JJ work_ln56cwsp7ffppl4wxeq7osqfuu 194 16 than than IN work_ln56cwsp7ffppl4wxeq7osqfuu 194 17 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 194 18 α α NNP work_ln56cwsp7ffppl4wxeq7osqfuu 194 19 - - HYPH work_ln56cwsp7ffppl4wxeq7osqfuu 194 20 index index NN work_ln56cwsp7ffppl4wxeq7osqfuu 194 21 to to IN work_ln56cwsp7ffppl4wxeq7osqfuu 194 22 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 194 23 analytical analytical JJ work_ln56cwsp7ffppl4wxeq7osqfuu 194 24 study study NN work_ln56cwsp7ffppl4wxeq7osqfuu 194 25 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 194 26 utilitarianism utilitarianism NN work_ln56cwsp7ffppl4wxeq7osqfuu 194 27 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 195 1 The the DT work_ln56cwsp7ffppl4wxeq7osqfuu 195 2 source source NN work_ln56cwsp7ffppl4wxeq7osqfuu 195 3 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 195 4 difficulty difficulty NN work_ln56cwsp7ffppl4wxeq7osqfuu 195 5 lies lie VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 195 6 in in IN work_ln56cwsp7ffppl4wxeq7osqfuu 195 7 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 195 8 dependency dependency NN work_ln56cwsp7ffppl4wxeq7osqfuu 195 9 across across IN work_ln56cwsp7ffppl4wxeq7osqfuu 195 10 alternatives alternative NNS work_ln56cwsp7ffppl4wxeq7osqfuu 195 11 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 196 1 To to TO work_ln56cwsp7ffppl4wxeq7osqfuu 196 2 determine determine VB work_ln56cwsp7ffppl4wxeq7osqfuu 196 3 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 196 4 probability probability NN work_ln56cwsp7ffppl4wxeq7osqfuu 196 5 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 196 6 an an DT work_ln56cwsp7ffppl4wxeq7osqfuu 196 7 alternative alternative NN work_ln56cwsp7ffppl4wxeq7osqfuu 196 8 being be VBG work_ln56cwsp7ffppl4wxeq7osqfuu 196 9 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 196 10 utilitarian utilitarian JJ work_ln56cwsp7ffppl4wxeq7osqfuu 196 11 alternative alternative NN work_ln56cwsp7ffppl4wxeq7osqfuu 196 12 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 196 13 it -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 196 14 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 196 15 necessary necessary JJ work_ln56cwsp7ffppl4wxeq7osqfuu 196 16 to to TO work_ln56cwsp7ffppl4wxeq7osqfuu 196 17 take take VB work_ln56cwsp7ffppl4wxeq7osqfuu 196 18 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 196 19 whole whole JJ work_ln56cwsp7ffppl4wxeq7osqfuu 196 20 society society NN work_ln56cwsp7ffppl4wxeq7osqfuu 196 21 into into IN work_ln56cwsp7ffppl4wxeq7osqfuu 196 22 account account NN work_ln56cwsp7ffppl4wxeq7osqfuu 196 23 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 197 1 This this DT work_ln56cwsp7ffppl4wxeq7osqfuu 197 2 dependency dependency NN work_ln56cwsp7ffppl4wxeq7osqfuu 197 3 drastically drastically RB work_ln56cwsp7ffppl4wxeq7osqfuu 197 4 limits limit VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 197 5 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 197 6 analytical analytical JJ work_ln56cwsp7ffppl4wxeq7osqfuu 197 7 tractability tractability NN work_ln56cwsp7ffppl4wxeq7osqfuu 197 8 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 197 9 utilitarianism utilitarianism NN work_ln56cwsp7ffppl4wxeq7osqfuu 197 10 in in IN work_ln56cwsp7ffppl4wxeq7osqfuu 197 11 terms term NNS work_ln56cwsp7ffppl4wxeq7osqfuu 197 12 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 197 13 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 197 14 β β NNP work_ln56cwsp7ffppl4wxeq7osqfuu 197 15 - - HYPH work_ln56cwsp7ffppl4wxeq7osqfuu 197 16 index index NN work_ln56cwsp7ffppl4wxeq7osqfuu 197 17 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 198 1 For for IN work_ln56cwsp7ffppl4wxeq7osqfuu 198 2 this this DT work_ln56cwsp7ffppl4wxeq7osqfuu 198 3 reason reason NN work_ln56cwsp7ffppl4wxeq7osqfuu 198 4 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 198 5 we -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 198 6 begin begin VBP work_ln56cwsp7ffppl4wxeq7osqfuu 198 7 with with IN work_ln56cwsp7ffppl4wxeq7osqfuu 198 8 9 9 CD work_ln56cwsp7ffppl4wxeq7osqfuu 198 9 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 198 10 formal formal JJ work_ln56cwsp7ffppl4wxeq7osqfuu 198 11 study study NN work_ln56cwsp7ffppl4wxeq7osqfuu 198 12 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 198 13 a a DT work_ln56cwsp7ffppl4wxeq7osqfuu 198 14 small small JJ work_ln56cwsp7ffppl4wxeq7osqfuu 198 15 society society NN work_ln56cwsp7ffppl4wxeq7osqfuu 198 16 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 198 17 a a DT work_ln56cwsp7ffppl4wxeq7osqfuu 198 18 2×3 2×3 CD work_ln56cwsp7ffppl4wxeq7osqfuu 198 19 society society NN work_ln56cwsp7ffppl4wxeq7osqfuu 198 20 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 198 21 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 198 22 a a DT work_ln56cwsp7ffppl4wxeq7osqfuu 198 23 complete complete JJ work_ln56cwsp7ffppl4wxeq7osqfuu 198 24 range range NN work_ln56cwsp7ffppl4wxeq7osqfuu 198 25 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 198 26 cultures culture NNS work_ln56cwsp7ffppl4wxeq7osqfuu 198 27 with with IN work_ln56cwsp7ffppl4wxeq7osqfuu 198 28 symmetric symmetric JJ work_ln56cwsp7ffppl4wxeq7osqfuu 198 29 density density NN work_ln56cwsp7ffppl4wxeq7osqfuu 198 30 functions function NNS work_ln56cwsp7ffppl4wxeq7osqfuu 198 31 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 198 32 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 198 33 then then RB work_ln56cwsp7ffppl4wxeq7osqfuu 198 34 we -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 198 35 run run VBP work_ln56cwsp7ffppl4wxeq7osqfuu 198 36 a a DT work_ln56cwsp7ffppl4wxeq7osqfuu 198 37 set set NN work_ln56cwsp7ffppl4wxeq7osqfuu 198 38 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 198 39 simulations simulation NNS work_ln56cwsp7ffppl4wxeq7osqfuu 198 40 to to TO work_ln56cwsp7ffppl4wxeq7osqfuu 198 41 approach approach VB work_ln56cwsp7ffppl4wxeq7osqfuu 198 42 larger large JJR work_ln56cwsp7ffppl4wxeq7osqfuu 198 43 societies society NNS work_ln56cwsp7ffppl4wxeq7osqfuu 198 44 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 199 1 Our -PRON- PRP$ work_ln56cwsp7ffppl4wxeq7osqfuu 199 2 analytical analytical JJ work_ln56cwsp7ffppl4wxeq7osqfuu 199 3 results result NNS work_ln56cwsp7ffppl4wxeq7osqfuu 199 4 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 199 5 small small JJ work_ln56cwsp7ffppl4wxeq7osqfuu 199 6 societies society NNS work_ln56cwsp7ffppl4wxeq7osqfuu 199 7 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 199 8 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 199 9 computational computational JJ work_ln56cwsp7ffppl4wxeq7osqfuu 199 10 analysis analysis NN work_ln56cwsp7ffppl4wxeq7osqfuu 199 11 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 199 12 larger large JJR work_ln56cwsp7ffppl4wxeq7osqfuu 199 13 societies society NNS work_ln56cwsp7ffppl4wxeq7osqfuu 199 14 provide provide VBP work_ln56cwsp7ffppl4wxeq7osqfuu 199 15 analogous analogous JJ work_ln56cwsp7ffppl4wxeq7osqfuu 199 16 results result NNS work_ln56cwsp7ffppl4wxeq7osqfuu 199 17 as as IN work_ln56cwsp7ffppl4wxeq7osqfuu 199 18 those those DT work_ln56cwsp7ffppl4wxeq7osqfuu 199 19 obtained obtain VBN work_ln56cwsp7ffppl4wxeq7osqfuu 199 20 in in IN work_ln56cwsp7ffppl4wxeq7osqfuu 199 21 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 199 22 formal formal JJ work_ln56cwsp7ffppl4wxeq7osqfuu 199 23 study study NN work_ln56cwsp7ffppl4wxeq7osqfuu 199 24 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 199 25 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 199 26 α α NNP work_ln56cwsp7ffppl4wxeq7osqfuu 199 27 - - NN work_ln56cwsp7ffppl4wxeq7osqfuu 199 28 index index NN work_ln56cwsp7ffppl4wxeq7osqfuu 199 29 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 200 1 This this DT work_ln56cwsp7ffppl4wxeq7osqfuu 200 2 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 200 3 reassuring reassure VBG work_ln56cwsp7ffppl4wxeq7osqfuu 200 4 since since IN work_ln56cwsp7ffppl4wxeq7osqfuu 200 5 it -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 200 6 indicates indicate VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 200 7 that that IN work_ln56cwsp7ffppl4wxeq7osqfuu 200 8 there there EX work_ln56cwsp7ffppl4wxeq7osqfuu 200 9 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 200 10 a a DT work_ln56cwsp7ffppl4wxeq7osqfuu 200 11 great great JJ work_ln56cwsp7ffppl4wxeq7osqfuu 200 12 deal deal NN work_ln56cwsp7ffppl4wxeq7osqfuu 200 13 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 200 14 consistency consistency NN work_ln56cwsp7ffppl4wxeq7osqfuu 200 15 across across IN work_ln56cwsp7ffppl4wxeq7osqfuu 200 16 indices index NNS work_ln56cwsp7ffppl4wxeq7osqfuu 200 17 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 201 1 What what WP work_ln56cwsp7ffppl4wxeq7osqfuu 201 2 matters matter VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 201 3 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 201 4 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 201 5 social social JJ work_ln56cwsp7ffppl4wxeq7osqfuu 201 6 welfare welfare NN work_ln56cwsp7ffppl4wxeq7osqfuu 201 7 function function NN work_ln56cwsp7ffppl4wxeq7osqfuu 201 8 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 201 9 not not RB work_ln56cwsp7ffppl4wxeq7osqfuu 201 10 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 201 11 particular particular JJ work_ln56cwsp7ffppl4wxeq7osqfuu 201 12 way way NN work_ln56cwsp7ffppl4wxeq7osqfuu 201 13 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 201 14 measuring measure VBG work_ln56cwsp7ffppl4wxeq7osqfuu 201 15 success success NN work_ln56cwsp7ffppl4wxeq7osqfuu 201 16 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 202 1 Finally finally RB work_ln56cwsp7ffppl4wxeq7osqfuu 202 2 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 202 3 our -PRON- PRP$ work_ln56cwsp7ffppl4wxeq7osqfuu 202 4 analysis analysis NN work_ln56cwsp7ffppl4wxeq7osqfuu 202 5 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 202 6 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 202 7 γ γ NNP work_ln56cwsp7ffppl4wxeq7osqfuu 202 8 - - HYPH work_ln56cwsp7ffppl4wxeq7osqfuu 202 9 index index NN work_ln56cwsp7ffppl4wxeq7osqfuu 202 10 exploits exploit VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 202 11 a a DT work_ln56cwsp7ffppl4wxeq7osqfuu 202 12 symmetry symmetry NN work_ln56cwsp7ffppl4wxeq7osqfuu 202 13 relation relation NN work_ln56cwsp7ffppl4wxeq7osqfuu 202 14 with with IN work_ln56cwsp7ffppl4wxeq7osqfuu 202 15 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 202 16 β β NNP work_ln56cwsp7ffppl4wxeq7osqfuu 202 17 - - HYPH work_ln56cwsp7ffppl4wxeq7osqfuu 202 18 index index NN work_ln56cwsp7ffppl4wxeq7osqfuu 202 19 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 202 20 allowing allow VBG work_ln56cwsp7ffppl4wxeq7osqfuu 202 21 us -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 202 22 to to TO work_ln56cwsp7ffppl4wxeq7osqfuu 202 23 immediately immediately RB work_ln56cwsp7ffppl4wxeq7osqfuu 202 24 reach reach VB work_ln56cwsp7ffppl4wxeq7osqfuu 202 25 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 202 26 same same JJ work_ln56cwsp7ffppl4wxeq7osqfuu 202 27 conclusions conclusion NNS work_ln56cwsp7ffppl4wxeq7osqfuu 202 28 as as IN work_ln56cwsp7ffppl4wxeq7osqfuu 202 29 those those DT work_ln56cwsp7ffppl4wxeq7osqfuu 202 30 reached reach VBN work_ln56cwsp7ffppl4wxeq7osqfuu 202 31 with with IN work_ln56cwsp7ffppl4wxeq7osqfuu 202 32 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 202 33 β β NN work_ln56cwsp7ffppl4wxeq7osqfuu 202 34 - - HYPH work_ln56cwsp7ffppl4wxeq7osqfuu 202 35 index index NN work_ln56cwsp7ffppl4wxeq7osqfuu 202 36 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 203 1 We -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 203 2 organize organize VBP work_ln56cwsp7ffppl4wxeq7osqfuu 203 3 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 203 4 study study NN work_ln56cwsp7ffppl4wxeq7osqfuu 203 5 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 203 6 utilitarianism utilitarianism NN work_ln56cwsp7ffppl4wxeq7osqfuu 203 7 by by IN work_ln56cwsp7ffppl4wxeq7osqfuu 203 8 first first RB work_ln56cwsp7ffppl4wxeq7osqfuu 203 9 giving give VBG work_ln56cwsp7ffppl4wxeq7osqfuu 203 10 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 203 11 general general JJ work_ln56cwsp7ffppl4wxeq7osqfuu 203 12 results result NNS work_ln56cwsp7ffppl4wxeq7osqfuu 203 13 obtained obtain VBN work_ln56cwsp7ffppl4wxeq7osqfuu 203 14 with with IN work_ln56cwsp7ffppl4wxeq7osqfuu 203 15 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 203 16 α α NNP work_ln56cwsp7ffppl4wxeq7osqfuu 203 17 - - HYPH work_ln56cwsp7ffppl4wxeq7osqfuu 203 18 index index NN work_ln56cwsp7ffppl4wxeq7osqfuu 203 19 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 203 20 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 203 21 we -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 203 22 then then RB work_ln56cwsp7ffppl4wxeq7osqfuu 203 23 turn turn VBP work_ln56cwsp7ffppl4wxeq7osqfuu 203 24 to to IN work_ln56cwsp7ffppl4wxeq7osqfuu 203 25 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 203 26 study study NN work_ln56cwsp7ffppl4wxeq7osqfuu 203 27 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 203 28 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 203 29 β- β- XX work_ln56cwsp7ffppl4wxeq7osqfuu 203 30 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 203 31 γ γ NNPS work_ln56cwsp7ffppl4wxeq7osqfuu 203 32 - - HYPH work_ln56cwsp7ffppl4wxeq7osqfuu 203 33 indices index NNS work_ln56cwsp7ffppl4wxeq7osqfuu 203 34 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 204 1 3.1 3.1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 204 2 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 205 1 The the DT work_ln56cwsp7ffppl4wxeq7osqfuu 205 2 αUT αut NN work_ln56cwsp7ffppl4wxeq7osqfuu 205 3 -index -index NNP work_ln56cwsp7ffppl4wxeq7osqfuu 205 4 : : : work_ln56cwsp7ffppl4wxeq7osqfuu 205 5 Evaluating evaluate VBG work_ln56cwsp7ffppl4wxeq7osqfuu 205 6 Decision Decision NNP work_ln56cwsp7ffppl4wxeq7osqfuu 205 7 Rules rule NNS work_ln56cwsp7ffppl4wxeq7osqfuu 205 8 in in IN work_ln56cwsp7ffppl4wxeq7osqfuu 205 9 terms term NNS work_ln56cwsp7ffppl4wxeq7osqfuu 205 10 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 205 11 Expected expected JJ work_ln56cwsp7ffppl4wxeq7osqfuu 205 12 Value Value NNP work_ln56cwsp7ffppl4wxeq7osqfuu 205 13 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 206 1 Theorem theorem NN work_ln56cwsp7ffppl4wxeq7osqfuu 206 2 3.1 3.1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 206 3 below below RB work_ln56cwsp7ffppl4wxeq7osqfuu 206 4 provides provide VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 206 5 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 206 6 main main JJ work_ln56cwsp7ffppl4wxeq7osqfuu 206 7 result result NN work_ln56cwsp7ffppl4wxeq7osqfuu 206 8 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 206 9 utilitarianism utilitarianism NN work_ln56cwsp7ffppl4wxeq7osqfuu 206 10 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 207 1 It -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 207 2 first first RB work_ln56cwsp7ffppl4wxeq7osqfuu 207 3 identifies identify VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 207 4 a a DT work_ln56cwsp7ffppl4wxeq7osqfuu 207 5 scor- scor- JJ work_ln56cwsp7ffppl4wxeq7osqfuu 207 6 ing ing NN work_ln56cwsp7ffppl4wxeq7osqfuu 207 7 rule rule NN work_ln56cwsp7ffppl4wxeq7osqfuu 207 8 as as IN work_ln56cwsp7ffppl4wxeq7osqfuu 207 9 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 207 10 maximum maximum JJ work_ln56cwsp7ffppl4wxeq7osqfuu 207 11 optimal optimal JJ work_ln56cwsp7ffppl4wxeq7osqfuu 207 12 decision decision NN work_ln56cwsp7ffppl4wxeq7osqfuu 207 13 rule rule NN work_ln56cwsp7ffppl4wxeq7osqfuu 207 14 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 207 15 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 207 16 then then RB work_ln56cwsp7ffppl4wxeq7osqfuu 207 17 it -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 207 18 characterizes characterize VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 207 19 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 207 20 exact exact JJ work_ln56cwsp7ffppl4wxeq7osqfuu 207 21 shape shape NN work_ln56cwsp7ffppl4wxeq7osqfuu 207 22 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 207 23 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 207 24 scoring score VBG work_ln56cwsp7ffppl4wxeq7osqfuu 207 25 rule rule NN work_ln56cwsp7ffppl4wxeq7osqfuu 207 26 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 208 1 Importantly importantly RB work_ln56cwsp7ffppl4wxeq7osqfuu 208 2 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 208 3 it -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 208 4 does do VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 208 5 so so RB work_ln56cwsp7ffppl4wxeq7osqfuu 208 6 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 208 7 any any DT work_ln56cwsp7ffppl4wxeq7osqfuu 208 8 n n NNP work_ln56cwsp7ffppl4wxeq7osqfuu 208 9 × × NN work_ln56cwsp7ffppl4wxeq7osqfuu 208 10 k k NN work_ln56cwsp7ffppl4wxeq7osqfuu 208 11 society society NN work_ln56cwsp7ffppl4wxeq7osqfuu 208 12 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 208 13 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 208 14 any any DT work_ln56cwsp7ffppl4wxeq7osqfuu 208 15 culture culture NN work_ln56cwsp7ffppl4wxeq7osqfuu 208 16 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 209 1 Theorem theorem NN work_ln56cwsp7ffppl4wxeq7osqfuu 209 2 3.1 3.1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 209 3 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 210 1 For for IN work_ln56cwsp7ffppl4wxeq7osqfuu 210 2 n×k n×k JJ work_ln56cwsp7ffppl4wxeq7osqfuu 210 3 societies society NNS work_ln56cwsp7ffppl4wxeq7osqfuu 210 4 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 210 5 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 210 6 every every DT work_ln56cwsp7ffppl4wxeq7osqfuu 210 7 culture culture NN work_ln56cwsp7ffppl4wxeq7osqfuu 210 8 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 210 9 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 210 10 maximum maximum JJ work_ln56cwsp7ffppl4wxeq7osqfuu 210 11 αUT αut CD work_ln56cwsp7ffppl4wxeq7osqfuu 210 12 -optimal -optimal JJ work_ln56cwsp7ffppl4wxeq7osqfuu 210 13 rule rule NN work_ln56cwsp7ffppl4wxeq7osqfuu 210 14 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 210 15 a a DT work_ln56cwsp7ffppl4wxeq7osqfuu 210 16 scoring score VBG work_ln56cwsp7ffppl4wxeq7osqfuu 210 17 rule rule NN work_ln56cwsp7ffppl4wxeq7osqfuu 210 18 with with IN work_ln56cwsp7ffppl4wxeq7osqfuu 210 19 S∗l S∗l HYPH work_ln56cwsp7ffppl4wxeq7osqfuu 210 20 = = SYM work_ln56cwsp7ffppl4wxeq7osqfuu 210 21 E[U(l)]−E[U(1 e[u(l)]−e[u(1 ADD work_ln56cwsp7ffppl4wxeq7osqfuu 210 22 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 210 23 ] ] -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 210 24 E[U(k)]−E[U(1 E[U(k)]−E[U(1 NNP work_ln56cwsp7ffppl4wxeq7osqfuu 210 25 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 210 26 ] ] -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 210 27 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 210 28 l l NN work_ln56cwsp7ffppl4wxeq7osqfuu 210 29 ∈{1 ∈{1 NNP work_ln56cwsp7ffppl4wxeq7osqfuu 210 30 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 210 31 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 211 1 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 212 1 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 213 1 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 213 2 k k NNP work_ln56cwsp7ffppl4wxeq7osqfuu 213 3 } } -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 213 4 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 214 1 Theorem theorem NN work_ln56cwsp7ffppl4wxeq7osqfuu 214 2 3.1 3.1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 214 3 shows show VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 214 4 that that IN work_ln56cwsp7ffppl4wxeq7osqfuu 214 5 there there EX work_ln56cwsp7ffppl4wxeq7osqfuu 214 6 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 214 7 a a DT work_ln56cwsp7ffppl4wxeq7osqfuu 214 8 mapping mapping NN work_ln56cwsp7ffppl4wxeq7osqfuu 214 9 from from IN work_ln56cwsp7ffppl4wxeq7osqfuu 214 10 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 214 11 culture culture NN work_ln56cwsp7ffppl4wxeq7osqfuu 214 12 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 214 13 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 214 14 society society NN work_ln56cwsp7ffppl4wxeq7osqfuu 214 15 to to IN work_ln56cwsp7ffppl4wxeq7osqfuu 214 16 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 214 17 optimal optimal JJ work_ln56cwsp7ffppl4wxeq7osqfuu 214 18 decision decision NN work_ln56cwsp7ffppl4wxeq7osqfuu 214 19 rule rule NN work_ln56cwsp7ffppl4wxeq7osqfuu 214 20 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 215 1 A a DT work_ln56cwsp7ffppl4wxeq7osqfuu 215 2 culture culture NN work_ln56cwsp7ffppl4wxeq7osqfuu 215 3 determines determine VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 215 4 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 215 5 first first JJ work_ln56cwsp7ffppl4wxeq7osqfuu 215 6 moment moment NN work_ln56cwsp7ffppl4wxeq7osqfuu 215 7 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 215 8 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 215 9 order order NN work_ln56cwsp7ffppl4wxeq7osqfuu 215 10 statistics statistic NNS work_ln56cwsp7ffppl4wxeq7osqfuu 215 11 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 215 12 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 215 13 this this DT work_ln56cwsp7ffppl4wxeq7osqfuu 215 14 in in IN work_ln56cwsp7ffppl4wxeq7osqfuu 215 15 turn turn NN work_ln56cwsp7ffppl4wxeq7osqfuu 215 16 characterizes characterize VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 215 17 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 215 18 optimal optimal JJ work_ln56cwsp7ffppl4wxeq7osqfuu 215 19 decision decision NN work_ln56cwsp7ffppl4wxeq7osqfuu 215 20 rule rule NN work_ln56cwsp7ffppl4wxeq7osqfuu 215 21 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 216 1 This this DT work_ln56cwsp7ffppl4wxeq7osqfuu 216 2 raises raise VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 216 3 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 216 4 question question NN work_ln56cwsp7ffppl4wxeq7osqfuu 216 5 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 216 6 what what WP work_ln56cwsp7ffppl4wxeq7osqfuu 216 7 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 216 8 optimal optimal JJ work_ln56cwsp7ffppl4wxeq7osqfuu 216 9 decision decision NN work_ln56cwsp7ffppl4wxeq7osqfuu 216 10 rules rule NNS work_ln56cwsp7ffppl4wxeq7osqfuu 216 11 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 216 12 especially especially RB work_ln56cwsp7ffppl4wxeq7osqfuu 216 13 prominent prominent JJ work_ln56cwsp7ffppl4wxeq7osqfuu 216 14 cultures culture NNS work_ln56cwsp7ffppl4wxeq7osqfuu 216 15 are be VBP work_ln56cwsp7ffppl4wxeq7osqfuu 216 16 like like IN work_ln56cwsp7ffppl4wxeq7osqfuu 216 17 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 217 1 The the DT work_ln56cwsp7ffppl4wxeq7osqfuu 217 2 follow- follow- JJ work_ln56cwsp7ffppl4wxeq7osqfuu 217 3 ing ing NNP work_ln56cwsp7ffppl4wxeq7osqfuu 217 4 corollary corollary NN work_ln56cwsp7ffppl4wxeq7osqfuu 217 5 represents represent VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 217 6 a a DT work_ln56cwsp7ffppl4wxeq7osqfuu 217 7 first first JJ work_ln56cwsp7ffppl4wxeq7osqfuu 217 8 illustration illustration NN work_ln56cwsp7ffppl4wxeq7osqfuu 217 9 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 218 1 Corollary Corollary NNP work_ln56cwsp7ffppl4wxeq7osqfuu 218 2 3.2 3.2 CD work_ln56cwsp7ffppl4wxeq7osqfuu 218 3 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 219 1 The the DT work_ln56cwsp7ffppl4wxeq7osqfuu 219 2 maximum maximum JJ work_ln56cwsp7ffppl4wxeq7osqfuu 219 3 αUT αut CD work_ln56cwsp7ffppl4wxeq7osqfuu 219 4 -optimal -optimal JJ work_ln56cwsp7ffppl4wxeq7osqfuu 219 5 rule rule NN work_ln56cwsp7ffppl4wxeq7osqfuu 219 6 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 219 7 Borda Borda NNP work_ln56cwsp7ffppl4wxeq7osqfuu 219 8 : : : work_ln56cwsp7ffppl4wxeq7osqfuu 219 9 • • VB work_ln56cwsp7ffppl4wxeq7osqfuu 219 10 For for IN work_ln56cwsp7ffppl4wxeq7osqfuu 219 11 n×k n×k JJ work_ln56cwsp7ffppl4wxeq7osqfuu 219 12 societies society NNS work_ln56cwsp7ffppl4wxeq7osqfuu 219 13 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 219 14 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 219 15 every every DT work_ln56cwsp7ffppl4wxeq7osqfuu 219 16 culture culture NN work_ln56cwsp7ffppl4wxeq7osqfuu 219 17 such such JJ work_ln56cwsp7ffppl4wxeq7osqfuu 219 18 that that DT work_ln56cwsp7ffppl4wxeq7osqfuu 219 19 E[U(l+1)]−E[U(l E[U(l+1)]−E[U(l NNP work_ln56cwsp7ffppl4wxeq7osqfuu 219 20 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 219 21 ] ] -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 219 22 = = NFP work_ln56cwsp7ffppl4wxeq7osqfuu 219 23 c c NN work_ln56cwsp7ffppl4wxeq7osqfuu 219 24 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 219 25 with with IN work_ln56cwsp7ffppl4wxeq7osqfuu 219 26 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 219 27 ≤ ≤ NN work_ln56cwsp7ffppl4wxeq7osqfuu 219 28 l l NN work_ln56cwsp7ffppl4wxeq7osqfuu 219 29 ≤ ≤ NN work_ln56cwsp7ffppl4wxeq7osqfuu 219 30 n− n− NNP work_ln56cwsp7ffppl4wxeq7osqfuu 219 31 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 219 32 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 220 1 • • VB work_ln56cwsp7ffppl4wxeq7osqfuu 220 2 In in IN work_ln56cwsp7ffppl4wxeq7osqfuu 220 3 particular particular JJ work_ln56cwsp7ffppl4wxeq7osqfuu 220 4 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 220 5 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 220 6 uniform uniform JJ work_ln56cwsp7ffppl4wxeq7osqfuu 220 7 distribution distribution NN work_ln56cwsp7ffppl4wxeq7osqfuu 220 8 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 221 1 • • VB work_ln56cwsp7ffppl4wxeq7osqfuu 221 2 For for IN work_ln56cwsp7ffppl4wxeq7osqfuu 221 3 n× n× NNP work_ln56cwsp7ffppl4wxeq7osqfuu 221 4 3 3 CD work_ln56cwsp7ffppl4wxeq7osqfuu 221 5 societies society NNS work_ln56cwsp7ffppl4wxeq7osqfuu 221 6 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 221 7 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 221 8 every every DT work_ln56cwsp7ffppl4wxeq7osqfuu 221 9 culture culture NN work_ln56cwsp7ffppl4wxeq7osqfuu 221 10 with with IN work_ln56cwsp7ffppl4wxeq7osqfuu 221 11 a a DT work_ln56cwsp7ffppl4wxeq7osqfuu 221 12 symmetric symmetric JJ work_ln56cwsp7ffppl4wxeq7osqfuu 221 13 density density NN work_ln56cwsp7ffppl4wxeq7osqfuu 221 14 function function NN work_ln56cwsp7ffppl4wxeq7osqfuu 221 15 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 222 1 Corollary Corollary NNP work_ln56cwsp7ffppl4wxeq7osqfuu 222 2 3.2 3.2 CD work_ln56cwsp7ffppl4wxeq7osqfuu 222 3 points point NNS work_ln56cwsp7ffppl4wxeq7osqfuu 222 4 to to IN work_ln56cwsp7ffppl4wxeq7osqfuu 222 5 a a DT work_ln56cwsp7ffppl4wxeq7osqfuu 222 6 prominent prominent JJ work_ln56cwsp7ffppl4wxeq7osqfuu 222 7 decision decision NN work_ln56cwsp7ffppl4wxeq7osqfuu 222 8 rule rule NN work_ln56cwsp7ffppl4wxeq7osqfuu 222 9 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 222 10 Borda Borda NNP work_ln56cwsp7ffppl4wxeq7osqfuu 222 11 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 222 12 as as IN work_ln56cwsp7ffppl4wxeq7osqfuu 222 13 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 222 14 optimal optimal JJ work_ln56cwsp7ffppl4wxeq7osqfuu 222 15 rule rule NN work_ln56cwsp7ffppl4wxeq7osqfuu 222 16 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 222 17 a a DT work_ln56cwsp7ffppl4wxeq7osqfuu 222 18 wide wide JJ work_ln56cwsp7ffppl4wxeq7osqfuu 222 19 range range NN work_ln56cwsp7ffppl4wxeq7osqfuu 222 20 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 222 21 cultures culture NNS work_ln56cwsp7ffppl4wxeq7osqfuu 222 22 with with IN work_ln56cwsp7ffppl4wxeq7osqfuu 222 23 density density NN work_ln56cwsp7ffppl4wxeq7osqfuu 222 24 functions function NNS work_ln56cwsp7ffppl4wxeq7osqfuu 222 25 satisfying satisfy VBG work_ln56cwsp7ffppl4wxeq7osqfuu 222 26 a a DT work_ln56cwsp7ffppl4wxeq7osqfuu 222 27 regularity regularity NN work_ln56cwsp7ffppl4wxeq7osqfuu 222 28 condition condition NN work_ln56cwsp7ffppl4wxeq7osqfuu 222 29 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 223 1 But but CC work_ln56cwsp7ffppl4wxeq7osqfuu 223 2 there there EX work_ln56cwsp7ffppl4wxeq7osqfuu 223 3 are be VBP work_ln56cwsp7ffppl4wxeq7osqfuu 223 4 many many JJ work_ln56cwsp7ffppl4wxeq7osqfuu 223 5 other other JJ work_ln56cwsp7ffppl4wxeq7osqfuu 223 6 relevant relevant JJ work_ln56cwsp7ffppl4wxeq7osqfuu 223 7 cultures culture NNS work_ln56cwsp7ffppl4wxeq7osqfuu 223 8 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 223 9 which which WDT work_ln56cwsp7ffppl4wxeq7osqfuu 223 10 to to TO work_ln56cwsp7ffppl4wxeq7osqfuu 223 11 obtain obtain VB work_ln56cwsp7ffppl4wxeq7osqfuu 223 12 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 223 13 optimal optimal JJ work_ln56cwsp7ffppl4wxeq7osqfuu 223 14 scoring score VBG work_ln56cwsp7ffppl4wxeq7osqfuu 223 15 rule rule NN work_ln56cwsp7ffppl4wxeq7osqfuu 223 16 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 224 1 Consider consider VB work_ln56cwsp7ffppl4wxeq7osqfuu 224 2 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 224 3 normal normal JJ work_ln56cwsp7ffppl4wxeq7osqfuu 224 4 distribution distribution NN work_ln56cwsp7ffppl4wxeq7osqfuu 224 5 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 224 6 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 224 7 example example NN work_ln56cwsp7ffppl4wxeq7osqfuu 224 8 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 225 1 The the DT work_ln56cwsp7ffppl4wxeq7osqfuu 225 2 expected expect VBN work_ln56cwsp7ffppl4wxeq7osqfuu 225 3 value value NN work_ln56cwsp7ffppl4wxeq7osqfuu 225 4 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 225 5 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 225 6 order order NN work_ln56cwsp7ffppl4wxeq7osqfuu 225 7 sta- sta- VBP work_ln56cwsp7ffppl4wxeq7osqfuu 225 8 tistics tistic NNS work_ln56cwsp7ffppl4wxeq7osqfuu 225 9 from from IN work_ln56cwsp7ffppl4wxeq7osqfuu 225 10 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 225 11 normal normal JJ work_ln56cwsp7ffppl4wxeq7osqfuu 225 12 distribution distribution NN work_ln56cwsp7ffppl4wxeq7osqfuu 225 13 are be VBP work_ln56cwsp7ffppl4wxeq7osqfuu 225 14 tabularized tabularize VBN work_ln56cwsp7ffppl4wxeq7osqfuu 225 15 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 225 16 see see VB work_ln56cwsp7ffppl4wxeq7osqfuu 225 17 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 225 18 e.g. e.g. RB work_ln56cwsp7ffppl4wxeq7osqfuu 225 19 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 225 20 Teichroew Teichroew NNP work_ln56cwsp7ffppl4wxeq7osqfuu 225 21 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 225 22 1956 1956 CD work_ln56cwsp7ffppl4wxeq7osqfuu 225 23 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 225 24 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 226 1 From from IN work_ln56cwsp7ffppl4wxeq7osqfuu 226 2 10 10 CD work_ln56cwsp7ffppl4wxeq7osqfuu 226 3 inspection inspection NN work_ln56cwsp7ffppl4wxeq7osqfuu 226 4 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 226 5 these these DT work_ln56cwsp7ffppl4wxeq7osqfuu 226 6 values value NNS work_ln56cwsp7ffppl4wxeq7osqfuu 226 7 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 226 8 it -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 226 9 immediately immediately RB work_ln56cwsp7ffppl4wxeq7osqfuu 226 10 emerges emerge VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 226 11 that that IN work_ln56cwsp7ffppl4wxeq7osqfuu 226 12 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 226 13 αUT αut CD work_ln56cwsp7ffppl4wxeq7osqfuu 226 14 -optimal -optimal JJ work_ln56cwsp7ffppl4wxeq7osqfuu 226 15 decision decision NN work_ln56cwsp7ffppl4wxeq7osqfuu 226 16 rule rule NN work_ln56cwsp7ffppl4wxeq7osqfuu 226 17 in in IN work_ln56cwsp7ffppl4wxeq7osqfuu 226 18 this this DT work_ln56cwsp7ffppl4wxeq7osqfuu 226 19 case case NN work_ln56cwsp7ffppl4wxeq7osqfuu 226 20 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 226 21 a a DT work_ln56cwsp7ffppl4wxeq7osqfuu 226 22 scoring score VBG work_ln56cwsp7ffppl4wxeq7osqfuu 226 23 rule rule NN work_ln56cwsp7ffppl4wxeq7osqfuu 226 24 where where WRB work_ln56cwsp7ffppl4wxeq7osqfuu 226 25 S∗l+1 S∗l+1 NNS work_ln56cwsp7ffppl4wxeq7osqfuu 226 26 −S∗l −S∗l NNP work_ln56cwsp7ffppl4wxeq7osqfuu 226 27 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 226 28 a a DT work_ln56cwsp7ffppl4wxeq7osqfuu 226 29 symmetric symmetric JJ work_ln56cwsp7ffppl4wxeq7osqfuu 226 30 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 226 31 convex convex NNP work_ln56cwsp7ffppl4wxeq7osqfuu 226 32 function function NN work_ln56cwsp7ffppl4wxeq7osqfuu 226 33 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 227 1 A a DT work_ln56cwsp7ffppl4wxeq7osqfuu 227 2 more more RBR work_ln56cwsp7ffppl4wxeq7osqfuu 227 3 extreme extreme JJ work_ln56cwsp7ffppl4wxeq7osqfuu 227 4 version version NN work_ln56cwsp7ffppl4wxeq7osqfuu 227 5 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 227 6 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 227 7 above above JJ work_ln56cwsp7ffppl4wxeq7osqfuu 227 8 emerges emerge NNS work_ln56cwsp7ffppl4wxeq7osqfuu 227 9 when when WRB work_ln56cwsp7ffppl4wxeq7osqfuu 227 10 considering consider VBG work_ln56cwsp7ffppl4wxeq7osqfuu 227 11 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 227 12 Cauchy Cauchy NNP work_ln56cwsp7ffppl4wxeq7osqfuu 227 13 distribution distribution NN work_ln56cwsp7ffppl4wxeq7osqfuu 227 14 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 227 15 see see VB work_ln56cwsp7ffppl4wxeq7osqfuu 227 16 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 227 17 e.g. e.g. RB work_ln56cwsp7ffppl4wxeq7osqfuu 227 18 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 227 19 Barnett Barnett NNP work_ln56cwsp7ffppl4wxeq7osqfuu 227 20 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 227 21 1966 1966 CD work_ln56cwsp7ffppl4wxeq7osqfuu 227 22 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 227 23 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 227 24 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 227 25 expected expect VBN work_ln56cwsp7ffppl4wxeq7osqfuu 227 26 values value NNS work_ln56cwsp7ffppl4wxeq7osqfuu 227 27 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 227 28 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 227 29 Cauchy Cauchy NNP work_ln56cwsp7ffppl4wxeq7osqfuu 227 30 order order NN work_ln56cwsp7ffppl4wxeq7osqfuu 227 31 statistics statistic NNS work_ln56cwsp7ffppl4wxeq7osqfuu 227 32 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 227 33 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 228 1 In in IN work_ln56cwsp7ffppl4wxeq7osqfuu 228 2 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 228 3 latter latter JJ work_ln56cwsp7ffppl4wxeq7osqfuu 228 4 case case NN work_ln56cwsp7ffppl4wxeq7osqfuu 228 5 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 228 6 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 228 7 optimal optimal JJ work_ln56cwsp7ffppl4wxeq7osqfuu 228 8 scoring score VBG work_ln56cwsp7ffppl4wxeq7osqfuu 228 9 rule rule NN work_ln56cwsp7ffppl4wxeq7osqfuu 228 10 tends tend VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 228 11 to to TO work_ln56cwsp7ffppl4wxeq7osqfuu 228 12 discriminate discriminate VB work_ln56cwsp7ffppl4wxeq7osqfuu 228 13 only only RB work_ln56cwsp7ffppl4wxeq7osqfuu 228 14 between between IN work_ln56cwsp7ffppl4wxeq7osqfuu 228 15 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 228 16 very very RB work_ln56cwsp7ffppl4wxeq7osqfuu 228 17 best good JJS work_ln56cwsp7ffppl4wxeq7osqfuu 228 18 alternative alternative NN work_ln56cwsp7ffppl4wxeq7osqfuu 228 19 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 228 20 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 228 21 very very RB work_ln56cwsp7ffppl4wxeq7osqfuu 228 22 worst bad JJS work_ln56cwsp7ffppl4wxeq7osqfuu 228 23 alternative alternative NN work_ln56cwsp7ffppl4wxeq7osqfuu 228 24 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 228 25 all all PDT work_ln56cwsp7ffppl4wxeq7osqfuu 228 26 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 228 27 rest rest NN work_ln56cwsp7ffppl4wxeq7osqfuu 228 28 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 229 1 We -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 229 2 can can MD work_ln56cwsp7ffppl4wxeq7osqfuu 229 3 further further RB work_ln56cwsp7ffppl4wxeq7osqfuu 229 4 apply apply VB work_ln56cwsp7ffppl4wxeq7osqfuu 229 5 our -PRON- PRP$ work_ln56cwsp7ffppl4wxeq7osqfuu 229 6 Theorem theorem NN work_ln56cwsp7ffppl4wxeq7osqfuu 229 7 3.1 3.1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 229 8 to to IN work_ln56cwsp7ffppl4wxeq7osqfuu 229 9 other other JJ work_ln56cwsp7ffppl4wxeq7osqfuu 229 10 classes class NNS work_ln56cwsp7ffppl4wxeq7osqfuu 229 11 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 229 12 probability probability NN work_ln56cwsp7ffppl4wxeq7osqfuu 229 13 distributions distribution NNS work_ln56cwsp7ffppl4wxeq7osqfuu 229 14 via via IN work_ln56cwsp7ffppl4wxeq7osqfuu 229 15 known know VBN work_ln56cwsp7ffppl4wxeq7osqfuu 229 16 results result NNS work_ln56cwsp7ffppl4wxeq7osqfuu 229 17 in in IN work_ln56cwsp7ffppl4wxeq7osqfuu 229 18 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 229 19 literature literature NN work_ln56cwsp7ffppl4wxeq7osqfuu 229 20 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 229 21 order order NN work_ln56cwsp7ffppl4wxeq7osqfuu 229 22 statistics statistic NNS work_ln56cwsp7ffppl4wxeq7osqfuu 229 23 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 230 1 By by IN work_ln56cwsp7ffppl4wxeq7osqfuu 230 2 way way NN work_ln56cwsp7ffppl4wxeq7osqfuu 230 3 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 230 4 illustration illustration NN work_ln56cwsp7ffppl4wxeq7osqfuu 230 5 consider consider VBP work_ln56cwsp7ffppl4wxeq7osqfuu 230 6 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 230 7 following follow VBG work_ln56cwsp7ffppl4wxeq7osqfuu 230 8 class class NN work_ln56cwsp7ffppl4wxeq7osqfuu 230 9 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 230 10 probability probability NN work_ln56cwsp7ffppl4wxeq7osqfuu 230 11 distributions distribution NNS work_ln56cwsp7ffppl4wxeq7osqfuu 230 12 F F NNP work_ln56cwsp7ffppl4wxeq7osqfuu 230 13 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 230 14 see see VB work_ln56cwsp7ffppl4wxeq7osqfuu 230 15 Kamps Kamps NNP work_ln56cwsp7ffppl4wxeq7osqfuu 230 16 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 230 17 1991 1991 CD work_ln56cwsp7ffppl4wxeq7osqfuu 230 18 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 230 19 1992 1992 CD work_ln56cwsp7ffppl4wxeq7osqfuu 230 20 ; ; : work_ln56cwsp7ffppl4wxeq7osqfuu 230 21 see see VB work_ln56cwsp7ffppl4wxeq7osqfuu 230 22 also also RB work_ln56cwsp7ffppl4wxeq7osqfuu 230 23 Balakrishnan Balakrishnan NNP work_ln56cwsp7ffppl4wxeq7osqfuu 230 24 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 230 25 Sultan Sultan NNP work_ln56cwsp7ffppl4wxeq7osqfuu 230 26 1998 1998 CD work_ln56cwsp7ffppl4wxeq7osqfuu 230 27 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 230 28 : : : work_ln56cwsp7ffppl4wxeq7osqfuu 230 29 d d NNP work_ln56cwsp7ffppl4wxeq7osqfuu 230 30 dt dt NNP work_ln56cwsp7ffppl4wxeq7osqfuu 230 31 F−1(t F−1(t NNP work_ln56cwsp7ffppl4wxeq7osqfuu 230 32 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 230 33 = = NN work_ln56cwsp7ffppl4wxeq7osqfuu 230 34 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 230 35 d d NN work_ln56cwsp7ffppl4wxeq7osqfuu 230 36 tp(1 tp(1 NN work_ln56cwsp7ffppl4wxeq7osqfuu 230 37 − − NNP work_ln56cwsp7ffppl4wxeq7osqfuu 230 38 t)q−p−1 t)q−p−1 NNP work_ln56cwsp7ffppl4wxeq7osqfuu 230 39 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 230 40 t t NNP work_ln56cwsp7ffppl4wxeq7osqfuu 230 41 ∈ ∈ NNP work_ln56cwsp7ffppl4wxeq7osqfuu 230 42 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 230 43 0 0 CD work_ln56cwsp7ffppl4wxeq7osqfuu 230 44 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 230 45 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 230 46 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 230 47 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 230 48 where where WRB work_ln56cwsp7ffppl4wxeq7osqfuu 230 49 p p NNP work_ln56cwsp7ffppl4wxeq7osqfuu 230 50 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 230 51 q q NNP work_ln56cwsp7ffppl4wxeq7osqfuu 230 52 are be VBP work_ln56cwsp7ffppl4wxeq7osqfuu 230 53 integers integer NNS work_ln56cwsp7ffppl4wxeq7osqfuu 230 54 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 230 55 d d NN work_ln56cwsp7ffppl4wxeq7osqfuu 230 56 > > XX work_ln56cwsp7ffppl4wxeq7osqfuu 230 57 0 0 CD work_ln56cwsp7ffppl4wxeq7osqfuu 230 58 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 231 1 The the DT work_ln56cwsp7ffppl4wxeq7osqfuu 231 2 values value NNS work_ln56cwsp7ffppl4wxeq7osqfuu 231 3 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 231 4 parameters parameter NNS work_ln56cwsp7ffppl4wxeq7osqfuu 231 5 p p NNP work_ln56cwsp7ffppl4wxeq7osqfuu 231 6 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 231 7 q q NNP work_ln56cwsp7ffppl4wxeq7osqfuu 231 8 determine determine VBP work_ln56cwsp7ffppl4wxeq7osqfuu 231 9 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 231 10 probability probability NN work_ln56cwsp7ffppl4wxeq7osqfuu 231 11 distribution distribution NN work_ln56cwsp7ffppl4wxeq7osqfuu 231 12 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 232 1 For for IN work_ln56cwsp7ffppl4wxeq7osqfuu 232 2 example example NN work_ln56cwsp7ffppl4wxeq7osqfuu 232 3 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 232 4 if if IN work_ln56cwsp7ffppl4wxeq7osqfuu 232 5 p p NN work_ln56cwsp7ffppl4wxeq7osqfuu 232 6 = = SYM work_ln56cwsp7ffppl4wxeq7osqfuu 232 7 q q NN work_ln56cwsp7ffppl4wxeq7osqfuu 232 8 = = SYM work_ln56cwsp7ffppl4wxeq7osqfuu 232 9 0 0 NFP work_ln56cwsp7ffppl4wxeq7osqfuu 232 10 we -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 232 11 get get VBP work_ln56cwsp7ffppl4wxeq7osqfuu 232 12 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 232 13 expo- expo- JJ work_ln56cwsp7ffppl4wxeq7osqfuu 232 14 nential nential JJ work_ln56cwsp7ffppl4wxeq7osqfuu 232 15 distribution distribution NN work_ln56cwsp7ffppl4wxeq7osqfuu 232 16 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 232 17 if if IN work_ln56cwsp7ffppl4wxeq7osqfuu 232 18 p p NN work_ln56cwsp7ffppl4wxeq7osqfuu 232 19 = = SYM work_ln56cwsp7ffppl4wxeq7osqfuu 232 20 q q NNP work_ln56cwsp7ffppl4wxeq7osqfuu 232 21 = = SYM work_ln56cwsp7ffppl4wxeq7osqfuu 232 22 −1 −1 NNP work_ln56cwsp7ffppl4wxeq7osqfuu 232 23 we -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 232 24 get get VBP work_ln56cwsp7ffppl4wxeq7osqfuu 232 25 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 232 26 logistic logistic JJ work_ln56cwsp7ffppl4wxeq7osqfuu 232 27 distribution distribution NN work_ln56cwsp7ffppl4wxeq7osqfuu 232 28 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 232 29 if if IN work_ln56cwsp7ffppl4wxeq7osqfuu 232 30 p p NN work_ln56cwsp7ffppl4wxeq7osqfuu 232 31 > > XX work_ln56cwsp7ffppl4wxeq7osqfuu 232 32 −1 −1 NNP work_ln56cwsp7ffppl4wxeq7osqfuu 232 33 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 232 34 q q NNP work_ln56cwsp7ffppl4wxeq7osqfuu 232 35 = = SYM work_ln56cwsp7ffppl4wxeq7osqfuu 232 36 p p NN work_ln56cwsp7ffppl4wxeq7osqfuu 232 37 + + SYM work_ln56cwsp7ffppl4wxeq7osqfuu 232 38 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 232 39 we -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 232 40 get get VBP work_ln56cwsp7ffppl4wxeq7osqfuu 232 41 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 232 42 power power NN work_ln56cwsp7ffppl4wxeq7osqfuu 232 43 function function NN work_ln56cwsp7ffppl4wxeq7osqfuu 232 44 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 232 45 etc etc FW work_ln56cwsp7ffppl4wxeq7osqfuu 232 46 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 233 1 We -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 233 2 can can MD work_ln56cwsp7ffppl4wxeq7osqfuu 233 3 then then RB work_ln56cwsp7ffppl4wxeq7osqfuu 233 4 establish establish VB work_ln56cwsp7ffppl4wxeq7osqfuu 233 5 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 233 6 following follow VBG work_ln56cwsp7ffppl4wxeq7osqfuu 233 7 result result NN work_ln56cwsp7ffppl4wxeq7osqfuu 233 8 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 233 9 this this DT work_ln56cwsp7ffppl4wxeq7osqfuu 233 10 class class NN work_ln56cwsp7ffppl4wxeq7osqfuu 233 11 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 233 12 probability probability NN work_ln56cwsp7ffppl4wxeq7osqfuu 233 13 distributions distribution NNS work_ln56cwsp7ffppl4wxeq7osqfuu 233 14 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 234 1 Theorem theorem NN work_ln56cwsp7ffppl4wxeq7osqfuu 234 2 3.3 3.3 CD work_ln56cwsp7ffppl4wxeq7osqfuu 234 3 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 235 1 For for IN work_ln56cwsp7ffppl4wxeq7osqfuu 235 2 n n DT work_ln56cwsp7ffppl4wxeq7osqfuu 235 3 × × NN work_ln56cwsp7ffppl4wxeq7osqfuu 235 4 k k NN work_ln56cwsp7ffppl4wxeq7osqfuu 235 5 societies society NNS work_ln56cwsp7ffppl4wxeq7osqfuu 235 6 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 235 7 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 235 8 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 235 9 class class NN work_ln56cwsp7ffppl4wxeq7osqfuu 235 10 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 235 11 cultures cultures NNP work_ln56cwsp7ffppl4wxeq7osqfuu 235 12 F F NNP work_ln56cwsp7ffppl4wxeq7osqfuu 235 13 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 235 14 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 235 15 maximum maximum JJ work_ln56cwsp7ffppl4wxeq7osqfuu 235 16 αUT αut CD work_ln56cwsp7ffppl4wxeq7osqfuu 235 17 -optimal -optimal JJ work_ln56cwsp7ffppl4wxeq7osqfuu 235 18 rule rule NN work_ln56cwsp7ffppl4wxeq7osqfuu 235 19 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 235 20 a a DT work_ln56cwsp7ffppl4wxeq7osqfuu 235 21 scoring score VBG work_ln56cwsp7ffppl4wxeq7osqfuu 235 22 rule rule NN work_ln56cwsp7ffppl4wxeq7osqfuu 235 23 with with IN work_ln56cwsp7ffppl4wxeq7osqfuu 235 24 S∗l s∗l CD work_ln56cwsp7ffppl4wxeq7osqfuu 235 25 = = SYM work_ln56cwsp7ffppl4wxeq7osqfuu 235 26 ∑l ∑l PRP$ work_ln56cwsp7ffppl4wxeq7osqfuu 235 27 h=2 h=2 NNP work_ln56cwsp7ffppl4wxeq7osqfuu 235 28 E[U e[u CD work_ln56cwsp7ffppl4wxeq7osqfuu 235 29 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 235 30 h h NNP work_ln56cwsp7ffppl4wxeq7osqfuu 235 31 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 235 32 ] ] -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 235 33 − − NNP work_ln56cwsp7ffppl4wxeq7osqfuu 235 34 E[U(h−1)]∑k E[U(h−1)]∑k NNP work_ln56cwsp7ffppl4wxeq7osqfuu 235 35 h=2 h=2 NNP work_ln56cwsp7ffppl4wxeq7osqfuu 235 36 E[U(h E[U(h NNP work_ln56cwsp7ffppl4wxeq7osqfuu 235 37 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 235 38 ] ] -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 235 39 − − NNP work_ln56cwsp7ffppl4wxeq7osqfuu 235 40 E[U(h−1 E[U(h−1 NNP work_ln56cwsp7ffppl4wxeq7osqfuu 235 41 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 235 42 ] ] -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 235 43 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 235 44 l l NN work_ln56cwsp7ffppl4wxeq7osqfuu 235 45 ∈{1 ∈{1 NNP work_ln56cwsp7ffppl4wxeq7osqfuu 235 46 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 235 47 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 236 1 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 237 1 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 238 1 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 238 2 k k NNP work_ln56cwsp7ffppl4wxeq7osqfuu 238 3 } } -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 238 4 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 238 5 with with IN work_ln56cwsp7ffppl4wxeq7osqfuu 238 6 E[U(h E[U(h NNP work_ln56cwsp7ffppl4wxeq7osqfuu 238 7 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 238 8 ] ] -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 238 9 − − NNP work_ln56cwsp7ffppl4wxeq7osqfuu 238 10 E[U(h−1 E[U(h−1 NNP work_ln56cwsp7ffppl4wxeq7osqfuu 238 11 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 238 12 ] ] -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 238 13 = = FW work_ln56cwsp7ffppl4wxeq7osqfuu 238 14 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 238 15 k k NNP work_ln56cwsp7ffppl4wxeq7osqfuu 238 16 h−1 h−1 NNP work_ln56cwsp7ffppl4wxeq7osqfuu 238 17 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 238 18 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 238 19 h+p)(k+qh+p h+p)(k+qh+p NNP work_ln56cwsp7ffppl4wxeq7osqfuu 238 20 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 238 21 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 239 1 The the DT work_ln56cwsp7ffppl4wxeq7osqfuu 239 2 introduction introduction NN work_ln56cwsp7ffppl4wxeq7osqfuu 239 3 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 239 4 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 239 5 values value NNS work_ln56cwsp7ffppl4wxeq7osqfuu 239 6 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 239 7 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 239 8 parameters parameter NNS work_ln56cwsp7ffppl4wxeq7osqfuu 239 9 into into IN work_ln56cwsp7ffppl4wxeq7osqfuu 239 10 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 239 11 equations equation NNS work_ln56cwsp7ffppl4wxeq7osqfuu 239 12 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 239 13 Theorem Theorem NNP work_ln56cwsp7ffppl4wxeq7osqfuu 239 14 3.3 3.3 CD work_ln56cwsp7ffppl4wxeq7osqfuu 239 15 immediately immediately RB work_ln56cwsp7ffppl4wxeq7osqfuu 239 16 gives give VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 239 17 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 239 18 optimal optimal JJ work_ln56cwsp7ffppl4wxeq7osqfuu 239 19 scoring score VBG work_ln56cwsp7ffppl4wxeq7osqfuu 239 20 rule rule NN work_ln56cwsp7ffppl4wxeq7osqfuu 239 21 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 240 1 By by IN work_ln56cwsp7ffppl4wxeq7osqfuu 240 2 way way NN work_ln56cwsp7ffppl4wxeq7osqfuu 240 3 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 240 4 illustration illustration NN work_ln56cwsp7ffppl4wxeq7osqfuu 240 5 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 240 6 let let VB work_ln56cwsp7ffppl4wxeq7osqfuu 240 7 k k NN work_ln56cwsp7ffppl4wxeq7osqfuu 240 8 = = SYM work_ln56cwsp7ffppl4wxeq7osqfuu 240 9 3 3 CD work_ln56cwsp7ffppl4wxeq7osqfuu 240 10 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 241 1 It -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 241 2 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 241 3 immediate immediate JJ work_ln56cwsp7ffppl4wxeq7osqfuu 241 4 that that IN work_ln56cwsp7ffppl4wxeq7osqfuu 241 5 when when WRB work_ln56cwsp7ffppl4wxeq7osqfuu 241 6 there there EX work_ln56cwsp7ffppl4wxeq7osqfuu 241 7 are be VBP work_ln56cwsp7ffppl4wxeq7osqfuu 241 8 three three CD work_ln56cwsp7ffppl4wxeq7osqfuu 241 9 alternatives alternative NNS work_ln56cwsp7ffppl4wxeq7osqfuu 241 10 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 241 11 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 241 12 optimal optimal JJ work_ln56cwsp7ffppl4wxeq7osqfuu 241 13 scoring score VBG work_ln56cwsp7ffppl4wxeq7osqfuu 241 14 rule rule NN work_ln56cwsp7ffppl4wxeq7osqfuu 241 15 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 241 16 well well RB work_ln56cwsp7ffppl4wxeq7osqfuu 241 17 - - HYPH work_ln56cwsp7ffppl4wxeq7osqfuu 241 18 defined define VBN work_ln56cwsp7ffppl4wxeq7osqfuu 241 19 by by IN work_ln56cwsp7ffppl4wxeq7osqfuu 241 20 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 241 21 value value NN work_ln56cwsp7ffppl4wxeq7osqfuu 241 22 assigned assign VBN work_ln56cwsp7ffppl4wxeq7osqfuu 241 23 to to IN work_ln56cwsp7ffppl4wxeq7osqfuu 241 24 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 241 25 middle middle JJ work_ln56cwsp7ffppl4wxeq7osqfuu 241 26 alternative alternative NN work_ln56cwsp7ffppl4wxeq7osqfuu 241 27 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 242 1 Corollary Corollary NNP work_ln56cwsp7ffppl4wxeq7osqfuu 242 2 3.4 3.4 CD work_ln56cwsp7ffppl4wxeq7osqfuu 242 3 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 243 1 For for IN work_ln56cwsp7ffppl4wxeq7osqfuu 243 2 n n DT work_ln56cwsp7ffppl4wxeq7osqfuu 243 3 × × NNS work_ln56cwsp7ffppl4wxeq7osqfuu 243 4 3 3 CD work_ln56cwsp7ffppl4wxeq7osqfuu 243 5 societies society NNS work_ln56cwsp7ffppl4wxeq7osqfuu 243 6 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 243 7 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 243 8 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 243 9 class class NN work_ln56cwsp7ffppl4wxeq7osqfuu 243 10 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 243 11 cultures cultures NNP work_ln56cwsp7ffppl4wxeq7osqfuu 243 12 F F NNP work_ln56cwsp7ffppl4wxeq7osqfuu 243 13 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 243 14 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 243 15 maximum maximum JJ work_ln56cwsp7ffppl4wxeq7osqfuu 243 16 αUT αut CD work_ln56cwsp7ffppl4wxeq7osqfuu 243 17 -optimal -optimal JJ work_ln56cwsp7ffppl4wxeq7osqfuu 243 18 rule rule NN work_ln56cwsp7ffppl4wxeq7osqfuu 243 19 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 243 20 a a DT work_ln56cwsp7ffppl4wxeq7osqfuu 243 21 scoring score VBG work_ln56cwsp7ffppl4wxeq7osqfuu 243 22 rule rule NN work_ln56cwsp7ffppl4wxeq7osqfuu 243 23 with with IN work_ln56cwsp7ffppl4wxeq7osqfuu 243 24 S S NNP work_ln56cwsp7ffppl4wxeq7osqfuu 243 25 ∗2 ∗2 NNP work_ln56cwsp7ffppl4wxeq7osqfuu 243 26 = = SYM work_ln56cwsp7ffppl4wxeq7osqfuu 243 27 1−p+q 1−p+q CD work_ln56cwsp7ffppl4wxeq7osqfuu 243 28 3+q 3+q CD work_ln56cwsp7ffppl4wxeq7osqfuu 243 29 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 243 30 where where WRB work_ln56cwsp7ffppl4wxeq7osqfuu 243 31 p p NNP work_ln56cwsp7ffppl4wxeq7osqfuu 243 32 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 243 33 q q NNP work_ln56cwsp7ffppl4wxeq7osqfuu 243 34 are be VBP work_ln56cwsp7ffppl4wxeq7osqfuu 243 35 integers integer NNS work_ln56cwsp7ffppl4wxeq7osqfuu 243 36 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 244 1 The the DT work_ln56cwsp7ffppl4wxeq7osqfuu 244 2 above above JJ work_ln56cwsp7ffppl4wxeq7osqfuu 244 3 corollary corollary NN work_ln56cwsp7ffppl4wxeq7osqfuu 244 4 provides provide VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 244 5 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 244 6 optimal optimal JJ work_ln56cwsp7ffppl4wxeq7osqfuu 244 7 scoring score VBG work_ln56cwsp7ffppl4wxeq7osqfuu 244 8 rule rule NN work_ln56cwsp7ffppl4wxeq7osqfuu 244 9 contingent contingent NN work_ln56cwsp7ffppl4wxeq7osqfuu 244 10 on on IN work_ln56cwsp7ffppl4wxeq7osqfuu 244 11 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 244 12 values value NNS work_ln56cwsp7ffppl4wxeq7osqfuu 244 13 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 244 14 parameters parameter NNS work_ln56cwsp7ffppl4wxeq7osqfuu 244 15 p p NNP work_ln56cwsp7ffppl4wxeq7osqfuu 244 16 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 244 17 q q NNP work_ln56cwsp7ffppl4wxeq7osqfuu 244 18 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 244 19 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 244 20 hence hence RB work_ln56cwsp7ffppl4wxeq7osqfuu 244 21 contingent contingent JJ work_ln56cwsp7ffppl4wxeq7osqfuu 244 22 on on IN work_ln56cwsp7ffppl4wxeq7osqfuu 244 23 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 244 24 culture culture NN work_ln56cwsp7ffppl4wxeq7osqfuu 244 25 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 244 26 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 244 27 society society NN work_ln56cwsp7ffppl4wxeq7osqfuu 244 28 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 245 1 11 11 CD work_ln56cwsp7ffppl4wxeq7osqfuu 245 2 3.2 3.2 CD work_ln56cwsp7ffppl4wxeq7osqfuu 245 3 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 246 1 The the DT work_ln56cwsp7ffppl4wxeq7osqfuu 246 2 βUT βut NN work_ln56cwsp7ffppl4wxeq7osqfuu 246 3 -index -index NN work_ln56cwsp7ffppl4wxeq7osqfuu 246 4 : : : work_ln56cwsp7ffppl4wxeq7osqfuu 246 5 Evaluating evaluate VBG work_ln56cwsp7ffppl4wxeq7osqfuu 246 6 Decision Decision NNP work_ln56cwsp7ffppl4wxeq7osqfuu 246 7 Rules rule NNS work_ln56cwsp7ffppl4wxeq7osqfuu 246 8 in in IN work_ln56cwsp7ffppl4wxeq7osqfuu 246 9 terms term NNS work_ln56cwsp7ffppl4wxeq7osqfuu 246 10 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 246 11 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 246 12 Probability Probability NNP work_ln56cwsp7ffppl4wxeq7osqfuu 246 13 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 246 14 Selecting select VBG work_ln56cwsp7ffppl4wxeq7osqfuu 246 15 an an DT work_ln56cwsp7ffppl4wxeq7osqfuu 246 16 Optimal Optimal NNP work_ln56cwsp7ffppl4wxeq7osqfuu 246 17 Alternative alternative NN work_ln56cwsp7ffppl4wxeq7osqfuu 246 18 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 247 1 Due due IN work_ln56cwsp7ffppl4wxeq7osqfuu 247 2 to to IN work_ln56cwsp7ffppl4wxeq7osqfuu 247 3 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 247 4 analytical analytical JJ work_ln56cwsp7ffppl4wxeq7osqfuu 247 5 complexity complexity NN work_ln56cwsp7ffppl4wxeq7osqfuu 247 6 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 247 7 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 247 8 study study NN work_ln56cwsp7ffppl4wxeq7osqfuu 247 9 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 247 10 utilitarianism utilitarianism NN work_ln56cwsp7ffppl4wxeq7osqfuu 247 11 through through IN work_ln56cwsp7ffppl4wxeq7osqfuu 247 12 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 247 13 lens lens NN work_ln56cwsp7ffppl4wxeq7osqfuu 247 14 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 247 15 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 247 16 βUT βut NN work_ln56cwsp7ffppl4wxeq7osqfuu 247 17 -index -index VBN work_ln56cwsp7ffppl4wxeq7osqfuu 247 18 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 247 19 we -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 247 20 begin begin VBP work_ln56cwsp7ffppl4wxeq7osqfuu 247 21 with with IN work_ln56cwsp7ffppl4wxeq7osqfuu 247 22 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 247 23 formal formal JJ work_ln56cwsp7ffppl4wxeq7osqfuu 247 24 study study NN work_ln56cwsp7ffppl4wxeq7osqfuu 247 25 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 247 26 a a DT work_ln56cwsp7ffppl4wxeq7osqfuu 247 27 small small JJ work_ln56cwsp7ffppl4wxeq7osqfuu 247 28 society society NN work_ln56cwsp7ffppl4wxeq7osqfuu 247 29 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 247 30 a a DT work_ln56cwsp7ffppl4wxeq7osqfuu 247 31 2×3 2×3 CD work_ln56cwsp7ffppl4wxeq7osqfuu 247 32 society society NN work_ln56cwsp7ffppl4wxeq7osqfuu 247 33 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 247 34 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 247 35 a a DT work_ln56cwsp7ffppl4wxeq7osqfuu 247 36 complete complete JJ work_ln56cwsp7ffppl4wxeq7osqfuu 247 37 range range NN work_ln56cwsp7ffppl4wxeq7osqfuu 247 38 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 247 39 cultures culture NNS work_ln56cwsp7ffppl4wxeq7osqfuu 247 40 with with IN work_ln56cwsp7ffppl4wxeq7osqfuu 247 41 symmetric symmetric JJ work_ln56cwsp7ffppl4wxeq7osqfuu 247 42 density density NN work_ln56cwsp7ffppl4wxeq7osqfuu 247 43 functions function NNS work_ln56cwsp7ffppl4wxeq7osqfuu 247 44 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 247 45 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 247 46 we -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 247 47 then then RB work_ln56cwsp7ffppl4wxeq7osqfuu 247 48 run run VBP work_ln56cwsp7ffppl4wxeq7osqfuu 247 49 a a DT work_ln56cwsp7ffppl4wxeq7osqfuu 247 50 set set NN work_ln56cwsp7ffppl4wxeq7osqfuu 247 51 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 247 52 simulations simulation NNS work_ln56cwsp7ffppl4wxeq7osqfuu 247 53 to to TO work_ln56cwsp7ffppl4wxeq7osqfuu 247 54 approach approach VB work_ln56cwsp7ffppl4wxeq7osqfuu 247 55 larger large JJR work_ln56cwsp7ffppl4wxeq7osqfuu 247 56 societies society NNS work_ln56cwsp7ffppl4wxeq7osqfuu 247 57 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 248 1 In in IN work_ln56cwsp7ffppl4wxeq7osqfuu 248 2 societies society NNS work_ln56cwsp7ffppl4wxeq7osqfuu 248 3 with with IN work_ln56cwsp7ffppl4wxeq7osqfuu 248 4 n n NN work_ln56cwsp7ffppl4wxeq7osqfuu 248 5 = = SYM work_ln56cwsp7ffppl4wxeq7osqfuu 248 6 2 2 CD work_ln56cwsp7ffppl4wxeq7osqfuu 248 7 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 248 8 k k NN work_ln56cwsp7ffppl4wxeq7osqfuu 248 9 = = SYM work_ln56cwsp7ffppl4wxeq7osqfuu 248 10 3 3 CD work_ln56cwsp7ffppl4wxeq7osqfuu 248 11 there there EX work_ln56cwsp7ffppl4wxeq7osqfuu 248 12 are be VBP work_ln56cwsp7ffppl4wxeq7osqfuu 248 13 5 5 CD work_ln56cwsp7ffppl4wxeq7osqfuu 248 14 different different JJ work_ln56cwsp7ffppl4wxeq7osqfuu 248 15 scoring scoring NN work_ln56cwsp7ffppl4wxeq7osqfuu 248 16 rules rule NNS work_ln56cwsp7ffppl4wxeq7osqfuu 248 17 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 248 18 since since IN work_ln56cwsp7ffppl4wxeq7osqfuu 248 19 every every DT work_ln56cwsp7ffppl4wxeq7osqfuu 248 20 S2 s2 NN work_ln56cwsp7ffppl4wxeq7osqfuu 248 21 ∈ ∈ , work_ln56cwsp7ffppl4wxeq7osqfuu 248 22 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 248 23 0 0 NFP work_ln56cwsp7ffppl4wxeq7osqfuu 248 24 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 248 25 1/2 1/2 CD work_ln56cwsp7ffppl4wxeq7osqfuu 248 26 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 248 27 represents represent VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 248 28 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 248 29 same same JJ work_ln56cwsp7ffppl4wxeq7osqfuu 248 30 scoring scoring JJ work_ln56cwsp7ffppl4wxeq7osqfuu 248 31 rule rule NN work_ln56cwsp7ffppl4wxeq7osqfuu 248 32 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 248 33 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 248 34 similarly similarly RB work_ln56cwsp7ffppl4wxeq7osqfuu 248 35 every every DT work_ln56cwsp7ffppl4wxeq7osqfuu 248 36 S2 s2 NN work_ln56cwsp7ffppl4wxeq7osqfuu 248 37 ∈ ∈ , work_ln56cwsp7ffppl4wxeq7osqfuu 248 38 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 248 39 1/2 1/2 CD work_ln56cwsp7ffppl4wxeq7osqfuu 248 40 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 248 41 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 248 42 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 248 43 also also RB work_ln56cwsp7ffppl4wxeq7osqfuu 248 44 represents represent VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 248 45 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 248 46 same same JJ work_ln56cwsp7ffppl4wxeq7osqfuu 248 47 scoring scoring NN work_ln56cwsp7ffppl4wxeq7osqfuu 248 48 rule.5 rule.5 . work_ln56cwsp7ffppl4wxeq7osqfuu 248 49 Hence Hence NNP work_ln56cwsp7ffppl4wxeq7osqfuu 248 50 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 248 51 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 248 52 set set NN work_ln56cwsp7ffppl4wxeq7osqfuu 248 53 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 248 54 different different JJ work_ln56cwsp7ffppl4wxeq7osqfuu 248 55 scoring scoring NN work_ln56cwsp7ffppl4wxeq7osqfuu 248 56 rules rule NNS work_ln56cwsp7ffppl4wxeq7osqfuu 248 57 when when WRB work_ln56cwsp7ffppl4wxeq7osqfuu 248 58 n n CC work_ln56cwsp7ffppl4wxeq7osqfuu 248 59 = = SYM work_ln56cwsp7ffppl4wxeq7osqfuu 248 60 2 2 CD work_ln56cwsp7ffppl4wxeq7osqfuu 248 61 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 248 62 k k NN work_ln56cwsp7ffppl4wxeq7osqfuu 248 63 = = SYM work_ln56cwsp7ffppl4wxeq7osqfuu 248 64 3 3 CD work_ln56cwsp7ffppl4wxeq7osqfuu 248 65 comprises comprise VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 248 66 plurality plurality NN work_ln56cwsp7ffppl4wxeq7osqfuu 248 67 with with IN work_ln56cwsp7ffppl4wxeq7osqfuu 248 68 S2Pl s2pl CD work_ln56cwsp7ffppl4wxeq7osqfuu 248 69 = = SYM work_ln56cwsp7ffppl4wxeq7osqfuu 248 70 0 0 NFP work_ln56cwsp7ffppl4wxeq7osqfuu 248 71 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 248 72 Borda Borda NNP work_ln56cwsp7ffppl4wxeq7osqfuu 248 73 with with IN work_ln56cwsp7ffppl4wxeq7osqfuu 248 74 S S NNP work_ln56cwsp7ffppl4wxeq7osqfuu 248 75 2 2 CD work_ln56cwsp7ffppl4wxeq7osqfuu 248 76 Bd Bd NNP work_ln56cwsp7ffppl4wxeq7osqfuu 248 77 = = SYM work_ln56cwsp7ffppl4wxeq7osqfuu 248 78 1/2 1/2 CD work_ln56cwsp7ffppl4wxeq7osqfuu 248 79 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 248 80 negative negative JJ work_ln56cwsp7ffppl4wxeq7osqfuu 248 81 with with IN work_ln56cwsp7ffppl4wxeq7osqfuu 248 82 S2Ng s2ng CD work_ln56cwsp7ffppl4wxeq7osqfuu 248 83 = = SYM work_ln56cwsp7ffppl4wxeq7osqfuu 248 84 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 248 85 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 248 86 an an DT work_ln56cwsp7ffppl4wxeq7osqfuu 248 87 explosion explosion NN work_ln56cwsp7ffppl4wxeq7osqfuu 248 88 rule rule NN work_ln56cwsp7ffppl4wxeq7osqfuu 248 89 with with IN work_ln56cwsp7ffppl4wxeq7osqfuu 248 90 any any DT work_ln56cwsp7ffppl4wxeq7osqfuu 248 91 value value NN work_ln56cwsp7ffppl4wxeq7osqfuu 248 92 S s NN work_ln56cwsp7ffppl4wxeq7osqfuu 248 93 2 2 CD work_ln56cwsp7ffppl4wxeq7osqfuu 248 94 Ex ex NN work_ln56cwsp7ffppl4wxeq7osqfuu 248 95 ∈ ∈ IN work_ln56cwsp7ffppl4wxeq7osqfuu 248 96 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 248 97 1/2 1/2 CD work_ln56cwsp7ffppl4wxeq7osqfuu 248 98 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 248 99 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 248 100 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 248 101 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 248 102 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 248 103 an an DT work_ln56cwsp7ffppl4wxeq7osqfuu 248 104 implosion implosion NN work_ln56cwsp7ffppl4wxeq7osqfuu 248 105 rule rule NN work_ln56cwsp7ffppl4wxeq7osqfuu 248 106 with with IN work_ln56cwsp7ffppl4wxeq7osqfuu 248 107 any any DT work_ln56cwsp7ffppl4wxeq7osqfuu 248 108 value value NN work_ln56cwsp7ffppl4wxeq7osqfuu 248 109 S2Im s2im CD work_ln56cwsp7ffppl4wxeq7osqfuu 248 110 ∈ ∈ NNP work_ln56cwsp7ffppl4wxeq7osqfuu 248 111 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 248 112 0 0 CD work_ln56cwsp7ffppl4wxeq7osqfuu 248 113 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 248 114 1/2 1/2 CD work_ln56cwsp7ffppl4wxeq7osqfuu 248 115 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 248 116 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 249 1 We -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 249 2 study study VBP work_ln56cwsp7ffppl4wxeq7osqfuu 249 3 a a DT work_ln56cwsp7ffppl4wxeq7osqfuu 249 4 collection collection NN work_ln56cwsp7ffppl4wxeq7osqfuu 249 5 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 249 6 cultures culture NNS work_ln56cwsp7ffppl4wxeq7osqfuu 249 7 with with IN work_ln56cwsp7ffppl4wxeq7osqfuu 249 8 symmetric symmetric JJ work_ln56cwsp7ffppl4wxeq7osqfuu 249 9 density density NN work_ln56cwsp7ffppl4wxeq7osqfuu 249 10 functions function NNS work_ln56cwsp7ffppl4wxeq7osqfuu 249 11 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 250 1 Take take VB work_ln56cwsp7ffppl4wxeq7osqfuu 250 2 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 250 3 para- para- JJ work_ln56cwsp7ffppl4wxeq7osqfuu 250 4 bolic bolic NN work_ln56cwsp7ffppl4wxeq7osqfuu 250 5 function function NN work_ln56cwsp7ffppl4wxeq7osqfuu 250 6 f(x f(x NNP work_ln56cwsp7ffppl4wxeq7osqfuu 250 7 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 250 8 = = NFP work_ln56cwsp7ffppl4wxeq7osqfuu 250 9 ax2 ax2 NNP work_ln56cwsp7ffppl4wxeq7osqfuu 250 10 + + CC work_ln56cwsp7ffppl4wxeq7osqfuu 250 11 bx+c bx+c NNP work_ln56cwsp7ffppl4wxeq7osqfuu 250 12 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 250 13 with with IN work_ln56cwsp7ffppl4wxeq7osqfuu 250 14 x x SYM work_ln56cwsp7ffppl4wxeq7osqfuu 250 15 ∈ ∈ NNP work_ln56cwsp7ffppl4wxeq7osqfuu 250 16 [ [ -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 250 17 0 0 CD work_ln56cwsp7ffppl4wxeq7osqfuu 250 18 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 250 19 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 250 20 ] ] -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 250 21 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 251 1 Now now RB work_ln56cwsp7ffppl4wxeq7osqfuu 251 2 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 251 3 in in IN work_ln56cwsp7ffppl4wxeq7osqfuu 251 4 order order NN work_ln56cwsp7ffppl4wxeq7osqfuu 251 5 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 251 6 f(x f(x NNP work_ln56cwsp7ffppl4wxeq7osqfuu 251 7 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 251 8 to to TO work_ln56cwsp7ffppl4wxeq7osqfuu 251 9 represent represent VB work_ln56cwsp7ffppl4wxeq7osqfuu 251 10 a a DT work_ln56cwsp7ffppl4wxeq7osqfuu 251 11 symmetric symmetric JJ work_ln56cwsp7ffppl4wxeq7osqfuu 251 12 density density NN work_ln56cwsp7ffppl4wxeq7osqfuu 251 13 function function NN work_ln56cwsp7ffppl4wxeq7osqfuu 251 14 it -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 251 15 must must MD work_ln56cwsp7ffppl4wxeq7osqfuu 251 16 be be VB work_ln56cwsp7ffppl4wxeq7osqfuu 251 17 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 251 18 case case NN work_ln56cwsp7ffppl4wxeq7osqfuu 251 19 that that IN work_ln56cwsp7ffppl4wxeq7osqfuu 251 20 a a DT work_ln56cwsp7ffppl4wxeq7osqfuu 251 21 = = -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 251 22 −b −b CD work_ln56cwsp7ffppl4wxeq7osqfuu 251 23 = = SYM work_ln56cwsp7ffppl4wxeq7osqfuu 251 24 −(1−c −(1−c NNP work_ln56cwsp7ffppl4wxeq7osqfuu 251 25 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 251 26 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 251 27 with with IN work_ln56cwsp7ffppl4wxeq7osqfuu 251 28 c c NNP work_ln56cwsp7ffppl4wxeq7osqfuu 251 29 tak- tak- NN work_ln56cwsp7ffppl4wxeq7osqfuu 251 30 ing e VBG work_ln56cwsp7ffppl4wxeq7osqfuu 251 31 values value NNS work_ln56cwsp7ffppl4wxeq7osqfuu 251 32 in in IN work_ln56cwsp7ffppl4wxeq7osqfuu 251 33 [ [ -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 251 34 0 0 CD work_ln56cwsp7ffppl4wxeq7osqfuu 251 35 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 251 36 3 3 CD work_ln56cwsp7ffppl4wxeq7osqfuu 251 37 ] ] -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 251 38 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 252 1 Note note VB work_ln56cwsp7ffppl4wxeq7osqfuu 252 2 that that IN work_ln56cwsp7ffppl4wxeq7osqfuu 252 3 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 252 4 c c NN work_ln56cwsp7ffppl4wxeq7osqfuu 252 5 = = SYM work_ln56cwsp7ffppl4wxeq7osqfuu 252 6 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 252 7 case case NN work_ln56cwsp7ffppl4wxeq7osqfuu 252 8 corresponds correspond VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 252 9 to to IN work_ln56cwsp7ffppl4wxeq7osqfuu 252 10 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 252 11 uniform uniform JJ work_ln56cwsp7ffppl4wxeq7osqfuu 252 12 distribution distribution NN work_ln56cwsp7ffppl4wxeq7osqfuu 252 13 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 253 1 Values value NNS work_ln56cwsp7ffppl4wxeq7osqfuu 253 2 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 253 3 c c NN work_ln56cwsp7ffppl4wxeq7osqfuu 253 4 ∈ ∈ RB work_ln56cwsp7ffppl4wxeq7osqfuu 253 5 [ [ -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 253 6 0 0 CD work_ln56cwsp7ffppl4wxeq7osqfuu 253 7 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 253 8 1 1 LS work_ln56cwsp7ffppl4wxeq7osqfuu 253 9 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 253 10 correspond correspond VB work_ln56cwsp7ffppl4wxeq7osqfuu 253 11 to to TO work_ln56cwsp7ffppl4wxeq7osqfuu 253 12 strictly strictly RB work_ln56cwsp7ffppl4wxeq7osqfuu 253 13 concave concave VB work_ln56cwsp7ffppl4wxeq7osqfuu 253 14 density density NN work_ln56cwsp7ffppl4wxeq7osqfuu 253 15 functions function NNS work_ln56cwsp7ffppl4wxeq7osqfuu 253 16 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 254 1 That that RB work_ln56cwsp7ffppl4wxeq7osqfuu 254 2 is is RB work_ln56cwsp7ffppl4wxeq7osqfuu 254 3 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 254 4 lower low JJR work_ln56cwsp7ffppl4wxeq7osqfuu 254 5 values value NNS work_ln56cwsp7ffppl4wxeq7osqfuu 254 6 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 254 7 c c NN work_ln56cwsp7ffppl4wxeq7osqfuu 254 8 represent represent VBP work_ln56cwsp7ffppl4wxeq7osqfuu 254 9 higher high JJR work_ln56cwsp7ffppl4wxeq7osqfuu 254 10 levels level NNS work_ln56cwsp7ffppl4wxeq7osqfuu 254 11 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 254 12 consensus consensus NN work_ln56cwsp7ffppl4wxeq7osqfuu 254 13 on on IN work_ln56cwsp7ffppl4wxeq7osqfuu 254 14 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 254 15 evaluation evaluation NN work_ln56cwsp7ffppl4wxeq7osqfuu 254 16 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 254 17 an an DT work_ln56cwsp7ffppl4wxeq7osqfuu 254 18 alternative alternative NN work_ln56cwsp7ffppl4wxeq7osqfuu 254 19 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 255 1 Finally finally RB work_ln56cwsp7ffppl4wxeq7osqfuu 255 2 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 255 3 values value NNS work_ln56cwsp7ffppl4wxeq7osqfuu 255 4 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 255 5 c c NN work_ln56cwsp7ffppl4wxeq7osqfuu 255 6 ∈ ∈ NN work_ln56cwsp7ffppl4wxeq7osqfuu 255 7 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 255 8 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 255 9 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 255 10 3 3 LS work_ln56cwsp7ffppl4wxeq7osqfuu 255 11 ] ] -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 255 12 correspond correspond VB work_ln56cwsp7ffppl4wxeq7osqfuu 255 13 to to IN work_ln56cwsp7ffppl4wxeq7osqfuu 255 14 strictly strictly RB work_ln56cwsp7ffppl4wxeq7osqfuu 255 15 convex convex NNP work_ln56cwsp7ffppl4wxeq7osqfuu 255 16 density density NN work_ln56cwsp7ffppl4wxeq7osqfuu 255 17 functions function NNS work_ln56cwsp7ffppl4wxeq7osqfuu 255 18 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 256 1 Hence hence RB work_ln56cwsp7ffppl4wxeq7osqfuu 256 2 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 256 3 higher high JJR work_ln56cwsp7ffppl4wxeq7osqfuu 256 4 values value NNS work_ln56cwsp7ffppl4wxeq7osqfuu 256 5 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 256 6 c c NN work_ln56cwsp7ffppl4wxeq7osqfuu 256 7 represent represent VBP work_ln56cwsp7ffppl4wxeq7osqfuu 256 8 higher high JJR work_ln56cwsp7ffppl4wxeq7osqfuu 256 9 levels level NNS work_ln56cwsp7ffppl4wxeq7osqfuu 256 10 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 256 11 extremism extremism NN work_ln56cwsp7ffppl4wxeq7osqfuu 256 12 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 257 1 Theorem theorem NN work_ln56cwsp7ffppl4wxeq7osqfuu 257 2 3.5 3.5 CD work_ln56cwsp7ffppl4wxeq7osqfuu 257 3 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 258 1 For for IN work_ln56cwsp7ffppl4wxeq7osqfuu 258 2 2 2 CD work_ln56cwsp7ffppl4wxeq7osqfuu 258 3 × × CD work_ln56cwsp7ffppl4wxeq7osqfuu 258 4 3 3 CD work_ln56cwsp7ffppl4wxeq7osqfuu 258 5 societies society NNS work_ln56cwsp7ffppl4wxeq7osqfuu 258 6 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 258 7 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 258 8 any any DT work_ln56cwsp7ffppl4wxeq7osqfuu 258 9 culture culture NN work_ln56cwsp7ffppl4wxeq7osqfuu 258 10 with with IN work_ln56cwsp7ffppl4wxeq7osqfuu 258 11 a a DT work_ln56cwsp7ffppl4wxeq7osqfuu 258 12 symmetric symmetric JJ work_ln56cwsp7ffppl4wxeq7osqfuu 258 13 parabolic parabolic JJ work_ln56cwsp7ffppl4wxeq7osqfuu 258 14 function function NN work_ln56cwsp7ffppl4wxeq7osqfuu 258 15 : : : work_ln56cwsp7ffppl4wxeq7osqfuu 258 16 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 258 17 1 1 LS work_ln56cwsp7ffppl4wxeq7osqfuu 258 18 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 258 19 The the DT work_ln56cwsp7ffppl4wxeq7osqfuu 258 20 maximum maximum JJ work_ln56cwsp7ffppl4wxeq7osqfuu 258 21 βUT βut NN work_ln56cwsp7ffppl4wxeq7osqfuu 258 22 -optimal -optimal JJ work_ln56cwsp7ffppl4wxeq7osqfuu 258 23 rule rule NN work_ln56cwsp7ffppl4wxeq7osqfuu 258 24 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 258 25 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 258 26 implosion implosion NN work_ln56cwsp7ffppl4wxeq7osqfuu 258 27 scoring score VBG work_ln56cwsp7ffppl4wxeq7osqfuu 258 28 rule rule NN work_ln56cwsp7ffppl4wxeq7osqfuu 258 29 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 259 1 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 259 2 2 2 LS work_ln56cwsp7ffppl4wxeq7osqfuu 259 3 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 259 4 The the DT work_ln56cwsp7ffppl4wxeq7osqfuu 259 5 intersection intersection NN work_ln56cwsp7ffppl4wxeq7osqfuu 259 6 between between IN work_ln56cwsp7ffppl4wxeq7osqfuu 259 7 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 259 8 alternatives alternative NNS work_ln56cwsp7ffppl4wxeq7osqfuu 259 9 selected select VBN work_ln56cwsp7ffppl4wxeq7osqfuu 259 10 by by IN work_ln56cwsp7ffppl4wxeq7osqfuu 259 11 Borda Borda NNP work_ln56cwsp7ffppl4wxeq7osqfuu 259 12 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 259 13 those those DT work_ln56cwsp7ffppl4wxeq7osqfuu 259 14 selected select VBN work_ln56cwsp7ffppl4wxeq7osqfuu 259 15 by by IN work_ln56cwsp7ffppl4wxeq7osqfuu 259 16 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 259 17 maximum maximum JJ work_ln56cwsp7ffppl4wxeq7osqfuu 259 18 βUT βut NN work_ln56cwsp7ffppl4wxeq7osqfuu 259 19 -optimal -optimal JJ work_ln56cwsp7ffppl4wxeq7osqfuu 259 20 rule rule NN work_ln56cwsp7ffppl4wxeq7osqfuu 259 21 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 259 22 always always RB work_ln56cwsp7ffppl4wxeq7osqfuu 259 23 non non JJ work_ln56cwsp7ffppl4wxeq7osqfuu 259 24 - - JJ work_ln56cwsp7ffppl4wxeq7osqfuu 259 25 empty empty JJ work_ln56cwsp7ffppl4wxeq7osqfuu 259 26 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 260 1 The the DT work_ln56cwsp7ffppl4wxeq7osqfuu 260 2 analysis analysis NN work_ln56cwsp7ffppl4wxeq7osqfuu 260 3 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 260 4 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 260 5 2 2 CD work_ln56cwsp7ffppl4wxeq7osqfuu 260 6 × × NN work_ln56cwsp7ffppl4wxeq7osqfuu 260 7 3 3 CD work_ln56cwsp7ffppl4wxeq7osqfuu 260 8 case case NN work_ln56cwsp7ffppl4wxeq7osqfuu 260 9 shows show VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 260 10 that that IN work_ln56cwsp7ffppl4wxeq7osqfuu 260 11 any any DT work_ln56cwsp7ffppl4wxeq7osqfuu 260 12 scoring score VBG work_ln56cwsp7ffppl4wxeq7osqfuu 260 13 rule rule NN work_ln56cwsp7ffppl4wxeq7osqfuu 260 14 with with IN work_ln56cwsp7ffppl4wxeq7osqfuu 260 15 S2 s2 NN work_ln56cwsp7ffppl4wxeq7osqfuu 260 16 ∈ ∈ NNS work_ln56cwsp7ffppl4wxeq7osqfuu 260 17 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 260 18 0 0 CD work_ln56cwsp7ffppl4wxeq7osqfuu 260 19 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 260 20 1/2 1/2 CD work_ln56cwsp7ffppl4wxeq7osqfuu 260 21 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 260 22 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 260 23 βUT βut NN work_ln56cwsp7ffppl4wxeq7osqfuu 260 24 -optimal -optimal JJ work_ln56cwsp7ffppl4wxeq7osqfuu 260 25 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 261 1 Moreover moreover RB work_ln56cwsp7ffppl4wxeq7osqfuu 261 2 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 261 3 it -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 261 4 also also RB work_ln56cwsp7ffppl4wxeq7osqfuu 261 5 shows show VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 261 6 that that IN work_ln56cwsp7ffppl4wxeq7osqfuu 261 7 although although IN work_ln56cwsp7ffppl4wxeq7osqfuu 261 8 Borda Borda NNP work_ln56cwsp7ffppl4wxeq7osqfuu 261 9 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 261 10 not not RB work_ln56cwsp7ffppl4wxeq7osqfuu 261 11 βUT βut NN work_ln56cwsp7ffppl4wxeq7osqfuu 261 12 -optimal -optimal JJ work_ln56cwsp7ffppl4wxeq7osqfuu 261 13 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 261 14 it -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 261 15 comes come VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 261 16 close close RB work_ln56cwsp7ffppl4wxeq7osqfuu 261 17 to to IN work_ln56cwsp7ffppl4wxeq7osqfuu 261 18 being be VBG work_ln56cwsp7ffppl4wxeq7osqfuu 261 19 so so RB work_ln56cwsp7ffppl4wxeq7osqfuu 261 20 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 262 1 For for IN work_ln56cwsp7ffppl4wxeq7osqfuu 262 2 every every DT work_ln56cwsp7ffppl4wxeq7osqfuu 262 3 type type NN work_ln56cwsp7ffppl4wxeq7osqfuu 262 4 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 262 5 society society NN work_ln56cwsp7ffppl4wxeq7osqfuu 262 6 M M NNP work_ln56cwsp7ffppl4wxeq7osqfuu 262 7 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 262 8 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 262 9 alternatives alternative NNS work_ln56cwsp7ffppl4wxeq7osqfuu 262 10 selected select VBN work_ln56cwsp7ffppl4wxeq7osqfuu 262 11 by by IN work_ln56cwsp7ffppl4wxeq7osqfuu 262 12 Borda Borda NNP work_ln56cwsp7ffppl4wxeq7osqfuu 262 13 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 262 14 implosion implosion NN work_ln56cwsp7ffppl4wxeq7osqfuu 262 15 coincide coincide NN work_ln56cwsp7ffppl4wxeq7osqfuu 262 16 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 262 17 except except IN work_ln56cwsp7ffppl4wxeq7osqfuu 262 18 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 262 19 one one CD work_ln56cwsp7ffppl4wxeq7osqfuu 262 20 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 262 21 which which WDT work_ln56cwsp7ffppl4wxeq7osqfuu 262 22 in in IN work_ln56cwsp7ffppl4wxeq7osqfuu 262 23 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 262 24 proof proof NN work_ln56cwsp7ffppl4wxeq7osqfuu 262 25 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 262 26 Theorem theorem NN work_ln56cwsp7ffppl4wxeq7osqfuu 262 27 3.5 3.5 CD work_ln56cwsp7ffppl4wxeq7osqfuu 262 28 we -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 262 29 call call VBP work_ln56cwsp7ffppl4wxeq7osqfuu 262 30 societies society NNS work_ln56cwsp7ffppl4wxeq7osqfuu 262 31 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 262 32 type type NN work_ln56cwsp7ffppl4wxeq7osqfuu 262 33 4 4 CD work_ln56cwsp7ffppl4wxeq7osqfuu 262 34 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 262 35 where where WRB work_ln56cwsp7ffppl4wxeq7osqfuu 262 36 Borda Borda NNP work_ln56cwsp7ffppl4wxeq7osqfuu 262 37 randomizes randomize VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 262 38 between between IN work_ln56cwsp7ffppl4wxeq7osqfuu 262 39 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 262 40 3 3 CD work_ln56cwsp7ffppl4wxeq7osqfuu 262 41 alternatives alternative NNS work_ln56cwsp7ffppl4wxeq7osqfuu 262 42 while while IN work_ln56cwsp7ffppl4wxeq7osqfuu 262 43 implosion implosion NN work_ln56cwsp7ffppl4wxeq7osqfuu 262 44 randomizes randomize VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 262 45 between between IN work_ln56cwsp7ffppl4wxeq7osqfuu 262 46 2 2 CD work_ln56cwsp7ffppl4wxeq7osqfuu 262 47 alternatives alternative NNS work_ln56cwsp7ffppl4wxeq7osqfuu 262 48 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 263 1 We -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 263 2 extend extend VBP work_ln56cwsp7ffppl4wxeq7osqfuu 263 3 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 263 4 study study NN work_ln56cwsp7ffppl4wxeq7osqfuu 263 5 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 263 6 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 263 7 βUT βut NN work_ln56cwsp7ffppl4wxeq7osqfuu 263 8 -optimal -optimal JJ work_ln56cwsp7ffppl4wxeq7osqfuu 263 9 decision decision NN work_ln56cwsp7ffppl4wxeq7osqfuu 263 10 rule rule NN work_ln56cwsp7ffppl4wxeq7osqfuu 263 11 by by IN work_ln56cwsp7ffppl4wxeq7osqfuu 263 12 using use VBG work_ln56cwsp7ffppl4wxeq7osqfuu 263 13 computational computational JJ work_ln56cwsp7ffppl4wxeq7osqfuu 263 14 methods method NNS work_ln56cwsp7ffppl4wxeq7osqfuu 263 15 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 264 1 We -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 264 2 generate generate VBP work_ln56cwsp7ffppl4wxeq7osqfuu 264 3 random random JJ work_ln56cwsp7ffppl4wxeq7osqfuu 264 4 cardinal cardinal JJ work_ln56cwsp7ffppl4wxeq7osqfuu 264 5 societies society NNS work_ln56cwsp7ffppl4wxeq7osqfuu 264 6 from from IN work_ln56cwsp7ffppl4wxeq7osqfuu 264 7 three three CD work_ln56cwsp7ffppl4wxeq7osqfuu 264 8 different different JJ work_ln56cwsp7ffppl4wxeq7osqfuu 264 9 probability probability NN work_ln56cwsp7ffppl4wxeq7osqfuu 264 10 distributions distribution NNS work_ln56cwsp7ffppl4wxeq7osqfuu 264 11 : : : work_ln56cwsp7ffppl4wxeq7osqfuu 264 12 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 264 13 uniform uniform JJ work_ln56cwsp7ffppl4wxeq7osqfuu 264 14 distribution distribution NN work_ln56cwsp7ffppl4wxeq7osqfuu 264 15 on on IN work_ln56cwsp7ffppl4wxeq7osqfuu 264 16 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 264 17 interval interval NN work_ln56cwsp7ffppl4wxeq7osqfuu 264 18 [ [ -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 264 19 0 0 CD work_ln56cwsp7ffppl4wxeq7osqfuu 264 20 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 264 21 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 264 22 ] ] -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 264 23 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 264 24 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 264 25 standard standard JJ work_ln56cwsp7ffppl4wxeq7osqfuu 264 26 normal normal JJ work_ln56cwsp7ffppl4wxeq7osqfuu 264 27 distribution distribution NN work_ln56cwsp7ffppl4wxeq7osqfuu 264 28 on on IN work_ln56cwsp7ffppl4wxeq7osqfuu 264 29 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 264 30 interval interval NN work_ln56cwsp7ffppl4wxeq7osqfuu 264 31 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 264 32 −∞,∞ −∞,∞ NNP work_ln56cwsp7ffppl4wxeq7osqfuu 264 33 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 264 34 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 264 35 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 264 36 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 264 37 exponential exponential JJ work_ln56cwsp7ffppl4wxeq7osqfuu 264 38 distribution distribution NN work_ln56cwsp7ffppl4wxeq7osqfuu 264 39 on on IN work_ln56cwsp7ffppl4wxeq7osqfuu 264 40 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 264 41 interval interval NN work_ln56cwsp7ffppl4wxeq7osqfuu 264 42 [ [ -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 264 43 0,∞ 0,∞ NNP work_ln56cwsp7ffppl4wxeq7osqfuu 264 44 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 264 45 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 265 1 We -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 265 2 study study VBP work_ln56cwsp7ffppl4wxeq7osqfuu 265 3 societies society NNS work_ln56cwsp7ffppl4wxeq7osqfuu 265 4 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 265 5 2 2 CD work_ln56cwsp7ffppl4wxeq7osqfuu 265 6 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 265 7 3 3 CD work_ln56cwsp7ffppl4wxeq7osqfuu 265 8 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 265 9 5 5 CD work_ln56cwsp7ffppl4wxeq7osqfuu 265 10 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 265 11 10 10 CD work_ln56cwsp7ffppl4wxeq7osqfuu 265 12 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 265 13 100 100 CD work_ln56cwsp7ffppl4wxeq7osqfuu 265 14 individuals individual NNS work_ln56cwsp7ffppl4wxeq7osqfuu 265 15 with with IN work_ln56cwsp7ffppl4wxeq7osqfuu 265 16 preferences preference NNS work_ln56cwsp7ffppl4wxeq7osqfuu 265 17 over over IN work_ln56cwsp7ffppl4wxeq7osqfuu 265 18 3 3 CD work_ln56cwsp7ffppl4wxeq7osqfuu 265 19 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 265 20 4 4 CD work_ln56cwsp7ffppl4wxeq7osqfuu 265 21 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 265 22 5 5 CD work_ln56cwsp7ffppl4wxeq7osqfuu 265 23 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 265 24 7 7 CD work_ln56cwsp7ffppl4wxeq7osqfuu 265 25 alternatives alternative NNS work_ln56cwsp7ffppl4wxeq7osqfuu 265 26 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 266 1 The the DT work_ln56cwsp7ffppl4wxeq7osqfuu 266 2 technical technical JJ work_ln56cwsp7ffppl4wxeq7osqfuu 266 3 details detail NNS work_ln56cwsp7ffppl4wxeq7osqfuu 266 4 are be VBP work_ln56cwsp7ffppl4wxeq7osqfuu 266 5 contained contain VBN work_ln56cwsp7ffppl4wxeq7osqfuu 266 6 in in IN work_ln56cwsp7ffppl4wxeq7osqfuu 266 7 Appendix Appendix NNP work_ln56cwsp7ffppl4wxeq7osqfuu 266 8 B. B. NNP work_ln56cwsp7ffppl4wxeq7osqfuu 267 1 5We 5we CD work_ln56cwsp7ffppl4wxeq7osqfuu 267 2 say say VBP work_ln56cwsp7ffppl4wxeq7osqfuu 267 3 that that IN work_ln56cwsp7ffppl4wxeq7osqfuu 267 4 two two CD work_ln56cwsp7ffppl4wxeq7osqfuu 267 5 scoring score VBG work_ln56cwsp7ffppl4wxeq7osqfuu 267 6 rules rule NNS work_ln56cwsp7ffppl4wxeq7osqfuu 267 7 S S NNP work_ln56cwsp7ffppl4wxeq7osqfuu 267 8 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 267 9 S′ s′ NN work_ln56cwsp7ffppl4wxeq7osqfuu 267 10 are be VBP work_ln56cwsp7ffppl4wxeq7osqfuu 267 11 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 267 12 same same JJ work_ln56cwsp7ffppl4wxeq7osqfuu 267 13 if if IN work_ln56cwsp7ffppl4wxeq7osqfuu 267 14 S(M S(M NNP work_ln56cwsp7ffppl4wxeq7osqfuu 267 15 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 267 16 = = SYM work_ln56cwsp7ffppl4wxeq7osqfuu 267 17 S′(M S′(M NNP work_ln56cwsp7ffppl4wxeq7osqfuu 267 18 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 267 19 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 267 20 all all DT work_ln56cwsp7ffppl4wxeq7osqfuu 267 21 M. M. NNP work_ln56cwsp7ffppl4wxeq7osqfuu 267 22 12 12 CD work_ln56cwsp7ffppl4wxeq7osqfuu 267 23 The the DT work_ln56cwsp7ffppl4wxeq7osqfuu 267 24 main main JJ work_ln56cwsp7ffppl4wxeq7osqfuu 267 25 conclusion conclusion NN work_ln56cwsp7ffppl4wxeq7osqfuu 267 26 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 267 27 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 267 28 computational computational JJ work_ln56cwsp7ffppl4wxeq7osqfuu 267 29 analysis analysis NN work_ln56cwsp7ffppl4wxeq7osqfuu 267 30 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 267 31 very very RB work_ln56cwsp7ffppl4wxeq7osqfuu 267 32 clear clear JJ work_ln56cwsp7ffppl4wxeq7osqfuu 267 33 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 268 1 The the DT work_ln56cwsp7ffppl4wxeq7osqfuu 268 2 results result NNS work_ln56cwsp7ffppl4wxeq7osqfuu 268 3 across across IN work_ln56cwsp7ffppl4wxeq7osqfuu 268 4 probability probability NN work_ln56cwsp7ffppl4wxeq7osqfuu 268 5 distributions distribution NNS work_ln56cwsp7ffppl4wxeq7osqfuu 268 6 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 268 7 sizes size NNS work_ln56cwsp7ffppl4wxeq7osqfuu 268 8 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 268 9 societies society NNS work_ln56cwsp7ffppl4wxeq7osqfuu 268 10 are be VBP work_ln56cwsp7ffppl4wxeq7osqfuu 268 11 fully fully RB work_ln56cwsp7ffppl4wxeq7osqfuu 268 12 in in IN work_ln56cwsp7ffppl4wxeq7osqfuu 268 13 line line NN work_ln56cwsp7ffppl4wxeq7osqfuu 268 14 with with IN work_ln56cwsp7ffppl4wxeq7osqfuu 268 15 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 268 16 analytical analytical JJ work_ln56cwsp7ffppl4wxeq7osqfuu 268 17 results result NNS work_ln56cwsp7ffppl4wxeq7osqfuu 268 18 we -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 268 19 presented present VBD work_ln56cwsp7ffppl4wxeq7osqfuu 268 20 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 268 21 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 268 22 case case NN work_ln56cwsp7ffppl4wxeq7osqfuu 268 23 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 268 24 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 268 25 αUT αut NN work_ln56cwsp7ffppl4wxeq7osqfuu 268 26 -index -index NNP work_ln56cwsp7ffppl4wxeq7osqfuu 268 27 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 269 1 That that RB work_ln56cwsp7ffppl4wxeq7osqfuu 269 2 is is RB work_ln56cwsp7ffppl4wxeq7osqfuu 269 3 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 269 4 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 269 5 each each DT work_ln56cwsp7ffppl4wxeq7osqfuu 269 6 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 269 7 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 269 8 three three CD work_ln56cwsp7ffppl4wxeq7osqfuu 269 9 probability probability NN work_ln56cwsp7ffppl4wxeq7osqfuu 269 10 distributions distribution NNS work_ln56cwsp7ffppl4wxeq7osqfuu 269 11 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 269 12 sizes size NNS work_ln56cwsp7ffppl4wxeq7osqfuu 269 13 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 269 14 societies society NNS work_ln56cwsp7ffppl4wxeq7osqfuu 269 15 scrutinized scrutinize VBN work_ln56cwsp7ffppl4wxeq7osqfuu 269 16 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 269 17 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 269 18 scoring score VBG work_ln56cwsp7ffppl4wxeq7osqfuu 269 19 rule rule NN work_ln56cwsp7ffppl4wxeq7osqfuu 269 20 providing provide VBG work_ln56cwsp7ffppl4wxeq7osqfuu 269 21 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 269 22 highest high JJS work_ln56cwsp7ffppl4wxeq7osqfuu 269 23 βUT βut NN work_ln56cwsp7ffppl4wxeq7osqfuu 269 24 -value -value NN work_ln56cwsp7ffppl4wxeq7osqfuu 269 25 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 269 26 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 269 27 corresponding corresponding JJ work_ln56cwsp7ffppl4wxeq7osqfuu 269 28 one one CD work_ln56cwsp7ffppl4wxeq7osqfuu 269 29 as as IN work_ln56cwsp7ffppl4wxeq7osqfuu 269 30 stated state VBN work_ln56cwsp7ffppl4wxeq7osqfuu 269 31 in in IN work_ln56cwsp7ffppl4wxeq7osqfuu 269 32 Theorem Theorem NNP work_ln56cwsp7ffppl4wxeq7osqfuu 269 33 3.1 3.1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 269 34 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 270 1 In in IN work_ln56cwsp7ffppl4wxeq7osqfuu 270 2 particular particular JJ work_ln56cwsp7ffppl4wxeq7osqfuu 270 3 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 270 4 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 270 5 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 270 6 uniform uniform JJ work_ln56cwsp7ffppl4wxeq7osqfuu 270 7 distribution distribution NN work_ln56cwsp7ffppl4wxeq7osqfuu 270 8 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 270 9 highest high JJS work_ln56cwsp7ffppl4wxeq7osqfuu 270 10 βUT βut NN work_ln56cwsp7ffppl4wxeq7osqfuu 270 11 -value -value NN work_ln56cwsp7ffppl4wxeq7osqfuu 270 12 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 270 13 given give VBN work_ln56cwsp7ffppl4wxeq7osqfuu 270 14 by by IN work_ln56cwsp7ffppl4wxeq7osqfuu 270 15 Borda Borda NNP work_ln56cwsp7ffppl4wxeq7osqfuu 270 16 ; ; : work_ln56cwsp7ffppl4wxeq7osqfuu 270 17 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 270 18 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 270 19 normal normal JJ work_ln56cwsp7ffppl4wxeq7osqfuu 270 20 distribution distribution NN work_ln56cwsp7ffppl4wxeq7osqfuu 270 21 it -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 270 22 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 270 23 given give VBN work_ln56cwsp7ffppl4wxeq7osqfuu 270 24 by by IN work_ln56cwsp7ffppl4wxeq7osqfuu 270 25 a a DT work_ln56cwsp7ffppl4wxeq7osqfuu 270 26 scoring scoring JJ work_ln56cwsp7ffppl4wxeq7osqfuu 270 27 rule rule NN work_ln56cwsp7ffppl4wxeq7osqfuu 270 28 where where WRB work_ln56cwsp7ffppl4wxeq7osqfuu 270 29 S∗l+1 S∗l+1 NNS work_ln56cwsp7ffppl4wxeq7osqfuu 270 30 −S∗l −S∗l NNP work_ln56cwsp7ffppl4wxeq7osqfuu 270 31 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 270 32 a a DT work_ln56cwsp7ffppl4wxeq7osqfuu 270 33 symmetric symmetric JJ work_ln56cwsp7ffppl4wxeq7osqfuu 270 34 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 270 35 convex convex NNP work_ln56cwsp7ffppl4wxeq7osqfuu 270 36 function function VBP work_ln56cwsp7ffppl4wxeq7osqfuu 270 37 ; ; : work_ln56cwsp7ffppl4wxeq7osqfuu 270 38 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 270 39 finally finally RB work_ln56cwsp7ffppl4wxeq7osqfuu 270 40 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 270 41 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 270 42 exponential exponential JJ work_ln56cwsp7ffppl4wxeq7osqfuu 270 43 distribution distribution NN work_ln56cwsp7ffppl4wxeq7osqfuu 270 44 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 270 45 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 270 46 highest high JJS work_ln56cwsp7ffppl4wxeq7osqfuu 270 47 βUT βut NN work_ln56cwsp7ffppl4wxeq7osqfuu 270 48 -value -value NN work_ln56cwsp7ffppl4wxeq7osqfuu 270 49 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 270 50 given give VBN work_ln56cwsp7ffppl4wxeq7osqfuu 270 51 by by IN work_ln56cwsp7ffppl4wxeq7osqfuu 270 52 a a DT work_ln56cwsp7ffppl4wxeq7osqfuu 270 53 scoring scoring JJ work_ln56cwsp7ffppl4wxeq7osqfuu 270 54 rule rule NN work_ln56cwsp7ffppl4wxeq7osqfuu 270 55 where where WRB work_ln56cwsp7ffppl4wxeq7osqfuu 270 56 S∗l+1 S∗l+1 NNS work_ln56cwsp7ffppl4wxeq7osqfuu 270 57 −S∗l −S∗l NNP work_ln56cwsp7ffppl4wxeq7osqfuu 270 58 grows grow VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 270 59 exponentially.6 exponentially.6 CD work_ln56cwsp7ffppl4wxeq7osqfuu 270 60 3.3 3.3 CD work_ln56cwsp7ffppl4wxeq7osqfuu 270 61 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 271 1 The the DT work_ln56cwsp7ffppl4wxeq7osqfuu 271 2 γUT γut CD work_ln56cwsp7ffppl4wxeq7osqfuu 271 3 -index -index NNP work_ln56cwsp7ffppl4wxeq7osqfuu 271 4 : : : work_ln56cwsp7ffppl4wxeq7osqfuu 271 5 Evaluating evaluate VBG work_ln56cwsp7ffppl4wxeq7osqfuu 271 6 Decision Decision NNP work_ln56cwsp7ffppl4wxeq7osqfuu 271 7 Rules rule NNS work_ln56cwsp7ffppl4wxeq7osqfuu 271 8 in in IN work_ln56cwsp7ffppl4wxeq7osqfuu 271 9 terms term NNS work_ln56cwsp7ffppl4wxeq7osqfuu 271 10 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 271 11 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 271 12 Probabil- Probabil- NNP work_ln56cwsp7ffppl4wxeq7osqfuu 271 13 ity ity NN work_ln56cwsp7ffppl4wxeq7osqfuu 271 14 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 271 15 Not not RB work_ln56cwsp7ffppl4wxeq7osqfuu 271 16 Choosing choose VBG work_ln56cwsp7ffppl4wxeq7osqfuu 271 17 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 271 18 Worst bad JJS work_ln56cwsp7ffppl4wxeq7osqfuu 271 19 Alternative alternative NN work_ln56cwsp7ffppl4wxeq7osqfuu 271 20 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 272 1 It -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 272 2 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 272 3 not not RB work_ln56cwsp7ffppl4wxeq7osqfuu 272 4 difficult difficult JJ work_ln56cwsp7ffppl4wxeq7osqfuu 272 5 to to TO work_ln56cwsp7ffppl4wxeq7osqfuu 272 6 appreciate appreciate VB work_ln56cwsp7ffppl4wxeq7osqfuu 272 7 that that DT work_ln56cwsp7ffppl4wxeq7osqfuu 272 8 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 272 9 utilitarianism utilitarianism NN work_ln56cwsp7ffppl4wxeq7osqfuu 272 10 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 272 11 symmetry symmetry NN work_ln56cwsp7ffppl4wxeq7osqfuu 272 12 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 272 13 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 272 14 culture culture NN work_ln56cwsp7ffppl4wxeq7osqfuu 272 15 C C NNP work_ln56cwsp7ffppl4wxeq7osqfuu 272 16 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 272 17 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 272 18 γ γ NNP work_ln56cwsp7ffppl4wxeq7osqfuu 272 19 - - HYPH work_ln56cwsp7ffppl4wxeq7osqfuu 272 20 index index NN work_ln56cwsp7ffppl4wxeq7osqfuu 272 21 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 272 22 symmetric symmetric JJ work_ln56cwsp7ffppl4wxeq7osqfuu 272 23 to to IN work_ln56cwsp7ffppl4wxeq7osqfuu 272 24 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 272 25 β β NNP work_ln56cwsp7ffppl4wxeq7osqfuu 272 26 - - HYPH work_ln56cwsp7ffppl4wxeq7osqfuu 272 27 index index NN work_ln56cwsp7ffppl4wxeq7osqfuu 272 28 in in IN work_ln56cwsp7ffppl4wxeq7osqfuu 272 29 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 272 30 following following JJ work_ln56cwsp7ffppl4wxeq7osqfuu 272 31 sense sense NN work_ln56cwsp7ffppl4wxeq7osqfuu 272 32 : : : work_ln56cwsp7ffppl4wxeq7osqfuu 272 33 take take VB work_ln56cwsp7ffppl4wxeq7osqfuu 272 34 a a DT work_ln56cwsp7ffppl4wxeq7osqfuu 272 35 society society NN work_ln56cwsp7ffppl4wxeq7osqfuu 272 36 { { -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 272 37 Uli}i∈N Uli}i∈N NNP work_ln56cwsp7ffppl4wxeq7osqfuu 272 38 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 272 39 l∈K l∈K NNP work_ln56cwsp7ffppl4wxeq7osqfuu 272 40 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 272 41 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 272 42 let let VB work_ln56cwsp7ffppl4wxeq7osqfuu 272 43 l l PRP work_ln56cwsp7ffppl4wxeq7osqfuu 272 44 be be VB work_ln56cwsp7ffppl4wxeq7osqfuu 272 45 an an DT work_ln56cwsp7ffppl4wxeq7osqfuu 272 46 al- al- JJ work_ln56cwsp7ffppl4wxeq7osqfuu 272 47 ternative ternative NN work_ln56cwsp7ffppl4wxeq7osqfuu 272 48 giving give VBG work_ln56cwsp7ffppl4wxeq7osqfuu 272 49 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 272 50 highest high JJS work_ln56cwsp7ffppl4wxeq7osqfuu 272 51 utilitarian utilitarian JJ work_ln56cwsp7ffppl4wxeq7osqfuu 272 52 value value NN work_ln56cwsp7ffppl4wxeq7osqfuu 272 53 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 273 1 Write write VB work_ln56cwsp7ffppl4wxeq7osqfuu 273 2 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 273 3 following following JJ work_ln56cwsp7ffppl4wxeq7osqfuu 273 4 symmetric symmetric JJ work_ln56cwsp7ffppl4wxeq7osqfuu 273 5 society society NN work_ln56cwsp7ffppl4wxeq7osqfuu 273 6 { { -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 273 7 U U NNP work_ln56cwsp7ffppl4wxeq7osqfuu 273 8 ′li ′li NNP work_ln56cwsp7ffppl4wxeq7osqfuu 273 9 } } -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 273 10 i∈N i∈n JJ work_ln56cwsp7ffppl4wxeq7osqfuu 273 11 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 273 12 l∈K l∈k JJ work_ln56cwsp7ffppl4wxeq7osqfuu 273 13 with with IN work_ln56cwsp7ffppl4wxeq7osqfuu 273 14 U U NNP work_ln56cwsp7ffppl4wxeq7osqfuu 273 15 ′l ′l NNP work_ln56cwsp7ffppl4wxeq7osqfuu 273 16 i i NN work_ln56cwsp7ffppl4wxeq7osqfuu 273 17 = = SYM work_ln56cwsp7ffppl4wxeq7osqfuu 273 18 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 273 19 −Ulσ(i −Ulσ(i NNS work_ln56cwsp7ffppl4wxeq7osqfuu 273 20 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 273 21 where where WRB work_ln56cwsp7ffppl4wxeq7osqfuu 273 22 σ(i σ(i NN work_ln56cwsp7ffppl4wxeq7osqfuu 273 23 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 273 24 = = NFP work_ln56cwsp7ffppl4wxeq7osqfuu 273 25 n− n− NNP work_ln56cwsp7ffppl4wxeq7osqfuu 273 26 i i PRP work_ln56cwsp7ffppl4wxeq7osqfuu 273 27 + + CC work_ln56cwsp7ffppl4wxeq7osqfuu 273 28 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 273 29 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 274 1 It -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 274 2 follows follow VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 274 3 that that IN work_ln56cwsp7ffppl4wxeq7osqfuu 274 4 alternative alternative JJ work_ln56cwsp7ffppl4wxeq7osqfuu 274 5 l l NN work_ln56cwsp7ffppl4wxeq7osqfuu 274 6 in in IN work_ln56cwsp7ffppl4wxeq7osqfuu 274 7 society society NN work_ln56cwsp7ffppl4wxeq7osqfuu 274 8 { { -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 274 9 U U NNP work_ln56cwsp7ffppl4wxeq7osqfuu 274 10 ′li ′li NNP work_ln56cwsp7ffppl4wxeq7osqfuu 274 11 } } -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 274 12 i∈N i∈n JJ work_ln56cwsp7ffppl4wxeq7osqfuu 274 13 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 274 14 l∈K l∈K NNP work_ln56cwsp7ffppl4wxeq7osqfuu 274 15 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 274 16 one one CD work_ln56cwsp7ffppl4wxeq7osqfuu 274 17 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 274 18 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 274 19 worst bad JJS work_ln56cwsp7ffppl4wxeq7osqfuu 274 20 alternatives alternative NNS work_ln56cwsp7ffppl4wxeq7osqfuu 274 21 in in IN work_ln56cwsp7ffppl4wxeq7osqfuu 274 22 utilitarian utilitarian JJ work_ln56cwsp7ffppl4wxeq7osqfuu 274 23 terms term NNS work_ln56cwsp7ffppl4wxeq7osqfuu 274 24 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 275 1 Then then RB work_ln56cwsp7ffppl4wxeq7osqfuu 275 2 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 275 3 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 275 4 analytical analytical JJ work_ln56cwsp7ffppl4wxeq7osqfuu 275 5 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 275 6 simulation simulation NN work_ln56cwsp7ffppl4wxeq7osqfuu 275 7 results result NNS work_ln56cwsp7ffppl4wxeq7osqfuu 275 8 that that WDT work_ln56cwsp7ffppl4wxeq7osqfuu 275 9 we -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 275 10 obtained obtain VBD work_ln56cwsp7ffppl4wxeq7osqfuu 275 11 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 275 12 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 275 13 β β NNP work_ln56cwsp7ffppl4wxeq7osqfuu 275 14 - - HYPH work_ln56cwsp7ffppl4wxeq7osqfuu 275 15 index index NN work_ln56cwsp7ffppl4wxeq7osqfuu 275 16 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 275 17 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 275 18 symmetric symmetric JJ work_ln56cwsp7ffppl4wxeq7osqfuu 275 19 cultures culture NNS work_ln56cwsp7ffppl4wxeq7osqfuu 275 20 can can MD work_ln56cwsp7ffppl4wxeq7osqfuu 275 21 be be VB work_ln56cwsp7ffppl4wxeq7osqfuu 275 22 extrapolated extrapolate VBN work_ln56cwsp7ffppl4wxeq7osqfuu 275 23 to to IN work_ln56cwsp7ffppl4wxeq7osqfuu 275 24 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 275 25 case case NN work_ln56cwsp7ffppl4wxeq7osqfuu 275 26 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 275 27 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 275 28 γ γ NN work_ln56cwsp7ffppl4wxeq7osqfuu 275 29 - - HYPH work_ln56cwsp7ffppl4wxeq7osqfuu 275 30 index index NN work_ln56cwsp7ffppl4wxeq7osqfuu 275 31 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 276 1 To to TO work_ln56cwsp7ffppl4wxeq7osqfuu 276 2 complete complete VB work_ln56cwsp7ffppl4wxeq7osqfuu 276 3 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 276 4 picture picture NN work_ln56cwsp7ffppl4wxeq7osqfuu 276 5 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 276 6 we -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 276 7 run run VBP work_ln56cwsp7ffppl4wxeq7osqfuu 276 8 an an DT work_ln56cwsp7ffppl4wxeq7osqfuu 276 9 extra extra JJ work_ln56cwsp7ffppl4wxeq7osqfuu 276 10 set set NN work_ln56cwsp7ffppl4wxeq7osqfuu 276 11 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 276 12 simulations simulation NNS work_ln56cwsp7ffppl4wxeq7osqfuu 276 13 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 276 14 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 276 15 exponential exponential JJ work_ln56cwsp7ffppl4wxeq7osqfuu 276 16 distribution distribution NN work_ln56cwsp7ffppl4wxeq7osqfuu 276 17 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 276 18 an an DT work_ln56cwsp7ffppl4wxeq7osqfuu 276 19 asymmetric asymmetric JJ work_ln56cwsp7ffppl4wxeq7osqfuu 276 20 distri- distri- NN work_ln56cwsp7ffppl4wxeq7osqfuu 276 21 bution bution NN work_ln56cwsp7ffppl4wxeq7osqfuu 276 22 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 276 23 that that WDT work_ln56cwsp7ffppl4wxeq7osqfuu 276 24 points point VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 276 25 to to TO work_ln56cwsp7ffppl4wxeq7osqfuu 276 26 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 276 27 once once RB work_ln56cwsp7ffppl4wxeq7osqfuu 276 28 again again RB work_ln56cwsp7ffppl4wxeq7osqfuu 276 29 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 276 30 that that IN work_ln56cwsp7ffppl4wxeq7osqfuu 276 31 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 276 32 particular particular JJ work_ln56cwsp7ffppl4wxeq7osqfuu 276 33 index index NN work_ln56cwsp7ffppl4wxeq7osqfuu 276 34 to to TO work_ln56cwsp7ffppl4wxeq7osqfuu 276 35 measure measure VB work_ln56cwsp7ffppl4wxeq7osqfuu 276 36 performance performance NN work_ln56cwsp7ffppl4wxeq7osqfuu 276 37 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 276 38 not not RB work_ln56cwsp7ffppl4wxeq7osqfuu 276 39 essential essential JJ work_ln56cwsp7ffppl4wxeq7osqfuu 276 40 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 276 41 see see VB work_ln56cwsp7ffppl4wxeq7osqfuu 276 42 Appendix Appendix NNP work_ln56cwsp7ffppl4wxeq7osqfuu 276 43 B B NNP work_ln56cwsp7ffppl4wxeq7osqfuu 276 44 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 276 45 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 277 1 We -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 277 2 may may MD work_ln56cwsp7ffppl4wxeq7osqfuu 277 3 conclude conclude VB work_ln56cwsp7ffppl4wxeq7osqfuu 277 4 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 277 5 therefore therefore RB work_ln56cwsp7ffppl4wxeq7osqfuu 277 6 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 277 7 that that IN work_ln56cwsp7ffppl4wxeq7osqfuu 277 8 at at IN work_ln56cwsp7ffppl4wxeq7osqfuu 277 9 least least JJS work_ln56cwsp7ffppl4wxeq7osqfuu 277 10 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 277 11 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 277 12 cases case NNS work_ln56cwsp7ffppl4wxeq7osqfuu 277 13 computationally computationally RB work_ln56cwsp7ffppl4wxeq7osqfuu 277 14 scrutinized scrutinize VBN work_ln56cwsp7ffppl4wxeq7osqfuu 277 15 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 277 16 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 277 17 optimal optimal JJ work_ln56cwsp7ffppl4wxeq7osqfuu 277 18 decision decision NN work_ln56cwsp7ffppl4wxeq7osqfuu 277 19 rules rule NNS work_ln56cwsp7ffppl4wxeq7osqfuu 277 20 in in IN work_ln56cwsp7ffppl4wxeq7osqfuu 277 21 terms term NNS work_ln56cwsp7ffppl4wxeq7osqfuu 277 22 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 277 23 γUT γUT NNS work_ln56cwsp7ffppl4wxeq7osqfuu 277 24 are be VBP work_ln56cwsp7ffppl4wxeq7osqfuu 277 25 well well RB work_ln56cwsp7ffppl4wxeq7osqfuu 277 26 captured capture VBN work_ln56cwsp7ffppl4wxeq7osqfuu 277 27 in in IN work_ln56cwsp7ffppl4wxeq7osqfuu 277 28 Theorem Theorem NNP work_ln56cwsp7ffppl4wxeq7osqfuu 277 29 3.1 3.1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 277 30 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 278 1 4 4 LS work_ln56cwsp7ffppl4wxeq7osqfuu 278 2 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 279 1 Maximax Maximax NNP work_ln56cwsp7ffppl4wxeq7osqfuu 279 2 We -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 279 3 start start VBP work_ln56cwsp7ffppl4wxeq7osqfuu 279 4 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 279 5 analysis analysis NN work_ln56cwsp7ffppl4wxeq7osqfuu 279 6 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 279 7 maximax maximax NNP work_ln56cwsp7ffppl4wxeq7osqfuu 279 8 by by IN work_ln56cwsp7ffppl4wxeq7osqfuu 279 9 showing show VBG work_ln56cwsp7ffppl4wxeq7osqfuu 279 10 formally formally RB work_ln56cwsp7ffppl4wxeq7osqfuu 279 11 that that DT work_ln56cwsp7ffppl4wxeq7osqfuu 279 12 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 279 13 any any DT work_ln56cwsp7ffppl4wxeq7osqfuu 279 14 n×k n×k NNP work_ln56cwsp7ffppl4wxeq7osqfuu 279 15 society society NN work_ln56cwsp7ffppl4wxeq7osqfuu 279 16 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 279 17 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 279 18 any any DT work_ln56cwsp7ffppl4wxeq7osqfuu 279 19 culture culture NN work_ln56cwsp7ffppl4wxeq7osqfuu 279 20 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 279 21 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 279 22 maximum maximum JJ work_ln56cwsp7ffppl4wxeq7osqfuu 279 23 optimal optimal JJ work_ln56cwsp7ffppl4wxeq7osqfuu 279 24 decision decision NN work_ln56cwsp7ffppl4wxeq7osqfuu 279 25 rule rule NN work_ln56cwsp7ffppl4wxeq7osqfuu 279 26 in in IN work_ln56cwsp7ffppl4wxeq7osqfuu 279 27 terms term NNS work_ln56cwsp7ffppl4wxeq7osqfuu 279 28 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 279 29 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 279 30 probability probability NN work_ln56cwsp7ffppl4wxeq7osqfuu 279 31 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 279 32 selecting select VBG work_ln56cwsp7ffppl4wxeq7osqfuu 279 33 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 279 34 maximax maximax NNP work_ln56cwsp7ffppl4wxeq7osqfuu 279 35 alternatives alternative NNS work_ln56cwsp7ffppl4wxeq7osqfuu 279 36 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 279 37 a a DT work_ln56cwsp7ffppl4wxeq7osqfuu 279 38 scoring score VBG work_ln56cwsp7ffppl4wxeq7osqfuu 279 39 rule rule NN work_ln56cwsp7ffppl4wxeq7osqfuu 279 40 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 280 1 In in IN work_ln56cwsp7ffppl4wxeq7osqfuu 280 2 fact fact NN work_ln56cwsp7ffppl4wxeq7osqfuu 280 3 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 280 4 it -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 280 5 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 280 6 a a DT work_ln56cwsp7ffppl4wxeq7osqfuu 280 7 particularly particularly RB work_ln56cwsp7ffppl4wxeq7osqfuu 280 8 simple simple JJ work_ln56cwsp7ffppl4wxeq7osqfuu 280 9 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 280 10 widely widely RB work_ln56cwsp7ffppl4wxeq7osqfuu 280 11 used use VBN work_ln56cwsp7ffppl4wxeq7osqfuu 280 12 scoring score VBG work_ln56cwsp7ffppl4wxeq7osqfuu 280 13 rule rule NN work_ln56cwsp7ffppl4wxeq7osqfuu 280 14 : : : work_ln56cwsp7ffppl4wxeq7osqfuu 280 15 plurality plurality NN work_ln56cwsp7ffppl4wxeq7osqfuu 280 16 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 281 1 The the DT work_ln56cwsp7ffppl4wxeq7osqfuu 281 2 intuition intuition NN work_ln56cwsp7ffppl4wxeq7osqfuu 281 3 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 281 4 very very RB work_ln56cwsp7ffppl4wxeq7osqfuu 281 5 simple simple JJ work_ln56cwsp7ffppl4wxeq7osqfuu 281 6 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 282 1 Maxi- Maxi- NNP work_ln56cwsp7ffppl4wxeq7osqfuu 282 2 max max NNP work_ln56cwsp7ffppl4wxeq7osqfuu 282 3 evaluates evaluate VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 282 4 an an DT work_ln56cwsp7ffppl4wxeq7osqfuu 282 5 alternative alternative JJ work_ln56cwsp7ffppl4wxeq7osqfuu 282 6 l l NN work_ln56cwsp7ffppl4wxeq7osqfuu 282 7 in in IN work_ln56cwsp7ffppl4wxeq7osqfuu 282 8 terms term NNS work_ln56cwsp7ffppl4wxeq7osqfuu 282 9 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 282 10 that that DT work_ln56cwsp7ffppl4wxeq7osqfuu 282 11 individual individual NN work_ln56cwsp7ffppl4wxeq7osqfuu 282 12 that that IN work_ln56cwsp7ffppl4wxeq7osqfuu 282 13 most most JJS work_ln56cwsp7ffppl4wxeq7osqfuu 282 14 values value NNS work_ln56cwsp7ffppl4wxeq7osqfuu 282 15 alternative alternative VBP work_ln56cwsp7ffppl4wxeq7osqfuu 282 16 l. l. NNP work_ln56cwsp7ffppl4wxeq7osqfuu 282 17 It -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 282 18 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 282 19 very very RB work_ln56cwsp7ffppl4wxeq7osqfuu 282 20 likely likely JJ work_ln56cwsp7ffppl4wxeq7osqfuu 282 21 that that IN work_ln56cwsp7ffppl4wxeq7osqfuu 282 22 such such PDT work_ln56cwsp7ffppl4wxeq7osqfuu 282 23 an an DT work_ln56cwsp7ffppl4wxeq7osqfuu 282 24 individual individual JJ work_ln56cwsp7ffppl4wxeq7osqfuu 282 25 ranks rank VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 282 26 l l NN work_ln56cwsp7ffppl4wxeq7osqfuu 282 27 as as IN work_ln56cwsp7ffppl4wxeq7osqfuu 282 28 her -PRON- PRP$ work_ln56cwsp7ffppl4wxeq7osqfuu 282 29 most most RBS work_ln56cwsp7ffppl4wxeq7osqfuu 282 30 preferred preferred JJ work_ln56cwsp7ffppl4wxeq7osqfuu 282 31 alternative alternative NN work_ln56cwsp7ffppl4wxeq7osqfuu 282 32 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 283 1 Consequently consequently RB work_ln56cwsp7ffppl4wxeq7osqfuu 283 2 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 283 3 those those DT work_ln56cwsp7ffppl4wxeq7osqfuu 283 4 alternatives alternative NNS work_ln56cwsp7ffppl4wxeq7osqfuu 283 5 that that WDT work_ln56cwsp7ffppl4wxeq7osqfuu 283 6 are be VBP work_ln56cwsp7ffppl4wxeq7osqfuu 283 7 considered consider VBN work_ln56cwsp7ffppl4wxeq7osqfuu 283 8 by by IN work_ln56cwsp7ffppl4wxeq7osqfuu 283 9 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 283 10 highest high JJS work_ln56cwsp7ffppl4wxeq7osqfuu 283 11 number number NN work_ln56cwsp7ffppl4wxeq7osqfuu 283 12 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 283 13 indi- indi- NN work_ln56cwsp7ffppl4wxeq7osqfuu 283 14 viduals vidual NNS work_ln56cwsp7ffppl4wxeq7osqfuu 283 15 as as IN work_ln56cwsp7ffppl4wxeq7osqfuu 283 16 best good JJS work_ln56cwsp7ffppl4wxeq7osqfuu 283 17 are be VBP work_ln56cwsp7ffppl4wxeq7osqfuu 283 18 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 283 19 most most RBS work_ln56cwsp7ffppl4wxeq7osqfuu 283 20 likely likely JJ work_ln56cwsp7ffppl4wxeq7osqfuu 283 21 maximax maximax NNP work_ln56cwsp7ffppl4wxeq7osqfuu 283 22 alternatives alternative NNS work_ln56cwsp7ffppl4wxeq7osqfuu 283 23 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 284 1 Plurality plurality NN work_ln56cwsp7ffppl4wxeq7osqfuu 284 2 selects select NNS work_ln56cwsp7ffppl4wxeq7osqfuu 284 3 precisely precisely RB work_ln56cwsp7ffppl4wxeq7osqfuu 284 4 these these DT work_ln56cwsp7ffppl4wxeq7osqfuu 284 5 alternatives alternative NNS work_ln56cwsp7ffppl4wxeq7osqfuu 284 6 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 285 1 The the DT work_ln56cwsp7ffppl4wxeq7osqfuu 285 2 analytical analytical JJ work_ln56cwsp7ffppl4wxeq7osqfuu 285 3 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 285 4 computational computational JJ work_ln56cwsp7ffppl4wxeq7osqfuu 285 5 study study NN work_ln56cwsp7ffppl4wxeq7osqfuu 285 6 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 285 7 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 285 8 two two CD work_ln56cwsp7ffppl4wxeq7osqfuu 285 9 other other JJ work_ln56cwsp7ffppl4wxeq7osqfuu 285 10 indices index NNS work_ln56cwsp7ffppl4wxeq7osqfuu 285 11 reinforce reinforce VBP work_ln56cwsp7ffppl4wxeq7osqfuu 285 12 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 285 13 connection connection NN work_ln56cwsp7ffppl4wxeq7osqfuu 285 14 between between IN work_ln56cwsp7ffppl4wxeq7osqfuu 285 15 plurality plurality NN work_ln56cwsp7ffppl4wxeq7osqfuu 285 16 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 285 17 maximax maximax NNP work_ln56cwsp7ffppl4wxeq7osqfuu 285 18 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 286 1 6For 6For NFP work_ln56cwsp7ffppl4wxeq7osqfuu 286 2 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 286 3 sake sake NN work_ln56cwsp7ffppl4wxeq7osqfuu 286 4 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 286 5 comparison comparison NN work_ln56cwsp7ffppl4wxeq7osqfuu 286 6 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 286 7 Appendix Appendix NNP work_ln56cwsp7ffppl4wxeq7osqfuu 286 8 B B NNP work_ln56cwsp7ffppl4wxeq7osqfuu 286 9 reports report VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 286 10 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 286 11 βU βu NN work_ln56cwsp7ffppl4wxeq7osqfuu 286 12 T T NNP work_ln56cwsp7ffppl4wxeq7osqfuu 286 13 -values -values NNP work_ln56cwsp7ffppl4wxeq7osqfuu 286 14 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 286 15 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 286 16 optimal optimal JJ work_ln56cwsp7ffppl4wxeq7osqfuu 286 17 scoring score VBG work_ln56cwsp7ffppl4wxeq7osqfuu 286 18 rules rule NNS work_ln56cwsp7ffppl4wxeq7osqfuu 286 19 as as IN work_ln56cwsp7ffppl4wxeq7osqfuu 286 20 predicted predict VBN work_ln56cwsp7ffppl4wxeq7osqfuu 286 21 by by IN work_ln56cwsp7ffppl4wxeq7osqfuu 286 22 Theorem Theorem NNP work_ln56cwsp7ffppl4wxeq7osqfuu 286 23 3.1 3.1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 286 24 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 286 25 together together RB work_ln56cwsp7ffppl4wxeq7osqfuu 286 26 with with IN work_ln56cwsp7ffppl4wxeq7osqfuu 286 27 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 286 28 three three CD work_ln56cwsp7ffppl4wxeq7osqfuu 286 29 prominent prominent JJ work_ln56cwsp7ffppl4wxeq7osqfuu 286 30 scoring score VBG work_ln56cwsp7ffppl4wxeq7osqfuu 286 31 rules rule NNS work_ln56cwsp7ffppl4wxeq7osqfuu 286 32 – – : work_ln56cwsp7ffppl4wxeq7osqfuu 286 33 plurality plurality NN work_ln56cwsp7ffppl4wxeq7osqfuu 286 34 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 286 35 Borda Borda NNP work_ln56cwsp7ffppl4wxeq7osqfuu 286 36 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 286 37 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 286 38 negative negative JJ work_ln56cwsp7ffppl4wxeq7osqfuu 286 39 – – : work_ln56cwsp7ffppl4wxeq7osqfuu 286 40 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 286 41 each each DT work_ln56cwsp7ffppl4wxeq7osqfuu 286 42 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 286 43 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 286 44 societies society NNS work_ln56cwsp7ffppl4wxeq7osqfuu 286 45 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 286 46 cultures culture NNS work_ln56cwsp7ffppl4wxeq7osqfuu 286 47 under under IN work_ln56cwsp7ffppl4wxeq7osqfuu 286 48 scrutiny scrutiny NN work_ln56cwsp7ffppl4wxeq7osqfuu 286 49 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 287 1 13 13 CD work_ln56cwsp7ffppl4wxeq7osqfuu 287 2 We -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 287 3 start start VBP work_ln56cwsp7ffppl4wxeq7osqfuu 287 4 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 287 5 analysis analysis NN work_ln56cwsp7ffppl4wxeq7osqfuu 287 6 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 287 7 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 287 8 maximax maximax NNP work_ln56cwsp7ffppl4wxeq7osqfuu 287 9 case case NN work_ln56cwsp7ffppl4wxeq7osqfuu 287 10 by by IN work_ln56cwsp7ffppl4wxeq7osqfuu 287 11 first first RB work_ln56cwsp7ffppl4wxeq7osqfuu 287 12 giving give VBG work_ln56cwsp7ffppl4wxeq7osqfuu 287 13 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 287 14 general general JJ work_ln56cwsp7ffppl4wxeq7osqfuu 287 15 results result NNS work_ln56cwsp7ffppl4wxeq7osqfuu 287 16 reached reach VBN work_ln56cwsp7ffppl4wxeq7osqfuu 287 17 with with IN work_ln56cwsp7ffppl4wxeq7osqfuu 287 18 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 287 19 β β NN work_ln56cwsp7ffppl4wxeq7osqfuu 287 20 - - HYPH work_ln56cwsp7ffppl4wxeq7osqfuu 287 21 index index NN work_ln56cwsp7ffppl4wxeq7osqfuu 287 22 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 287 23 then then RB work_ln56cwsp7ffppl4wxeq7osqfuu 287 24 we -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 287 25 turn turn VBP work_ln56cwsp7ffppl4wxeq7osqfuu 287 26 to to IN work_ln56cwsp7ffppl4wxeq7osqfuu 287 27 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 287 28 study study NN work_ln56cwsp7ffppl4wxeq7osqfuu 287 29 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 287 30 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 287 31 α α NNP work_ln56cwsp7ffppl4wxeq7osqfuu 287 32 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 287 33 γ γ NNP work_ln56cwsp7ffppl4wxeq7osqfuu 287 34 - - HYPH work_ln56cwsp7ffppl4wxeq7osqfuu 287 35 indices index NNS work_ln56cwsp7ffppl4wxeq7osqfuu 287 36 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 288 1 4.1 4.1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 288 2 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 289 1 The the DT work_ln56cwsp7ffppl4wxeq7osqfuu 289 2 βMX βmx NN work_ln56cwsp7ffppl4wxeq7osqfuu 289 3 - - HYPH work_ln56cwsp7ffppl4wxeq7osqfuu 289 4 index index NN work_ln56cwsp7ffppl4wxeq7osqfuu 289 5 : : : work_ln56cwsp7ffppl4wxeq7osqfuu 289 6 Evaluating evaluate VBG work_ln56cwsp7ffppl4wxeq7osqfuu 289 7 Decision Decision NNP work_ln56cwsp7ffppl4wxeq7osqfuu 289 8 Rules rule NNS work_ln56cwsp7ffppl4wxeq7osqfuu 289 9 in in IN work_ln56cwsp7ffppl4wxeq7osqfuu 289 10 terms term NNS work_ln56cwsp7ffppl4wxeq7osqfuu 289 11 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 289 12 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 289 13 Probability Probability NNP work_ln56cwsp7ffppl4wxeq7osqfuu 289 14 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 289 15 Selecting select VBG work_ln56cwsp7ffppl4wxeq7osqfuu 289 16 an an DT work_ln56cwsp7ffppl4wxeq7osqfuu 289 17 Optimal Optimal NNP work_ln56cwsp7ffppl4wxeq7osqfuu 289 18 Alternative alternative NN work_ln56cwsp7ffppl4wxeq7osqfuu 289 19 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 290 1 Theorem theorem NN work_ln56cwsp7ffppl4wxeq7osqfuu 290 2 4.1 4.1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 290 3 below below RB work_ln56cwsp7ffppl4wxeq7osqfuu 290 4 shows show VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 290 5 that that IN work_ln56cwsp7ffppl4wxeq7osqfuu 290 6 something something NN work_ln56cwsp7ffppl4wxeq7osqfuu 290 7 as as RB work_ln56cwsp7ffppl4wxeq7osqfuu 290 8 simple simple JJ work_ln56cwsp7ffppl4wxeq7osqfuu 290 9 as as IN work_ln56cwsp7ffppl4wxeq7osqfuu 290 10 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 290 11 plurality plurality NN work_ln56cwsp7ffppl4wxeq7osqfuu 290 12 decision decision NN work_ln56cwsp7ffppl4wxeq7osqfuu 290 13 rule rule NN work_ln56cwsp7ffppl4wxeq7osqfuu 290 14 offers offer VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 290 15 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 290 16 highest high JJS work_ln56cwsp7ffppl4wxeq7osqfuu 290 17 probability probability NN work_ln56cwsp7ffppl4wxeq7osqfuu 290 18 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 290 19 selecting select VBG work_ln56cwsp7ffppl4wxeq7osqfuu 290 20 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 290 21 maximax maximax NNP work_ln56cwsp7ffppl4wxeq7osqfuu 290 22 alternative alternative NN work_ln56cwsp7ffppl4wxeq7osqfuu 290 23 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 291 1 Theorem theorem NN work_ln56cwsp7ffppl4wxeq7osqfuu 291 2 4.1 4.1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 291 3 does do VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 291 4 not not RB work_ln56cwsp7ffppl4wxeq7osqfuu 291 5 assume assume VB work_ln56cwsp7ffppl4wxeq7osqfuu 291 6 any any DT work_ln56cwsp7ffppl4wxeq7osqfuu 291 7 particular particular JJ work_ln56cwsp7ffppl4wxeq7osqfuu 291 8 probability probability NN work_ln56cwsp7ffppl4wxeq7osqfuu 291 9 distri- distri- NN work_ln56cwsp7ffppl4wxeq7osqfuu 291 10 bution bution NNP work_ln56cwsp7ffppl4wxeq7osqfuu 291 11 over over IN work_ln56cwsp7ffppl4wxeq7osqfuu 291 12 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 291 13 individual individual JJ work_ln56cwsp7ffppl4wxeq7osqfuu 291 14 utility utility NN work_ln56cwsp7ffppl4wxeq7osqfuu 291 15 values value NNS work_ln56cwsp7ffppl4wxeq7osqfuu 291 16 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 291 17 or or CC work_ln56cwsp7ffppl4wxeq7osqfuu 291 18 any any DT work_ln56cwsp7ffppl4wxeq7osqfuu 291 19 society society NN work_ln56cwsp7ffppl4wxeq7osqfuu 291 20 size size NN work_ln56cwsp7ffppl4wxeq7osqfuu 291 21 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 292 1 Theorem theorem NN work_ln56cwsp7ffppl4wxeq7osqfuu 292 2 4.1 4.1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 292 3 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 293 1 For for IN work_ln56cwsp7ffppl4wxeq7osqfuu 293 2 n×k n×k JJ work_ln56cwsp7ffppl4wxeq7osqfuu 293 3 societies society NNS work_ln56cwsp7ffppl4wxeq7osqfuu 293 4 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 293 5 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 293 6 any any DT work_ln56cwsp7ffppl4wxeq7osqfuu 293 7 culture culture NN work_ln56cwsp7ffppl4wxeq7osqfuu 293 8 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 293 9 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 293 10 maximum maximum JJ work_ln56cwsp7ffppl4wxeq7osqfuu 293 11 βMX βmx NN work_ln56cwsp7ffppl4wxeq7osqfuu 293 12 - - HYPH work_ln56cwsp7ffppl4wxeq7osqfuu 293 13 optimal optimal JJ work_ln56cwsp7ffppl4wxeq7osqfuu 293 14 rule rule NN work_ln56cwsp7ffppl4wxeq7osqfuu 293 15 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 293 16 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 293 17 plurality plurality NN work_ln56cwsp7ffppl4wxeq7osqfuu 293 18 scoring score VBG work_ln56cwsp7ffppl4wxeq7osqfuu 293 19 rule rule NN work_ln56cwsp7ffppl4wxeq7osqfuu 293 20 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 294 1 Corollary Corollary NNP work_ln56cwsp7ffppl4wxeq7osqfuu 294 2 4.2 4.2 CD work_ln56cwsp7ffppl4wxeq7osqfuu 294 3 reinforces reinforce VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 294 4 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 294 5 role role NN work_ln56cwsp7ffppl4wxeq7osqfuu 294 6 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 294 7 plurality plurality NN work_ln56cwsp7ffppl4wxeq7osqfuu 294 8 in in IN work_ln56cwsp7ffppl4wxeq7osqfuu 294 9 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 294 10 maximax maximax NNP work_ln56cwsp7ffppl4wxeq7osqfuu 294 11 ideal ideal NN work_ln56cwsp7ffppl4wxeq7osqfuu 294 12 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 294 13 justice justice NN work_ln56cwsp7ffppl4wxeq7osqfuu 294 14 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 295 1 It -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 295 2 shows show VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 295 3 that that IN work_ln56cwsp7ffppl4wxeq7osqfuu 295 4 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 295 5 as as IN work_ln56cwsp7ffppl4wxeq7osqfuu 295 6 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 295 7 society society NN work_ln56cwsp7ffppl4wxeq7osqfuu 295 8 grows grow VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 295 9 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 295 10 plurality plurality NN work_ln56cwsp7ffppl4wxeq7osqfuu 295 11 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 295 12 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 295 13 unique unique JJ work_ln56cwsp7ffppl4wxeq7osqfuu 295 14 optimal optimal NNP work_ln56cwsp7ffppl4wxeq7osqfuu 295 15 scoring score VBG work_ln56cwsp7ffppl4wxeq7osqfuu 295 16 rule rule NN work_ln56cwsp7ffppl4wxeq7osqfuu 295 17 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 296 1 Corollary Corollary NNP work_ln56cwsp7ffppl4wxeq7osqfuu 296 2 4.2 4.2 CD work_ln56cwsp7ffppl4wxeq7osqfuu 296 3 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 297 1 For for IN work_ln56cwsp7ffppl4wxeq7osqfuu 297 2 any any DT work_ln56cwsp7ffppl4wxeq7osqfuu 297 3 given give VBN work_ln56cwsp7ffppl4wxeq7osqfuu 297 4 k k NN work_ln56cwsp7ffppl4wxeq7osqfuu 297 5 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 297 6 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 297 7 any any DT work_ln56cwsp7ffppl4wxeq7osqfuu 297 8 culture culture NN work_ln56cwsp7ffppl4wxeq7osqfuu 297 9 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 297 10 when when WRB work_ln56cwsp7ffppl4wxeq7osqfuu 297 11 n n DT work_ln56cwsp7ffppl4wxeq7osqfuu 297 12 tends tend VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 297 13 to to IN work_ln56cwsp7ffppl4wxeq7osqfuu 297 14 infinity infinity NN work_ln56cwsp7ffppl4wxeq7osqfuu 297 15 plural- plural- NNP work_ln56cwsp7ffppl4wxeq7osqfuu 297 16 ity ity NN work_ln56cwsp7ffppl4wxeq7osqfuu 297 17 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 297 18 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 297 19 only only JJ work_ln56cwsp7ffppl4wxeq7osqfuu 297 20 scoring score VBG work_ln56cwsp7ffppl4wxeq7osqfuu 297 21 rule rule NN work_ln56cwsp7ffppl4wxeq7osqfuu 297 22 in in IN work_ln56cwsp7ffppl4wxeq7osqfuu 297 23 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 297 24 set set NN work_ln56cwsp7ffppl4wxeq7osqfuu 297 25 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 297 26 βMX βmx NN work_ln56cwsp7ffppl4wxeq7osqfuu 297 27 - - HYPH work_ln56cwsp7ffppl4wxeq7osqfuu 297 28 optimal optimal JJ work_ln56cwsp7ffppl4wxeq7osqfuu 297 29 scoring score VBG work_ln56cwsp7ffppl4wxeq7osqfuu 297 30 rules rule NNS work_ln56cwsp7ffppl4wxeq7osqfuu 297 31 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 298 1 Theorem theorem NN work_ln56cwsp7ffppl4wxeq7osqfuu 298 2 4.1 4.1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 298 3 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 298 4 Corollary Corollary NNP work_ln56cwsp7ffppl4wxeq7osqfuu 298 5 4.2 4.2 CD work_ln56cwsp7ffppl4wxeq7osqfuu 298 6 give give VBP work_ln56cwsp7ffppl4wxeq7osqfuu 298 7 a a DT work_ln56cwsp7ffppl4wxeq7osqfuu 298 8 very very RB work_ln56cwsp7ffppl4wxeq7osqfuu 298 9 clear clear JJ work_ln56cwsp7ffppl4wxeq7osqfuu 298 10 message message NN work_ln56cwsp7ffppl4wxeq7osqfuu 298 11 : : : work_ln56cwsp7ffppl4wxeq7osqfuu 298 12 if if IN work_ln56cwsp7ffppl4wxeq7osqfuu 298 13 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 298 14 interest interest NN work_ln56cwsp7ffppl4wxeq7osqfuu 298 15 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 298 16 in in IN work_ln56cwsp7ffppl4wxeq7osqfuu 298 17 maximax maximax NNP work_ln56cwsp7ffppl4wxeq7osqfuu 298 18 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 298 19 then then RB work_ln56cwsp7ffppl4wxeq7osqfuu 298 20 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 298 21 decision decision NN work_ln56cwsp7ffppl4wxeq7osqfuu 298 22 rule rule NN work_ln56cwsp7ffppl4wxeq7osqfuu 298 23 that that WDT work_ln56cwsp7ffppl4wxeq7osqfuu 298 24 should should MD work_ln56cwsp7ffppl4wxeq7osqfuu 298 25 be be VB work_ln56cwsp7ffppl4wxeq7osqfuu 298 26 implemented implement VBN work_ln56cwsp7ffppl4wxeq7osqfuu 298 27 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 298 28 as as RB work_ln56cwsp7ffppl4wxeq7osqfuu 298 29 simple simple JJ work_ln56cwsp7ffppl4wxeq7osqfuu 298 30 as as IN work_ln56cwsp7ffppl4wxeq7osqfuu 298 31 plurality plurality NN work_ln56cwsp7ffppl4wxeq7osqfuu 298 32 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 298 33 irrespective irrespective RB work_ln56cwsp7ffppl4wxeq7osqfuu 298 34 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 298 35 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 298 36 culture culture NN work_ln56cwsp7ffppl4wxeq7osqfuu 298 37 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 298 38 size size NN work_ln56cwsp7ffppl4wxeq7osqfuu 298 39 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 298 40 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 298 41 society society NN work_ln56cwsp7ffppl4wxeq7osqfuu 298 42 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 299 1 4.2 4.2 CD work_ln56cwsp7ffppl4wxeq7osqfuu 299 2 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 300 1 The the DT work_ln56cwsp7ffppl4wxeq7osqfuu 300 2 αMX αmx NN work_ln56cwsp7ffppl4wxeq7osqfuu 300 3 - - HYPH work_ln56cwsp7ffppl4wxeq7osqfuu 300 4 index index NN work_ln56cwsp7ffppl4wxeq7osqfuu 300 5 : : : work_ln56cwsp7ffppl4wxeq7osqfuu 300 6 Evaluating evaluate VBG work_ln56cwsp7ffppl4wxeq7osqfuu 300 7 Decision Decision NNP work_ln56cwsp7ffppl4wxeq7osqfuu 300 8 Rules rule NNS work_ln56cwsp7ffppl4wxeq7osqfuu 300 9 in in IN work_ln56cwsp7ffppl4wxeq7osqfuu 300 10 terms term NNS work_ln56cwsp7ffppl4wxeq7osqfuu 300 11 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 300 12 Expected expected JJ work_ln56cwsp7ffppl4wxeq7osqfuu 300 13 Value Value NNP work_ln56cwsp7ffppl4wxeq7osqfuu 300 14 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 301 1 We -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 301 2 start start VBP work_ln56cwsp7ffppl4wxeq7osqfuu 301 3 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 301 4 analysis analysis NN work_ln56cwsp7ffppl4wxeq7osqfuu 301 5 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 301 6 maximax maximax NNP work_ln56cwsp7ffppl4wxeq7osqfuu 301 7 in in IN work_ln56cwsp7ffppl4wxeq7osqfuu 301 8 terms term NNS work_ln56cwsp7ffppl4wxeq7osqfuu 301 9 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 301 10 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 301 11 α α NNP work_ln56cwsp7ffppl4wxeq7osqfuu 301 12 - - HYPH work_ln56cwsp7ffppl4wxeq7osqfuu 301 13 index index NN work_ln56cwsp7ffppl4wxeq7osqfuu 301 14 by by IN work_ln56cwsp7ffppl4wxeq7osqfuu 301 15 studying study VBG work_ln56cwsp7ffppl4wxeq7osqfuu 301 16 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 301 17 contribu- contribu- JJ work_ln56cwsp7ffppl4wxeq7osqfuu 301 18 tion tion NN work_ln56cwsp7ffppl4wxeq7osqfuu 301 19 made make VBN work_ln56cwsp7ffppl4wxeq7osqfuu 301 20 to to IN work_ln56cwsp7ffppl4wxeq7osqfuu 301 21 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 301 22 maximax maximax NNP work_ln56cwsp7ffppl4wxeq7osqfuu 301 23 expected expect VBD work_ln56cwsp7ffppl4wxeq7osqfuu 301 24 value value NN work_ln56cwsp7ffppl4wxeq7osqfuu 301 25 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 301 26 an an DT work_ln56cwsp7ffppl4wxeq7osqfuu 301 27 alternative alternative JJ work_ln56cwsp7ffppl4wxeq7osqfuu 301 28 l l NN work_ln56cwsp7ffppl4wxeq7osqfuu 301 29 by by IN work_ln56cwsp7ffppl4wxeq7osqfuu 301 30 adding add VBG work_ln56cwsp7ffppl4wxeq7osqfuu 301 31 one one CD work_ln56cwsp7ffppl4wxeq7osqfuu 301 32 extra extra JJ work_ln56cwsp7ffppl4wxeq7osqfuu 301 33 best good JJS work_ln56cwsp7ffppl4wxeq7osqfuu 301 34 order order NN work_ln56cwsp7ffppl4wxeq7osqfuu 301 35 statistic statistic NN work_ln56cwsp7ffppl4wxeq7osqfuu 301 36 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 301 37 as as IN work_ln56cwsp7ffppl4wxeq7osqfuu 301 38 opposed oppose VBN work_ln56cwsp7ffppl4wxeq7osqfuu 301 39 to to IN work_ln56cwsp7ffppl4wxeq7osqfuu 301 40 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 301 41 value value NN work_ln56cwsp7ffppl4wxeq7osqfuu 301 42 added add VBN work_ln56cwsp7ffppl4wxeq7osqfuu 301 43 by by IN work_ln56cwsp7ffppl4wxeq7osqfuu 301 44 a a DT work_ln56cwsp7ffppl4wxeq7osqfuu 301 45 second second JJ work_ln56cwsp7ffppl4wxeq7osqfuu 301 46 best good JJS work_ln56cwsp7ffppl4wxeq7osqfuu 301 47 order order NN work_ln56cwsp7ffppl4wxeq7osqfuu 301 48 statistic statistic NN work_ln56cwsp7ffppl4wxeq7osqfuu 301 49 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 301 50 when when WRB work_ln56cwsp7ffppl4wxeq7osqfuu 301 51 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 301 52 culture culture NN work_ln56cwsp7ffppl4wxeq7osqfuu 301 53 follows follow VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 301 54 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 301 55 uniform uniform JJ work_ln56cwsp7ffppl4wxeq7osqfuu 301 56 distribution distribution NN work_ln56cwsp7ffppl4wxeq7osqfuu 301 57 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 302 1 We -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 302 2 explore explore VBP work_ln56cwsp7ffppl4wxeq7osqfuu 302 3 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 302 4 extreme extreme JJ work_ln56cwsp7ffppl4wxeq7osqfuu 302 5 case case NN work_ln56cwsp7ffppl4wxeq7osqfuu 302 6 where where WRB work_ln56cwsp7ffppl4wxeq7osqfuu 302 7 everybody everybody NN work_ln56cwsp7ffppl4wxeq7osqfuu 302 8 ranks rank VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 302 9 alternative alternative JJ work_ln56cwsp7ffppl4wxeq7osqfuu 302 10 l l NNP work_ln56cwsp7ffppl4wxeq7osqfuu 302 11 as as IN work_ln56cwsp7ffppl4wxeq7osqfuu 302 12 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 302 13 best good JJS work_ln56cwsp7ffppl4wxeq7osqfuu 302 14 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 303 1 It -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 303 2 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 303 3 in in IN work_ln56cwsp7ffppl4wxeq7osqfuu 303 4 this this DT work_ln56cwsp7ffppl4wxeq7osqfuu 303 5 case case NN work_ln56cwsp7ffppl4wxeq7osqfuu 303 6 that that IN work_ln56cwsp7ffppl4wxeq7osqfuu 303 7 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 303 8 extra extra JJ work_ln56cwsp7ffppl4wxeq7osqfuu 303 9 expected expect VBN work_ln56cwsp7ffppl4wxeq7osqfuu 303 10 maximax maximax NNP work_ln56cwsp7ffppl4wxeq7osqfuu 303 11 value value NN work_ln56cwsp7ffppl4wxeq7osqfuu 303 12 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 303 13 adding add VBG work_ln56cwsp7ffppl4wxeq7osqfuu 303 14 one one CD work_ln56cwsp7ffppl4wxeq7osqfuu 303 15 best good JJS work_ln56cwsp7ffppl4wxeq7osqfuu 303 16 alternative alternative NN work_ln56cwsp7ffppl4wxeq7osqfuu 303 17 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 303 18 intuitively intuitively RB work_ln56cwsp7ffppl4wxeq7osqfuu 303 19 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 303 20 smallest small JJS work_ln56cwsp7ffppl4wxeq7osqfuu 303 21 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 304 1 We -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 304 2 show show VBP work_ln56cwsp7ffppl4wxeq7osqfuu 304 3 that that IN work_ln56cwsp7ffppl4wxeq7osqfuu 304 4 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 304 5 even even RB work_ln56cwsp7ffppl4wxeq7osqfuu 304 6 in in IN work_ln56cwsp7ffppl4wxeq7osqfuu 304 7 this this DT work_ln56cwsp7ffppl4wxeq7osqfuu 304 8 case case NN work_ln56cwsp7ffppl4wxeq7osqfuu 304 9 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 304 10 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 304 11 contribution contribution NN work_ln56cwsp7ffppl4wxeq7osqfuu 304 12 made make VBN work_ln56cwsp7ffppl4wxeq7osqfuu 304 13 to to IN work_ln56cwsp7ffppl4wxeq7osqfuu 304 14 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 304 15 expected expect VBN work_ln56cwsp7ffppl4wxeq7osqfuu 304 16 maximax maximax NN work_ln56cwsp7ffppl4wxeq7osqfuu 304 17 value value NN work_ln56cwsp7ffppl4wxeq7osqfuu 304 18 by by IN work_ln56cwsp7ffppl4wxeq7osqfuu 304 19 adding add VBG work_ln56cwsp7ffppl4wxeq7osqfuu 304 20 one one CD work_ln56cwsp7ffppl4wxeq7osqfuu 304 21 extra extra JJ work_ln56cwsp7ffppl4wxeq7osqfuu 304 22 best good JJS work_ln56cwsp7ffppl4wxeq7osqfuu 304 23 order order NN work_ln56cwsp7ffppl4wxeq7osqfuu 304 24 statistic statistic NN work_ln56cwsp7ffppl4wxeq7osqfuu 304 25 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 304 26 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 304 27 a a DT work_ln56cwsp7ffppl4wxeq7osqfuu 304 28 higher high JJR work_ln56cwsp7ffppl4wxeq7osqfuu 304 29 order order NN work_ln56cwsp7ffppl4wxeq7osqfuu 304 30 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 304 31 magnitude magnitude NN work_ln56cwsp7ffppl4wxeq7osqfuu 304 32 than than IN work_ln56cwsp7ffppl4wxeq7osqfuu 304 33 that that DT work_ln56cwsp7ffppl4wxeq7osqfuu 304 34 made make VBN work_ln56cwsp7ffppl4wxeq7osqfuu 304 35 by by IN work_ln56cwsp7ffppl4wxeq7osqfuu 304 36 adding add VBG work_ln56cwsp7ffppl4wxeq7osqfuu 304 37 a a DT work_ln56cwsp7ffppl4wxeq7osqfuu 304 38 second second JJ work_ln56cwsp7ffppl4wxeq7osqfuu 304 39 best good JJS work_ln56cwsp7ffppl4wxeq7osqfuu 304 40 order order NN work_ln56cwsp7ffppl4wxeq7osqfuu 304 41 statistic statistic NN work_ln56cwsp7ffppl4wxeq7osqfuu 304 42 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 305 1 Then then RB work_ln56cwsp7ffppl4wxeq7osqfuu 305 2 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 305 3 plurality plurality NN work_ln56cwsp7ffppl4wxeq7osqfuu 305 4 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 305 5 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 305 6 clear clear JJ work_ln56cwsp7ffppl4wxeq7osqfuu 305 7 candidate candidate NN work_ln56cwsp7ffppl4wxeq7osqfuu 305 8 to to TO work_ln56cwsp7ffppl4wxeq7osqfuu 305 9 be be VB work_ln56cwsp7ffppl4wxeq7osqfuu 305 10 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 305 11 optimal optimal JJ work_ln56cwsp7ffppl4wxeq7osqfuu 305 12 maximax maximax NNP work_ln56cwsp7ffppl4wxeq7osqfuu 305 13 decision decision NN work_ln56cwsp7ffppl4wxeq7osqfuu 305 14 rule rule NN work_ln56cwsp7ffppl4wxeq7osqfuu 305 15 in in IN work_ln56cwsp7ffppl4wxeq7osqfuu 305 16 terms term NNS work_ln56cwsp7ffppl4wxeq7osqfuu 305 17 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 305 18 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 305 19 α α NNP work_ln56cwsp7ffppl4wxeq7osqfuu 305 20 - - HYPH work_ln56cwsp7ffppl4wxeq7osqfuu 305 21 index index NN work_ln56cwsp7ffppl4wxeq7osqfuu 305 22 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 305 23 since since IN work_ln56cwsp7ffppl4wxeq7osqfuu 305 24 it -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 305 25 gives give VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 305 26 weight weight NN work_ln56cwsp7ffppl4wxeq7osqfuu 305 27 only only RB work_ln56cwsp7ffppl4wxeq7osqfuu 305 28 to to IN work_ln56cwsp7ffppl4wxeq7osqfuu 305 29 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 305 30 best good JJS work_ln56cwsp7ffppl4wxeq7osqfuu 305 31 random random JJ work_ln56cwsp7ffppl4wxeq7osqfuu 305 32 variables variable NNS work_ln56cwsp7ffppl4wxeq7osqfuu 305 33 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 306 1 Consider consider VB work_ln56cwsp7ffppl4wxeq7osqfuu 306 2 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 306 3 n×k n×k NNP work_ln56cwsp7ffppl4wxeq7osqfuu 306 4 society society NN work_ln56cwsp7ffppl4wxeq7osqfuu 306 5 M m NN work_ln56cwsp7ffppl4wxeq7osqfuu 306 6 such such JJ work_ln56cwsp7ffppl4wxeq7osqfuu 306 7 that that IN work_ln56cwsp7ffppl4wxeq7osqfuu 306 8 mli mli NNP work_ln56cwsp7ffppl4wxeq7osqfuu 306 9 = = NFP work_ln56cwsp7ffppl4wxeq7osqfuu 306 10 k k XX work_ln56cwsp7ffppl4wxeq7osqfuu 306 11 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 306 12 every every DT work_ln56cwsp7ffppl4wxeq7osqfuu 306 13 i i PRP work_ln56cwsp7ffppl4wxeq7osqfuu 306 14 ∈{1 ∈{1 PRP work_ln56cwsp7ffppl4wxeq7osqfuu 306 15 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 306 16 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 307 1 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 308 1 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 309 1 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 309 2 n n NNP work_ln56cwsp7ffppl4wxeq7osqfuu 309 3 } } -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 309 4 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 310 1 That that RB work_ln56cwsp7ffppl4wxeq7osqfuu 310 2 is is RB work_ln56cwsp7ffppl4wxeq7osqfuu 310 3 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 310 4 all all DT work_ln56cwsp7ffppl4wxeq7osqfuu 310 5 n n JJ work_ln56cwsp7ffppl4wxeq7osqfuu 310 6 individuals individual NNS work_ln56cwsp7ffppl4wxeq7osqfuu 310 7 in in IN work_ln56cwsp7ffppl4wxeq7osqfuu 310 8 society society NN work_ln56cwsp7ffppl4wxeq7osqfuu 310 9 M M NNP work_ln56cwsp7ffppl4wxeq7osqfuu 310 10 rank rank NN work_ln56cwsp7ffppl4wxeq7osqfuu 310 11 alternative alternative NN work_ln56cwsp7ffppl4wxeq7osqfuu 310 12 l l NNP work_ln56cwsp7ffppl4wxeq7osqfuu 310 13 as as IN work_ln56cwsp7ffppl4wxeq7osqfuu 310 14 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 310 15 best good JJS work_ln56cwsp7ffppl4wxeq7osqfuu 310 16 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 311 1 Consider consider VB work_ln56cwsp7ffppl4wxeq7osqfuu 311 2 also also RB work_ln56cwsp7ffppl4wxeq7osqfuu 311 3 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 311 4 following follow VBG work_ln56cwsp7ffppl4wxeq7osqfuu 311 5 two two CD work_ln56cwsp7ffppl4wxeq7osqfuu 311 6 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 311 7 n n NN work_ln56cwsp7ffppl4wxeq7osqfuu 311 8 + + CC work_ln56cwsp7ffppl4wxeq7osqfuu 311 9 1)×k 1)×k CD work_ln56cwsp7ffppl4wxeq7osqfuu 311 10 societies society NNS work_ln56cwsp7ffppl4wxeq7osqfuu 311 11 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 311 12 M M NNP work_ln56cwsp7ffppl4wxeq7osqfuu 311 13 ′ ′ ADD work_ln56cwsp7ffppl4wxeq7osqfuu 311 14 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 311 15 M M NNP work_ln56cwsp7ffppl4wxeq7osqfuu 311 16 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 311 17 such such JJ work_ln56cwsp7ffppl4wxeq7osqfuu 311 18 that that IN work_ln56cwsp7ffppl4wxeq7osqfuu 311 19 m′li m′li NNP work_ln56cwsp7ffppl4wxeq7osqfuu 311 20 = = SYM work_ln56cwsp7ffppl4wxeq7osqfuu 311 21 k k XX work_ln56cwsp7ffppl4wxeq7osqfuu 311 22 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 311 23 every every DT work_ln56cwsp7ffppl4wxeq7osqfuu 311 24 i i PRP work_ln56cwsp7ffppl4wxeq7osqfuu 311 25 ∈{1 ∈{1 PRP work_ln56cwsp7ffppl4wxeq7osqfuu 311 26 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 311 27 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 312 1 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 313 1 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 314 1 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 314 2 n n NNP work_ln56cwsp7ffppl4wxeq7osqfuu 314 3 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 314 4 n n NN work_ln56cwsp7ffppl4wxeq7osqfuu 314 5 + + CC work_ln56cwsp7ffppl4wxeq7osqfuu 314 6 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 314 7 } } -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 314 8 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 314 9 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 314 10 mli mli NNP work_ln56cwsp7ffppl4wxeq7osqfuu 314 11 = = SYM work_ln56cwsp7ffppl4wxeq7osqfuu 314 12 k k NNP work_ln56cwsp7ffppl4wxeq7osqfuu 314 13 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 314 14 every every DT work_ln56cwsp7ffppl4wxeq7osqfuu 314 15 i i NN work_ln56cwsp7ffppl4wxeq7osqfuu 314 16 ∈ ∈ IN work_ln56cwsp7ffppl4wxeq7osqfuu 314 17 { { -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 314 18 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 314 19 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 314 20 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 315 1 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 316 1 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 317 1 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 317 2 n n NNP work_ln56cwsp7ffppl4wxeq7osqfuu 317 3 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 317 4 n n NN work_ln56cwsp7ffppl4wxeq7osqfuu 317 5 + + CC work_ln56cwsp7ffppl4wxeq7osqfuu 317 6 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 317 7 } } -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 317 8 \ \ NN work_ln56cwsp7ffppl4wxeq7osqfuu 317 9 { { -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 317 10 j j NNP work_ln56cwsp7ffppl4wxeq7osqfuu 317 11 } } -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 317 12 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 317 13 mlj mlj NNP work_ln56cwsp7ffppl4wxeq7osqfuu 317 14 = = SYM work_ln56cwsp7ffppl4wxeq7osqfuu 317 15 k k NN work_ln56cwsp7ffppl4wxeq7osqfuu 317 16 − − NNP work_ln56cwsp7ffppl4wxeq7osqfuu 317 17 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 317 18 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 318 1 In in IN work_ln56cwsp7ffppl4wxeq7osqfuu 318 2 M M NNP work_ln56cwsp7ffppl4wxeq7osqfuu 318 3 ′ ′ NNP work_ln56cwsp7ffppl4wxeq7osqfuu 318 4 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 318 5 all all DT work_ln56cwsp7ffppl4wxeq7osqfuu 318 6 n n NN work_ln56cwsp7ffppl4wxeq7osqfuu 318 7 + + SYM work_ln56cwsp7ffppl4wxeq7osqfuu 318 8 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 318 9 14 14 CD work_ln56cwsp7ffppl4wxeq7osqfuu 318 10 individuals individual NNS work_ln56cwsp7ffppl4wxeq7osqfuu 318 11 rank rank NNP work_ln56cwsp7ffppl4wxeq7osqfuu 318 12 l l NN work_ln56cwsp7ffppl4wxeq7osqfuu 318 13 as as IN work_ln56cwsp7ffppl4wxeq7osqfuu 318 14 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 318 15 best good JJS work_ln56cwsp7ffppl4wxeq7osqfuu 318 16 alternative alternative NN work_ln56cwsp7ffppl4wxeq7osqfuu 318 17 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 318 18 while while IN work_ln56cwsp7ffppl4wxeq7osqfuu 318 19 in in IN work_ln56cwsp7ffppl4wxeq7osqfuu 318 20 M M NNP work_ln56cwsp7ffppl4wxeq7osqfuu 318 21 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 318 22 there there EX work_ln56cwsp7ffppl4wxeq7osqfuu 318 23 are be VBP work_ln56cwsp7ffppl4wxeq7osqfuu 318 24 n n IN work_ln56cwsp7ffppl4wxeq7osqfuu 318 25 individuals individual NNS work_ln56cwsp7ffppl4wxeq7osqfuu 318 26 who who WP work_ln56cwsp7ffppl4wxeq7osqfuu 318 27 rank rank VBP work_ln56cwsp7ffppl4wxeq7osqfuu 318 28 l l NN work_ln56cwsp7ffppl4wxeq7osqfuu 318 29 as as RB work_ln56cwsp7ffppl4wxeq7osqfuu 318 30 best good JJS work_ln56cwsp7ffppl4wxeq7osqfuu 318 31 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 318 32 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 318 33 one one CD work_ln56cwsp7ffppl4wxeq7osqfuu 318 34 that that WDT work_ln56cwsp7ffppl4wxeq7osqfuu 318 35 ranks rank VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 318 36 l l NNP work_ln56cwsp7ffppl4wxeq7osqfuu 318 37 as as IN work_ln56cwsp7ffppl4wxeq7osqfuu 318 38 second second RB work_ln56cwsp7ffppl4wxeq7osqfuu 318 39 best good JJS work_ln56cwsp7ffppl4wxeq7osqfuu 318 40 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 319 1 Now now RB work_ln56cwsp7ffppl4wxeq7osqfuu 319 2 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 319 3 taking take VBG work_ln56cwsp7ffppl4wxeq7osqfuu 319 4 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 319 5 n n NNP work_ln56cwsp7ffppl4wxeq7osqfuu 319 6 × × NNP work_ln56cwsp7ffppl4wxeq7osqfuu 319 7 k k NNP work_ln56cwsp7ffppl4wxeq7osqfuu 319 8 society society NNP work_ln56cwsp7ffppl4wxeq7osqfuu 319 9 M M NNP work_ln56cwsp7ffppl4wxeq7osqfuu 319 10 as as IN work_ln56cwsp7ffppl4wxeq7osqfuu 319 11 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 319 12 baseline baseline NN work_ln56cwsp7ffppl4wxeq7osqfuu 319 13 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 319 14 we -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 319 15 ask ask VBP work_ln56cwsp7ffppl4wxeq7osqfuu 319 16 what what WP work_ln56cwsp7ffppl4wxeq7osqfuu 319 17 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 319 18 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 319 19 marginal marginal JJ work_ln56cwsp7ffppl4wxeq7osqfuu 319 20 contribution contribution NN work_ln56cwsp7ffppl4wxeq7osqfuu 319 21 to to IN work_ln56cwsp7ffppl4wxeq7osqfuu 319 22 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 319 23 l l NNP work_ln56cwsp7ffppl4wxeq7osqfuu 319 24 - - HYPH work_ln56cwsp7ffppl4wxeq7osqfuu 319 25 th th NNP work_ln56cwsp7ffppl4wxeq7osqfuu 319 26 maximax maximax NNP work_ln56cwsp7ffppl4wxeq7osqfuu 319 27 expected expect VBD work_ln56cwsp7ffppl4wxeq7osqfuu 319 28 value value NN work_ln56cwsp7ffppl4wxeq7osqfuu 319 29 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 319 30 adding add VBG work_ln56cwsp7ffppl4wxeq7osqfuu 319 31 one one CD work_ln56cwsp7ffppl4wxeq7osqfuu 319 32 extra extra JJ work_ln56cwsp7ffppl4wxeq7osqfuu 319 33 individual individual NN work_ln56cwsp7ffppl4wxeq7osqfuu 319 34 who who WP work_ln56cwsp7ffppl4wxeq7osqfuu 319 35 ranks rank VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 319 36 l l NN work_ln56cwsp7ffppl4wxeq7osqfuu 319 37 as as IN work_ln56cwsp7ffppl4wxeq7osqfuu 319 38 best good JJS work_ln56cwsp7ffppl4wxeq7osqfuu 319 39 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 319 40 society society NN work_ln56cwsp7ffppl4wxeq7osqfuu 319 41 M m NN work_ln56cwsp7ffppl4wxeq7osqfuu 319 42 ′ ′ ADD work_ln56cwsp7ffppl4wxeq7osqfuu 319 43 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 319 44 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 320 1 Also also RB work_ln56cwsp7ffppl4wxeq7osqfuu 320 2 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 320 3 we -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 320 4 wonder wonder VBP work_ln56cwsp7ffppl4wxeq7osqfuu 320 5 about about IN work_ln56cwsp7ffppl4wxeq7osqfuu 320 6 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 320 7 marginal marginal JJ work_ln56cwsp7ffppl4wxeq7osqfuu 320 8 contribution contribution NN work_ln56cwsp7ffppl4wxeq7osqfuu 320 9 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 320 10 adding add VBG work_ln56cwsp7ffppl4wxeq7osqfuu 320 11 one one CD work_ln56cwsp7ffppl4wxeq7osqfuu 320 12 extra extra JJ work_ln56cwsp7ffppl4wxeq7osqfuu 320 13 individual individual NN work_ln56cwsp7ffppl4wxeq7osqfuu 320 14 who who WP work_ln56cwsp7ffppl4wxeq7osqfuu 320 15 ranks rank VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 320 16 l l NN work_ln56cwsp7ffppl4wxeq7osqfuu 320 17 as as IN work_ln56cwsp7ffppl4wxeq7osqfuu 320 18 second second RB work_ln56cwsp7ffppl4wxeq7osqfuu 320 19 - - HYPH work_ln56cwsp7ffppl4wxeq7osqfuu 320 20 best good JJS work_ln56cwsp7ffppl4wxeq7osqfuu 320 21 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 320 22 society society NN work_ln56cwsp7ffppl4wxeq7osqfuu 320 23 M M NNP work_ln56cwsp7ffppl4wxeq7osqfuu 320 24 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 320 25 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 321 1 Denote denote VB work_ln56cwsp7ffppl4wxeq7osqfuu 321 2 these these DT work_ln56cwsp7ffppl4wxeq7osqfuu 321 3 marginal marginal JJ work_ln56cwsp7ffppl4wxeq7osqfuu 321 4 contributions contribution NNS work_ln56cwsp7ffppl4wxeq7osqfuu 321 5 by by IN work_ln56cwsp7ffppl4wxeq7osqfuu 321 6 ∆ ∆ NN work_ln56cwsp7ffppl4wxeq7osqfuu 321 7 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 321 8 k k NNP work_ln56cwsp7ffppl4wxeq7osqfuu 321 9 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 321 10 n n NN work_ln56cwsp7ffppl4wxeq7osqfuu 321 11 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 321 12 ∆ ∆ NNP work_ln56cwsp7ffppl4wxeq7osqfuu 321 13 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 321 14 k−1 k−1 NNP work_ln56cwsp7ffppl4wxeq7osqfuu 321 15 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 321 16 n n NNP work_ln56cwsp7ffppl4wxeq7osqfuu 321 17 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 321 18 where where WRB work_ln56cwsp7ffppl4wxeq7osqfuu 321 19 ∆ ∆ NN work_ln56cwsp7ffppl4wxeq7osqfuu 321 20 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 321 21 k k NNP work_ln56cwsp7ffppl4wxeq7osqfuu 321 22 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 321 23 n n NNP work_ln56cwsp7ffppl4wxeq7osqfuu 321 24 = = SYM work_ln56cwsp7ffppl4wxeq7osqfuu 321 25 E[Ul(n+1)|M e[ul(n+1)|m CD work_ln56cwsp7ffppl4wxeq7osqfuu 321 26 ′l ′l NNP work_ln56cwsp7ffppl4wxeq7osqfuu 321 27 ] ] -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 321 28 − − NNP work_ln56cwsp7ffppl4wxeq7osqfuu 321 29 E[Ul(n)|M E[Ul(n)|M NNP work_ln56cwsp7ffppl4wxeq7osqfuu 321 30 l l NN work_ln56cwsp7ffppl4wxeq7osqfuu 321 31 ] ] -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 321 32 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 321 33 ∆ ∆ NNP work_ln56cwsp7ffppl4wxeq7osqfuu 321 34 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 321 35 k−1 k−1 NNP work_ln56cwsp7ffppl4wxeq7osqfuu 321 36 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 321 37 n n NNP work_ln56cwsp7ffppl4wxeq7osqfuu 321 38 = = SYM work_ln56cwsp7ffppl4wxeq7osqfuu 321 39 E[Ul(n+1)|M E[Ul(n+1)|M NNP work_ln56cwsp7ffppl4wxeq7osqfuu 321 40 l l NN work_ln56cwsp7ffppl4wxeq7osqfuu 321 41 ] ] -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 321 42 − − NNP work_ln56cwsp7ffppl4wxeq7osqfuu 321 43 E[Ul(n)|M E[Ul(n)|M NNP work_ln56cwsp7ffppl4wxeq7osqfuu 321 44 l l NN work_ln56cwsp7ffppl4wxeq7osqfuu 321 45 ] ] -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 321 46 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 322 1 The the DT work_ln56cwsp7ffppl4wxeq7osqfuu 322 2 ratio ratio NN work_ln56cwsp7ffppl4wxeq7osqfuu 322 3 ∆ ∆ NN work_ln56cwsp7ffppl4wxeq7osqfuu 322 4 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 322 5 k k NN work_ln56cwsp7ffppl4wxeq7osqfuu 322 6 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 322 7 n n NNP work_ln56cwsp7ffppl4wxeq7osqfuu 322 8 ∆ ∆ NN work_ln56cwsp7ffppl4wxeq7osqfuu 322 9 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 322 10 k−1 k−1 NNP work_ln56cwsp7ffppl4wxeq7osqfuu 322 11 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 322 12 n n NNP work_ln56cwsp7ffppl4wxeq7osqfuu 322 13 represents represent VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 322 14 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 322 15 ratio ratio NN work_ln56cwsp7ffppl4wxeq7osqfuu 322 16 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 322 17 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 322 18 marginal marginal JJ work_ln56cwsp7ffppl4wxeq7osqfuu 322 19 contributions contribution NNS work_ln56cwsp7ffppl4wxeq7osqfuu 322 20 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 322 21 an an DT work_ln56cwsp7ffppl4wxeq7osqfuu 322 22 extra extra JJ work_ln56cwsp7ffppl4wxeq7osqfuu 322 23 order order NN work_ln56cwsp7ffppl4wxeq7osqfuu 322 24 statistic statistic NN work_ln56cwsp7ffppl4wxeq7osqfuu 322 25 in in IN work_ln56cwsp7ffppl4wxeq7osqfuu 322 26 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 322 27 top top JJ work_ln56cwsp7ffppl4wxeq7osqfuu 322 28 positions position NNS work_ln56cwsp7ffppl4wxeq7osqfuu 322 29 k k NN work_ln56cwsp7ffppl4wxeq7osqfuu 322 30 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 322 31 k k NNP work_ln56cwsp7ffppl4wxeq7osqfuu 322 32 − − NNP work_ln56cwsp7ffppl4wxeq7osqfuu 322 33 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 322 34 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 323 1 Lemma Lemma NNP work_ln56cwsp7ffppl4wxeq7osqfuu 323 2 4.3 4.3 CD work_ln56cwsp7ffppl4wxeq7osqfuu 323 3 below below RB work_ln56cwsp7ffppl4wxeq7osqfuu 323 4 shows show VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 323 5 that that IN work_ln56cwsp7ffppl4wxeq7osqfuu 323 6 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 323 7 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 323 8 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 323 9 uniform uniform JJ work_ln56cwsp7ffppl4wxeq7osqfuu 323 10 distribution distribution NN work_ln56cwsp7ffppl4wxeq7osqfuu 323 11 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 323 12 when when WRB work_ln56cwsp7ffppl4wxeq7osqfuu 323 13 l(k l(k NNP work_ln56cwsp7ffppl4wxeq7osqfuu 323 14 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 323 15 = = NFP work_ln56cwsp7ffppl4wxeq7osqfuu 323 16 n n LS work_ln56cwsp7ffppl4wxeq7osqfuu 323 17 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 323 18 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 323 19 ad- ad- XX work_ln56cwsp7ffppl4wxeq7osqfuu 323 20 ditional ditional JJ work_ln56cwsp7ffppl4wxeq7osqfuu 323 21 expected expect VBN work_ln56cwsp7ffppl4wxeq7osqfuu 323 22 value value NN work_ln56cwsp7ffppl4wxeq7osqfuu 323 23 provided provide VBN work_ln56cwsp7ffppl4wxeq7osqfuu 323 24 by by IN work_ln56cwsp7ffppl4wxeq7osqfuu 323 25 one one CD work_ln56cwsp7ffppl4wxeq7osqfuu 323 26 extra extra JJ work_ln56cwsp7ffppl4wxeq7osqfuu 323 27 order order NN work_ln56cwsp7ffppl4wxeq7osqfuu 323 28 statistic statistic NN work_ln56cwsp7ffppl4wxeq7osqfuu 323 29 in in IN work_ln56cwsp7ffppl4wxeq7osqfuu 323 30 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 323 31 same same JJ work_ln56cwsp7ffppl4wxeq7osqfuu 323 32 position position NN work_ln56cwsp7ffppl4wxeq7osqfuu 323 33 k k NNP work_ln56cwsp7ffppl4wxeq7osqfuu 323 34 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 323 35 considerably considerably RB work_ln56cwsp7ffppl4wxeq7osqfuu 323 36 higher high JJR work_ln56cwsp7ffppl4wxeq7osqfuu 323 37 than than IN work_ln56cwsp7ffppl4wxeq7osqfuu 323 38 that that DT work_ln56cwsp7ffppl4wxeq7osqfuu 323 39 provided provide VBN work_ln56cwsp7ffppl4wxeq7osqfuu 323 40 by by IN work_ln56cwsp7ffppl4wxeq7osqfuu 323 41 one one CD work_ln56cwsp7ffppl4wxeq7osqfuu 323 42 extra extra JJ work_ln56cwsp7ffppl4wxeq7osqfuu 323 43 order order NN work_ln56cwsp7ffppl4wxeq7osqfuu 323 44 statistic statistic NN work_ln56cwsp7ffppl4wxeq7osqfuu 323 45 in in IN work_ln56cwsp7ffppl4wxeq7osqfuu 323 46 position position NN work_ln56cwsp7ffppl4wxeq7osqfuu 323 47 k−1 k−1 NNP work_ln56cwsp7ffppl4wxeq7osqfuu 323 48 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 324 1 Lemma Lemma NNP work_ln56cwsp7ffppl4wxeq7osqfuu 324 2 4.3 4.3 CD work_ln56cwsp7ffppl4wxeq7osqfuu 324 3 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 325 1 For for IN work_ln56cwsp7ffppl4wxeq7osqfuu 325 2 n×k n×k JJ work_ln56cwsp7ffppl4wxeq7osqfuu 325 3 societies society NNS work_ln56cwsp7ffppl4wxeq7osqfuu 325 4 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 325 5 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 325 6 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 325 7 uniform uniform JJ work_ln56cwsp7ffppl4wxeq7osqfuu 325 8 distribution distribution NN work_ln56cwsp7ffppl4wxeq7osqfuu 325 9 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 325 10 ∆ ∆ NN work_ln56cwsp7ffppl4wxeq7osqfuu 325 11 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 325 12 k k NNP work_ln56cwsp7ffppl4wxeq7osqfuu 325 13 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 325 14 n n NNP work_ln56cwsp7ffppl4wxeq7osqfuu 325 15 ∆ ∆ NN work_ln56cwsp7ffppl4wxeq7osqfuu 325 16 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 325 17 k−1 k−1 NNP work_ln56cwsp7ffppl4wxeq7osqfuu 325 18 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 325 19 n n NNP work_ln56cwsp7ffppl4wxeq7osqfuu 325 20 = = SYM work_ln56cwsp7ffppl4wxeq7osqfuu 325 21 k(n+1 k(n+1 NNP work_ln56cwsp7ffppl4wxeq7osqfuu 325 22 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 325 23 k−1 k−1 NNP work_ln56cwsp7ffppl4wxeq7osqfuu 325 24 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 326 1 Intuitively intuitively RB work_ln56cwsp7ffppl4wxeq7osqfuu 326 2 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 326 3 situation situation NN work_ln56cwsp7ffppl4wxeq7osqfuu 326 4 where where WRB work_ln56cwsp7ffppl4wxeq7osqfuu 326 5 everybody everybody NN work_ln56cwsp7ffppl4wxeq7osqfuu 326 6 ranks rank VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 326 7 l l NNP work_ln56cwsp7ffppl4wxeq7osqfuu 326 8 as as IN work_ln56cwsp7ffppl4wxeq7osqfuu 326 9 best good JJS work_ln56cwsp7ffppl4wxeq7osqfuu 326 10 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 326 11 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 326 12 worst bad JJS work_ln56cwsp7ffppl4wxeq7osqfuu 326 13 - - HYPH work_ln56cwsp7ffppl4wxeq7osqfuu 326 14 case case NN work_ln56cwsp7ffppl4wxeq7osqfuu 326 15 scenario scenario NN work_ln56cwsp7ffppl4wxeq7osqfuu 326 16 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 326 17 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 326 18 expected expect VBN work_ln56cwsp7ffppl4wxeq7osqfuu 326 19 marginal marginal JJ work_ln56cwsp7ffppl4wxeq7osqfuu 326 20 contribution contribution NN work_ln56cwsp7ffppl4wxeq7osqfuu 326 21 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 326 22 adding add VBG work_ln56cwsp7ffppl4wxeq7osqfuu 326 23 one one CD work_ln56cwsp7ffppl4wxeq7osqfuu 326 24 extra extra JJ work_ln56cwsp7ffppl4wxeq7osqfuu 326 25 individual individual NN work_ln56cwsp7ffppl4wxeq7osqfuu 326 26 who who WP work_ln56cwsp7ffppl4wxeq7osqfuu 326 27 rank rank VBP work_ln56cwsp7ffppl4wxeq7osqfuu 326 28 l l NN work_ln56cwsp7ffppl4wxeq7osqfuu 326 29 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 326 30 best good JJS work_ln56cwsp7ffppl4wxeq7osqfuu 326 31 alternative alternative NN work_ln56cwsp7ffppl4wxeq7osqfuu 326 32 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 327 1 Even even RB work_ln56cwsp7ffppl4wxeq7osqfuu 327 2 in in IN work_ln56cwsp7ffppl4wxeq7osqfuu 327 3 this this DT work_ln56cwsp7ffppl4wxeq7osqfuu 327 4 case case NN work_ln56cwsp7ffppl4wxeq7osqfuu 327 5 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 327 6 Lemma Lemma NNP work_ln56cwsp7ffppl4wxeq7osqfuu 327 7 4.3 4.3 CD work_ln56cwsp7ffppl4wxeq7osqfuu 327 8 shows show VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 327 9 that that IN work_ln56cwsp7ffppl4wxeq7osqfuu 327 10 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 327 11 order order NN work_ln56cwsp7ffppl4wxeq7osqfuu 327 12 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 327 13 magnitude magnitude NN work_ln56cwsp7ffppl4wxeq7osqfuu 327 14 in in IN work_ln56cwsp7ffppl4wxeq7osqfuu 327 15 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 327 16 expected expect VBN work_ln56cwsp7ffppl4wxeq7osqfuu 327 17 maximax maximax NNP work_ln56cwsp7ffppl4wxeq7osqfuu 327 18 value value NN work_ln56cwsp7ffppl4wxeq7osqfuu 327 19 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 327 20 an an DT work_ln56cwsp7ffppl4wxeq7osqfuu 327 21 extra extra JJ work_ln56cwsp7ffppl4wxeq7osqfuu 327 22 best good JJS work_ln56cwsp7ffppl4wxeq7osqfuu 327 23 random random JJ work_ln56cwsp7ffppl4wxeq7osqfuu 327 24 variable variable NN work_ln56cwsp7ffppl4wxeq7osqfuu 327 25 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 327 26 considerably considerably RB work_ln56cwsp7ffppl4wxeq7osqfuu 327 27 higher high JJR work_ln56cwsp7ffppl4wxeq7osqfuu 327 28 than than IN work_ln56cwsp7ffppl4wxeq7osqfuu 327 29 that that DT work_ln56cwsp7ffppl4wxeq7osqfuu 327 30 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 327 31 an an DT work_ln56cwsp7ffppl4wxeq7osqfuu 327 32 extra extra JJ work_ln56cwsp7ffppl4wxeq7osqfuu 327 33 second second JJ work_ln56cwsp7ffppl4wxeq7osqfuu 327 34 best good JJS work_ln56cwsp7ffppl4wxeq7osqfuu 327 35 random random JJ work_ln56cwsp7ffppl4wxeq7osqfuu 327 36 variable variable NN work_ln56cwsp7ffppl4wxeq7osqfuu 327 37 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 328 1 This this DT work_ln56cwsp7ffppl4wxeq7osqfuu 328 2 clearly clearly RB work_ln56cwsp7ffppl4wxeq7osqfuu 328 3 points point VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 328 4 to to IN work_ln56cwsp7ffppl4wxeq7osqfuu 328 5 plurality plurality NN work_ln56cwsp7ffppl4wxeq7osqfuu 328 6 as as IN work_ln56cwsp7ffppl4wxeq7osqfuu 328 7 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 328 8 candidate candidate NN work_ln56cwsp7ffppl4wxeq7osqfuu 328 9 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 328 10 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 328 11 optimal optimal JJ work_ln56cwsp7ffppl4wxeq7osqfuu 328 12 maximax maximax NNP work_ln56cwsp7ffppl4wxeq7osqfuu 328 13 decision decision NN work_ln56cwsp7ffppl4wxeq7osqfuu 328 14 rule rule NN work_ln56cwsp7ffppl4wxeq7osqfuu 328 15 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 329 1 Plurality plurality NN work_ln56cwsp7ffppl4wxeq7osqfuu 329 2 gives give VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 329 3 weight weight NN work_ln56cwsp7ffppl4wxeq7osqfuu 329 4 only only RB work_ln56cwsp7ffppl4wxeq7osqfuu 329 5 to to IN work_ln56cwsp7ffppl4wxeq7osqfuu 329 6 best good JJS work_ln56cwsp7ffppl4wxeq7osqfuu 329 7 random random JJ work_ln56cwsp7ffppl4wxeq7osqfuu 329 8 variables variable NNS work_ln56cwsp7ffppl4wxeq7osqfuu 329 9 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 329 10 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 329 11 hence hence RB work_ln56cwsp7ffppl4wxeq7osqfuu 329 12 selects select VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 329 13 alternatives alternative NNS work_ln56cwsp7ffppl4wxeq7osqfuu 329 14 with with IN work_ln56cwsp7ffppl4wxeq7osqfuu 329 15 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 329 16 highest high JJS work_ln56cwsp7ffppl4wxeq7osqfuu 329 17 number number NN work_ln56cwsp7ffppl4wxeq7osqfuu 329 18 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 329 19 best good JJS work_ln56cwsp7ffppl4wxeq7osqfuu 329 20 random random JJ work_ln56cwsp7ffppl4wxeq7osqfuu 329 21 variables variable NNS work_ln56cwsp7ffppl4wxeq7osqfuu 329 22 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 330 1 In in IN work_ln56cwsp7ffppl4wxeq7osqfuu 330 2 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 330 3 context context NN work_ln56cwsp7ffppl4wxeq7osqfuu 330 4 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 330 5 n n JJ work_ln56cwsp7ffppl4wxeq7osqfuu 330 6 individuals individual NNS work_ln56cwsp7ffppl4wxeq7osqfuu 330 7 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 330 8 3 3 CD work_ln56cwsp7ffppl4wxeq7osqfuu 330 9 alternatives alternative NNS work_ln56cwsp7ffppl4wxeq7osqfuu 330 10 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 330 11 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 330 12 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 330 13 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 330 14 uniform uniform NN work_ln56cwsp7ffppl4wxeq7osqfuu 330 15 distribu- distribu- NNP work_ln56cwsp7ffppl4wxeq7osqfuu 330 16 tion tion NN work_ln56cwsp7ffppl4wxeq7osqfuu 330 17 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 330 18 Proposition proposition NN work_ln56cwsp7ffppl4wxeq7osqfuu 330 19 4.4 4.4 CD work_ln56cwsp7ffppl4wxeq7osqfuu 330 20 below below IN work_ln56cwsp7ffppl4wxeq7osqfuu 330 21 first first RB work_ln56cwsp7ffppl4wxeq7osqfuu 330 22 provides provide VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 330 23 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 330 24 exact exact JJ work_ln56cwsp7ffppl4wxeq7osqfuu 330 25 formula formula NN work_ln56cwsp7ffppl4wxeq7osqfuu 330 26 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 330 27 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 330 28 computation computation NN work_ln56cwsp7ffppl4wxeq7osqfuu 330 29 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 330 30 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 330 31 maximax maximax NNP work_ln56cwsp7ffppl4wxeq7osqfuu 330 32 expected expect VBD work_ln56cwsp7ffppl4wxeq7osqfuu 330 33 value value NN work_ln56cwsp7ffppl4wxeq7osqfuu 330 34 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 330 35 any any DT work_ln56cwsp7ffppl4wxeq7osqfuu 330 36 alternative alternative NN work_ln56cwsp7ffppl4wxeq7osqfuu 330 37 l. l. NN work_ln56cwsp7ffppl4wxeq7osqfuu 330 38 Then then RB work_ln56cwsp7ffppl4wxeq7osqfuu 330 39 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 330 40 it -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 330 41 shows show VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 330 42 that that IN work_ln56cwsp7ffppl4wxeq7osqfuu 330 43 only only RB work_ln56cwsp7ffppl4wxeq7osqfuu 330 44 under under IN work_ln56cwsp7ffppl4wxeq7osqfuu 330 45 extreme extreme JJ work_ln56cwsp7ffppl4wxeq7osqfuu 330 46 circumstances circumstance NNS work_ln56cwsp7ffppl4wxeq7osqfuu 330 47 does do VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 330 48 plurality plurality NN work_ln56cwsp7ffppl4wxeq7osqfuu 330 49 prove prove VB work_ln56cwsp7ffppl4wxeq7osqfuu 330 50 not not RB work_ln56cwsp7ffppl4wxeq7osqfuu 330 51 to to TO work_ln56cwsp7ffppl4wxeq7osqfuu 330 52 be be VB work_ln56cwsp7ffppl4wxeq7osqfuu 330 53 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 330 54 αMX αmx NN work_ln56cwsp7ffppl4wxeq7osqfuu 330 55 - - HYPH work_ln56cwsp7ffppl4wxeq7osqfuu 330 56 optimal optimal JJ work_ln56cwsp7ffppl4wxeq7osqfuu 330 57 decision decision NN work_ln56cwsp7ffppl4wxeq7osqfuu 330 58 rule rule NN work_ln56cwsp7ffppl4wxeq7osqfuu 330 59 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 331 1 Proposition proposition NN work_ln56cwsp7ffppl4wxeq7osqfuu 331 2 4.4 4.4 CD work_ln56cwsp7ffppl4wxeq7osqfuu 331 3 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 332 1 For for IN work_ln56cwsp7ffppl4wxeq7osqfuu 332 2 n× n× NNP work_ln56cwsp7ffppl4wxeq7osqfuu 332 3 3 3 CD work_ln56cwsp7ffppl4wxeq7osqfuu 332 4 societies society NNS work_ln56cwsp7ffppl4wxeq7osqfuu 332 5 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 332 6 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 332 7 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 332 8 uniform uniform JJ work_ln56cwsp7ffppl4wxeq7osqfuu 332 9 distribution distribution NN work_ln56cwsp7ffppl4wxeq7osqfuu 332 10 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 332 11 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 332 12 1 1 LS work_ln56cwsp7ffppl4wxeq7osqfuu 332 13 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 332 14 E[Ul(n E[Ul(n NNP work_ln56cwsp7ffppl4wxeq7osqfuu 332 15 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 332 16 | | NNP work_ln56cwsp7ffppl4wxeq7osqfuu 332 17 M m NN work_ln56cwsp7ffppl4wxeq7osqfuu 332 18 ] ] -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 332 19 = = -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 332 20 ∑l(2 ∑l(2 NNP work_ln56cwsp7ffppl4wxeq7osqfuu 332 21 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 332 22 a=0 a=0 NFP work_ln56cwsp7ffppl4wxeq7osqfuu 332 23 ∑l(1 ∑l(1 NNP work_ln56cwsp7ffppl4wxeq7osqfuu 332 24 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 332 25 b=0 b=0 IN work_ln56cwsp7ffppl4wxeq7osqfuu 332 26 ∑3b ∑3b CD work_ln56cwsp7ffppl4wxeq7osqfuu 332 27 c=0 c=0 NN work_ln56cwsp7ffppl4wxeq7osqfuu 332 28 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 332 29 l(2 l(2 NNP work_ln56cwsp7ffppl4wxeq7osqfuu 332 30 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 332 31 a a LS work_ln56cwsp7ffppl4wxeq7osqfuu 332 32 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 332 33 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 332 34 l(1 l(1 NNP work_ln56cwsp7ffppl4wxeq7osqfuu 332 35 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 332 36 b b LS work_ln56cwsp7ffppl4wxeq7osqfuu 332 37 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 332 38 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 332 39 3b 3b NNP work_ln56cwsp7ffppl4wxeq7osqfuu 332 40 c c NN work_ln56cwsp7ffppl4wxeq7osqfuu 332 41 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 332 42 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 332 43 −1)a+b+c3l(2)−a2a −1)a+b+c3l(2)−a2a NNP work_ln56cwsp7ffppl4wxeq7osqfuu 332 44 3l 3l NNP work_ln56cwsp7ffppl4wxeq7osqfuu 332 45 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 332 46 3)+2l(2)+a+c 3)+2l(2)+a+c NNP work_ln56cwsp7ffppl4wxeq7osqfuu 332 47 3l(3)+2l(2)+a+c+1 3l(3)+2l(2)+a+c+1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 332 48 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 332 49 2 2 LS work_ln56cwsp7ffppl4wxeq7osqfuu 332 50 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 332 51 Let let VB work_ln56cwsp7ffppl4wxeq7osqfuu 332 52 h h NN work_ln56cwsp7ffppl4wxeq7osqfuu 332 53 be be VB work_ln56cwsp7ffppl4wxeq7osqfuu 332 54 an an DT work_ln56cwsp7ffppl4wxeq7osqfuu 332 55 αMX αmx NN work_ln56cwsp7ffppl4wxeq7osqfuu 332 56 - - HYPH work_ln56cwsp7ffppl4wxeq7osqfuu 332 57 optimal optimal JJ work_ln56cwsp7ffppl4wxeq7osqfuu 332 58 alternative alternative NN work_ln56cwsp7ffppl4wxeq7osqfuu 332 59 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 332 60 let let VB work_ln56cwsp7ffppl4wxeq7osqfuu 332 61 p p NN work_ln56cwsp7ffppl4wxeq7osqfuu 332 62 ∈ ∈ VB work_ln56cwsp7ffppl4wxeq7osqfuu 332 63 SPl(M)\{h SPl(M)\{h . work_ln56cwsp7ffppl4wxeq7osqfuu 332 64 } } -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 332 65 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 333 1 Then then RB work_ln56cwsp7ffppl4wxeq7osqfuu 333 2 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 333 3 M M NNP work_ln56cwsp7ffppl4wxeq7osqfuu 333 4 must must MD work_ln56cwsp7ffppl4wxeq7osqfuu 333 5 satisfy satisfy VB work_ln56cwsp7ffppl4wxeq7osqfuu 333 6 that that IN work_ln56cwsp7ffppl4wxeq7osqfuu 333 7 either either DT work_ln56cwsp7ffppl4wxeq7osqfuu 333 8 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 333 9 a a DT work_ln56cwsp7ffppl4wxeq7osqfuu 333 10 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 333 11 h(3 h(3 NN work_ln56cwsp7ffppl4wxeq7osqfuu 333 12 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 333 13 = = NFP work_ln56cwsp7ffppl4wxeq7osqfuu 333 14 p(3 p(3 NN work_ln56cwsp7ffppl4wxeq7osqfuu 333 15 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 333 16 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 333 17 h(2 h(2 NNP work_ln56cwsp7ffppl4wxeq7osqfuu 333 18 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 333 19 ≥ ≥ UH work_ln56cwsp7ffppl4wxeq7osqfuu 333 20 p(2 p(2 NN work_ln56cwsp7ffppl4wxeq7osqfuu 333 21 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 333 22 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 333 23 or or CC work_ln56cwsp7ffppl4wxeq7osqfuu 333 24 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 333 25 b b NN work_ln56cwsp7ffppl4wxeq7osqfuu 333 26 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 333 27 h(3 h(3 NN work_ln56cwsp7ffppl4wxeq7osqfuu 333 28 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 333 29 = = NFP work_ln56cwsp7ffppl4wxeq7osqfuu 333 30 p(3 p(3 NN work_ln56cwsp7ffppl4wxeq7osqfuu 333 31 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 333 32 − − NNP work_ln56cwsp7ffppl4wxeq7osqfuu 333 33 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 333 34 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 333 35 h(2 h(2 NNP work_ln56cwsp7ffppl4wxeq7osqfuu 333 36 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 333 37 > > NFP work_ln56cwsp7ffppl4wxeq7osqfuu 333 38 n−1 n−1 NNP work_ln56cwsp7ffppl4wxeq7osqfuu 333 39 2 2 CD work_ln56cwsp7ffppl4wxeq7osqfuu 333 40 Proposition Proposition NNP work_ln56cwsp7ffppl4wxeq7osqfuu 333 41 4.4 4.4 CD work_ln56cwsp7ffppl4wxeq7osqfuu 333 42 shows show VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 333 43 that that IN work_ln56cwsp7ffppl4wxeq7osqfuu 333 44 plurality plurality NN work_ln56cwsp7ffppl4wxeq7osqfuu 333 45 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 333 46 very very RB work_ln56cwsp7ffppl4wxeq7osqfuu 333 47 difficult difficult JJ work_ln56cwsp7ffppl4wxeq7osqfuu 333 48 to to TO work_ln56cwsp7ffppl4wxeq7osqfuu 333 49 beat beat VB work_ln56cwsp7ffppl4wxeq7osqfuu 333 50 in in IN work_ln56cwsp7ffppl4wxeq7osqfuu 333 51 terms term NNS work_ln56cwsp7ffppl4wxeq7osqfuu 333 52 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 333 53 its -PRON- PRP$ work_ln56cwsp7ffppl4wxeq7osqfuu 333 54 capacity capacity NN work_ln56cwsp7ffppl4wxeq7osqfuu 333 55 to to TO work_ln56cwsp7ffppl4wxeq7osqfuu 333 56 optimize optimize VB work_ln56cwsp7ffppl4wxeq7osqfuu 333 57 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 333 58 maximax maximax NNP work_ln56cwsp7ffppl4wxeq7osqfuu 333 59 expected expect VBD work_ln56cwsp7ffppl4wxeq7osqfuu 333 60 value value NN work_ln56cwsp7ffppl4wxeq7osqfuu 333 61 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 334 1 The the DT work_ln56cwsp7ffppl4wxeq7osqfuu 334 2 plurality plurality NN work_ln56cwsp7ffppl4wxeq7osqfuu 334 3 alternative alternative NN work_ln56cwsp7ffppl4wxeq7osqfuu 334 4 can can MD work_ln56cwsp7ffppl4wxeq7osqfuu 334 5 be be VB work_ln56cwsp7ffppl4wxeq7osqfuu 334 6 surpassed surpass VBN work_ln56cwsp7ffppl4wxeq7osqfuu 334 7 15 15 CD work_ln56cwsp7ffppl4wxeq7osqfuu 334 8 by by IN work_ln56cwsp7ffppl4wxeq7osqfuu 334 9 another another DT work_ln56cwsp7ffppl4wxeq7osqfuu 334 10 alternative alternative NN work_ln56cwsp7ffppl4wxeq7osqfuu 334 11 in in IN work_ln56cwsp7ffppl4wxeq7osqfuu 334 12 terms term NNS work_ln56cwsp7ffppl4wxeq7osqfuu 334 13 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 334 14 αMX αMX NNS work_ln56cwsp7ffppl4wxeq7osqfuu 334 15 if if IN work_ln56cwsp7ffppl4wxeq7osqfuu 334 16 about about IN work_ln56cwsp7ffppl4wxeq7osqfuu 334 17 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 334 18 same same JJ work_ln56cwsp7ffppl4wxeq7osqfuu 334 19 people people NNS work_ln56cwsp7ffppl4wxeq7osqfuu 334 20 rank rank VBP work_ln56cwsp7ffppl4wxeq7osqfuu 334 21 it -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 334 22 as as IN work_ln56cwsp7ffppl4wxeq7osqfuu 334 23 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 334 24 best good JJS work_ln56cwsp7ffppl4wxeq7osqfuu 334 25 alternative alternative NN work_ln56cwsp7ffppl4wxeq7osqfuu 334 26 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 334 27 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 334 28 many many JJ work_ln56cwsp7ffppl4wxeq7osqfuu 334 29 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 334 30 more more JJR work_ln56cwsp7ffppl4wxeq7osqfuu 334 31 people people NNS work_ln56cwsp7ffppl4wxeq7osqfuu 334 32 rank rank VBP work_ln56cwsp7ffppl4wxeq7osqfuu 334 33 it -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 334 34 as as IN work_ln56cwsp7ffppl4wxeq7osqfuu 334 35 second second RB work_ln56cwsp7ffppl4wxeq7osqfuu 334 36 - - HYPH work_ln56cwsp7ffppl4wxeq7osqfuu 334 37 best good JJS work_ln56cwsp7ffppl4wxeq7osqfuu 334 38 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 335 1 Clearly clearly RB work_ln56cwsp7ffppl4wxeq7osqfuu 335 2 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 335 3 these these DT work_ln56cwsp7ffppl4wxeq7osqfuu 335 4 are be VBP work_ln56cwsp7ffppl4wxeq7osqfuu 335 5 low- low- NN work_ln56cwsp7ffppl4wxeq7osqfuu 335 6 probability probability NN work_ln56cwsp7ffppl4wxeq7osqfuu 335 7 events event NNS work_ln56cwsp7ffppl4wxeq7osqfuu 335 8 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 335 9 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 335 10 hence hence RB work_ln56cwsp7ffppl4wxeq7osqfuu 335 11 plurality plurality NN work_ln56cwsp7ffppl4wxeq7osqfuu 335 12 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 335 13 very very RB work_ln56cwsp7ffppl4wxeq7osqfuu 335 14 likely likely JJ work_ln56cwsp7ffppl4wxeq7osqfuu 335 15 to to TO work_ln56cwsp7ffppl4wxeq7osqfuu 335 16 be be VB work_ln56cwsp7ffppl4wxeq7osqfuu 335 17 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 335 18 αMX αmx NN work_ln56cwsp7ffppl4wxeq7osqfuu 335 19 - - HYPH work_ln56cwsp7ffppl4wxeq7osqfuu 335 20 optimal optimal JJ work_ln56cwsp7ffppl4wxeq7osqfuu 335 21 decision decision NN work_ln56cwsp7ffppl4wxeq7osqfuu 335 22 rule rule NN work_ln56cwsp7ffppl4wxeq7osqfuu 335 23 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 336 1 In in IN work_ln56cwsp7ffppl4wxeq7osqfuu 336 2 accordance accordance NN work_ln56cwsp7ffppl4wxeq7osqfuu 336 3 with with IN work_ln56cwsp7ffppl4wxeq7osqfuu 336 4 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 336 5 above above JJ work_ln56cwsp7ffppl4wxeq7osqfuu 336 6 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 336 7 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 336 8 computational computational JJ work_ln56cwsp7ffppl4wxeq7osqfuu 336 9 studies study NNS work_ln56cwsp7ffppl4wxeq7osqfuu 336 10 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 336 11 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 336 12 uniform uniform NN work_ln56cwsp7ffppl4wxeq7osqfuu 336 13 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 336 14 normal normal JJ work_ln56cwsp7ffppl4wxeq7osqfuu 336 15 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 336 16 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 336 17 exponential exponential JJ work_ln56cwsp7ffppl4wxeq7osqfuu 336 18 distributions distribution NNS work_ln56cwsp7ffppl4wxeq7osqfuu 336 19 show show VBP work_ln56cwsp7ffppl4wxeq7osqfuu 336 20 that that IN work_ln56cwsp7ffppl4wxeq7osqfuu 336 21 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 336 22 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 336 23 every every DT work_ln56cwsp7ffppl4wxeq7osqfuu 336 24 single single JJ work_ln56cwsp7ffppl4wxeq7osqfuu 336 25 size size NN work_ln56cwsp7ffppl4wxeq7osqfuu 336 26 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 336 27 society society NN work_ln56cwsp7ffppl4wxeq7osqfuu 336 28 scrutinized scrutinize VBN work_ln56cwsp7ffppl4wxeq7osqfuu 336 29 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 336 30 plurality plurality NN work_ln56cwsp7ffppl4wxeq7osqfuu 336 31 or or CC work_ln56cwsp7ffppl4wxeq7osqfuu 336 32 a a DT work_ln56cwsp7ffppl4wxeq7osqfuu 336 33 scoring score VBG work_ln56cwsp7ffppl4wxeq7osqfuu 336 34 rule rule NN work_ln56cwsp7ffppl4wxeq7osqfuu 336 35 in in IN work_ln56cwsp7ffppl4wxeq7osqfuu 336 36 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 336 37 neighborhood neighborhood NN work_ln56cwsp7ffppl4wxeq7osqfuu 336 38 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 336 39 plurality plurality NN work_ln56cwsp7ffppl4wxeq7osqfuu 336 40 are be VBP work_ln56cwsp7ffppl4wxeq7osqfuu 336 41 always always RB work_ln56cwsp7ffppl4wxeq7osqfuu 336 42 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 336 43 αMX αmx XX work_ln56cwsp7ffppl4wxeq7osqfuu 336 44 - - HYPH work_ln56cwsp7ffppl4wxeq7osqfuu 336 45 optimal optimal JJ work_ln56cwsp7ffppl4wxeq7osqfuu 336 46 decision decision NN work_ln56cwsp7ffppl4wxeq7osqfuu 336 47 rule rule NN work_ln56cwsp7ffppl4wxeq7osqfuu 336 48 among among IN work_ln56cwsp7ffppl4wxeq7osqfuu 336 49 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 336 50 set set NN work_ln56cwsp7ffppl4wxeq7osqfuu 336 51 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 336 52 scoring score VBG work_ln56cwsp7ffppl4wxeq7osqfuu 336 53 rules rule NNS work_ln56cwsp7ffppl4wxeq7osqfuu 336 54 evaluated evaluate VBN work_ln56cwsp7ffppl4wxeq7osqfuu 336 55 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 336 56 see see VB work_ln56cwsp7ffppl4wxeq7osqfuu 336 57 Appendix Appendix NNP work_ln56cwsp7ffppl4wxeq7osqfuu 336 58 B B NNP work_ln56cwsp7ffppl4wxeq7osqfuu 336 59 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 336 60 details detail NNS work_ln56cwsp7ffppl4wxeq7osqfuu 336 61 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 336 62 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 337 1 4.3 4.3 LS work_ln56cwsp7ffppl4wxeq7osqfuu 337 2 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 338 1 The the DT work_ln56cwsp7ffppl4wxeq7osqfuu 338 2 γMX γmx NN work_ln56cwsp7ffppl4wxeq7osqfuu 338 3 - - HYPH work_ln56cwsp7ffppl4wxeq7osqfuu 338 4 index index NN work_ln56cwsp7ffppl4wxeq7osqfuu 338 5 : : : work_ln56cwsp7ffppl4wxeq7osqfuu 338 6 Evaluating evaluate VBG work_ln56cwsp7ffppl4wxeq7osqfuu 338 7 Decision Decision NNP work_ln56cwsp7ffppl4wxeq7osqfuu 338 8 Rules rule NNS work_ln56cwsp7ffppl4wxeq7osqfuu 338 9 in in IN work_ln56cwsp7ffppl4wxeq7osqfuu 338 10 terms term NNS work_ln56cwsp7ffppl4wxeq7osqfuu 338 11 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 338 12 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 338 13 Probability Probability NNP work_ln56cwsp7ffppl4wxeq7osqfuu 338 14 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 338 15 Not not RB work_ln56cwsp7ffppl4wxeq7osqfuu 338 16 Choosing choose VBG work_ln56cwsp7ffppl4wxeq7osqfuu 338 17 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 338 18 Worst bad JJS work_ln56cwsp7ffppl4wxeq7osqfuu 338 19 Alternative alternative NN work_ln56cwsp7ffppl4wxeq7osqfuu 338 20 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 339 1 We -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 339 2 start start VBP work_ln56cwsp7ffppl4wxeq7osqfuu 339 3 with with IN work_ln56cwsp7ffppl4wxeq7osqfuu 339 4 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 339 5 characterization characterization NN work_ln56cwsp7ffppl4wxeq7osqfuu 339 6 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 339 7 a a DT work_ln56cwsp7ffppl4wxeq7osqfuu 339 8 small small JJ work_ln56cwsp7ffppl4wxeq7osqfuu 339 9 society society NN work_ln56cwsp7ffppl4wxeq7osqfuu 339 10 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 340 1 Theorem theorem NN work_ln56cwsp7ffppl4wxeq7osqfuu 340 2 4.5 4.5 CD work_ln56cwsp7ffppl4wxeq7osqfuu 340 3 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 341 1 For for IN work_ln56cwsp7ffppl4wxeq7osqfuu 341 2 2 2 CD work_ln56cwsp7ffppl4wxeq7osqfuu 341 3 × × CD work_ln56cwsp7ffppl4wxeq7osqfuu 341 4 3 3 CD work_ln56cwsp7ffppl4wxeq7osqfuu 341 5 societies society NNS work_ln56cwsp7ffppl4wxeq7osqfuu 341 6 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 341 7 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 341 8 any any DT work_ln56cwsp7ffppl4wxeq7osqfuu 341 9 culture culture NN work_ln56cwsp7ffppl4wxeq7osqfuu 341 10 with with IN work_ln56cwsp7ffppl4wxeq7osqfuu 341 11 a a DT work_ln56cwsp7ffppl4wxeq7osqfuu 341 12 symmetric symmetric JJ work_ln56cwsp7ffppl4wxeq7osqfuu 341 13 parabolic parabolic JJ work_ln56cwsp7ffppl4wxeq7osqfuu 341 14 function function NN work_ln56cwsp7ffppl4wxeq7osqfuu 341 15 : : : work_ln56cwsp7ffppl4wxeq7osqfuu 341 16 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 341 17 1 1 LS work_ln56cwsp7ffppl4wxeq7osqfuu 341 18 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 341 19 Implosion implosion NN work_ln56cwsp7ffppl4wxeq7osqfuu 341 20 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 341 21 a a DT work_ln56cwsp7ffppl4wxeq7osqfuu 341 22 γMX γmx NN work_ln56cwsp7ffppl4wxeq7osqfuu 341 23 - - HYPH work_ln56cwsp7ffppl4wxeq7osqfuu 341 24 optimal optimal JJ work_ln56cwsp7ffppl4wxeq7osqfuu 341 25 decision decision NN work_ln56cwsp7ffppl4wxeq7osqfuu 341 26 rule rule NN work_ln56cwsp7ffppl4wxeq7osqfuu 341 27 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 342 1 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 342 2 2 2 LS work_ln56cwsp7ffppl4wxeq7osqfuu 342 3 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 342 4 The the DT work_ln56cwsp7ffppl4wxeq7osqfuu 342 5 intersection intersection NN work_ln56cwsp7ffppl4wxeq7osqfuu 342 6 between between IN work_ln56cwsp7ffppl4wxeq7osqfuu 342 7 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 342 8 alternatives alternative NNS work_ln56cwsp7ffppl4wxeq7osqfuu 342 9 selected select VBN work_ln56cwsp7ffppl4wxeq7osqfuu 342 10 by by IN work_ln56cwsp7ffppl4wxeq7osqfuu 342 11 plurality plurality NN work_ln56cwsp7ffppl4wxeq7osqfuu 342 12 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 342 13 those those DT work_ln56cwsp7ffppl4wxeq7osqfuu 342 14 selected select VBN work_ln56cwsp7ffppl4wxeq7osqfuu 342 15 by by IN work_ln56cwsp7ffppl4wxeq7osqfuu 342 16 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 342 17 maximum maximum JJ work_ln56cwsp7ffppl4wxeq7osqfuu 342 18 γMX γmx NN work_ln56cwsp7ffppl4wxeq7osqfuu 342 19 - - HYPH work_ln56cwsp7ffppl4wxeq7osqfuu 342 20 optimal optimal JJ work_ln56cwsp7ffppl4wxeq7osqfuu 342 21 decision decision NN work_ln56cwsp7ffppl4wxeq7osqfuu 342 22 rule rule NN work_ln56cwsp7ffppl4wxeq7osqfuu 342 23 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 342 24 always always RB work_ln56cwsp7ffppl4wxeq7osqfuu 342 25 non non JJ work_ln56cwsp7ffppl4wxeq7osqfuu 342 26 - - JJ work_ln56cwsp7ffppl4wxeq7osqfuu 342 27 empty empty JJ work_ln56cwsp7ffppl4wxeq7osqfuu 342 28 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 343 1 Note note VB work_ln56cwsp7ffppl4wxeq7osqfuu 343 2 that that IN work_ln56cwsp7ffppl4wxeq7osqfuu 343 3 implosion implosion NN work_ln56cwsp7ffppl4wxeq7osqfuu 343 4 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 343 5 not not RB work_ln56cwsp7ffppl4wxeq7osqfuu 343 6 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 343 7 maximum maximum JJ work_ln56cwsp7ffppl4wxeq7osqfuu 343 8 γMX γmx NN work_ln56cwsp7ffppl4wxeq7osqfuu 343 9 - - HYPH work_ln56cwsp7ffppl4wxeq7osqfuu 343 10 optimal optimal JJ work_ln56cwsp7ffppl4wxeq7osqfuu 343 11 decision decision NN work_ln56cwsp7ffppl4wxeq7osqfuu 343 12 rule rule NN work_ln56cwsp7ffppl4wxeq7osqfuu 343 13 since since IN work_ln56cwsp7ffppl4wxeq7osqfuu 343 14 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 343 15 in in IN work_ln56cwsp7ffppl4wxeq7osqfuu 343 16 soci- soci- NN work_ln56cwsp7ffppl4wxeq7osqfuu 343 17 eties etie NNS work_ln56cwsp7ffppl4wxeq7osqfuu 343 18 where where WRB work_ln56cwsp7ffppl4wxeq7osqfuu 343 19 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 343 20 two two CD work_ln56cwsp7ffppl4wxeq7osqfuu 343 21 individuals individual NNS work_ln56cwsp7ffppl4wxeq7osqfuu 343 22 share share VBP work_ln56cwsp7ffppl4wxeq7osqfuu 343 23 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 343 24 same same JJ work_ln56cwsp7ffppl4wxeq7osqfuu 343 25 ranking ranking NN work_ln56cwsp7ffppl4wxeq7osqfuu 343 26 over over IN work_ln56cwsp7ffppl4wxeq7osqfuu 343 27 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 343 28 alternatives alternative NNS work_ln56cwsp7ffppl4wxeq7osqfuu 343 29 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 343 30 implosion implosion NN work_ln56cwsp7ffppl4wxeq7osqfuu 343 31 selects select VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 343 32 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 343 33 single single JJ work_ln56cwsp7ffppl4wxeq7osqfuu 343 34 best good JJS work_ln56cwsp7ffppl4wxeq7osqfuu 343 35 alternative alternative NN work_ln56cwsp7ffppl4wxeq7osqfuu 343 36 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 343 37 instead instead RB work_ln56cwsp7ffppl4wxeq7osqfuu 343 38 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 343 39 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 343 40 two two CD work_ln56cwsp7ffppl4wxeq7osqfuu 343 41 better well JJR work_ln56cwsp7ffppl4wxeq7osqfuu 343 42 alternatives alternative NNS work_ln56cwsp7ffppl4wxeq7osqfuu 343 43 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 344 1 However however RB work_ln56cwsp7ffppl4wxeq7osqfuu 344 2 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 344 3 it -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 344 4 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 344 5 not not RB work_ln56cwsp7ffppl4wxeq7osqfuu 344 6 difficult difficult JJ work_ln56cwsp7ffppl4wxeq7osqfuu 344 7 to to TO work_ln56cwsp7ffppl4wxeq7osqfuu 344 8 see see VB work_ln56cwsp7ffppl4wxeq7osqfuu 344 9 that that DT work_ln56cwsp7ffppl4wxeq7osqfuu 344 10 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 344 11 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 344 12 general general JJ work_ln56cwsp7ffppl4wxeq7osqfuu 344 13 n×k n×k NNP work_ln56cwsp7ffppl4wxeq7osqfuu 344 14 societies society NNS work_ln56cwsp7ffppl4wxeq7osqfuu 344 15 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 344 16 plurality plurality NN work_ln56cwsp7ffppl4wxeq7osqfuu 344 17 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 344 18 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 344 19 natural natural JJ work_ln56cwsp7ffppl4wxeq7osqfuu 344 20 candidate candidate NN work_ln56cwsp7ffppl4wxeq7osqfuu 344 21 to to TO work_ln56cwsp7ffppl4wxeq7osqfuu 344 22 select select VB work_ln56cwsp7ffppl4wxeq7osqfuu 344 23 γMX γmx NN work_ln56cwsp7ffppl4wxeq7osqfuu 344 24 - - HYPH work_ln56cwsp7ffppl4wxeq7osqfuu 344 25 optimal optimal JJ work_ln56cwsp7ffppl4wxeq7osqfuu 344 26 alternatives alternative NNS work_ln56cwsp7ffppl4wxeq7osqfuu 344 27 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 345 1 Below below RB work_ln56cwsp7ffppl4wxeq7osqfuu 345 2 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 345 3 in in IN work_ln56cwsp7ffppl4wxeq7osqfuu 345 4 Proposition proposition NN work_ln56cwsp7ffppl4wxeq7osqfuu 345 5 4.6 4.6 CD work_ln56cwsp7ffppl4wxeq7osqfuu 345 6 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 345 7 we -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 345 8 show show VBP work_ln56cwsp7ffppl4wxeq7osqfuu 345 9 that that IN work_ln56cwsp7ffppl4wxeq7osqfuu 345 10 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 345 11 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 345 12 any any DT work_ln56cwsp7ffppl4wxeq7osqfuu 345 13 n n NNP work_ln56cwsp7ffppl4wxeq7osqfuu 345 14 × × NN work_ln56cwsp7ffppl4wxeq7osqfuu 345 15 k k NN work_ln56cwsp7ffppl4wxeq7osqfuu 345 16 society society NN work_ln56cwsp7ffppl4wxeq7osqfuu 345 17 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 345 18 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 345 19 any any DT work_ln56cwsp7ffppl4wxeq7osqfuu 345 20 culture culture NN work_ln56cwsp7ffppl4wxeq7osqfuu 345 21 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 345 22 whenever whenever WRB work_ln56cwsp7ffppl4wxeq7osqfuu 345 23 there there EX work_ln56cwsp7ffppl4wxeq7osqfuu 345 24 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 345 25 a a DT work_ln56cwsp7ffppl4wxeq7osqfuu 345 26 set set NN work_ln56cwsp7ffppl4wxeq7osqfuu 345 27 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 345 28 alternatives alternative NNS work_ln56cwsp7ffppl4wxeq7osqfuu 345 29 Pareto Pareto NNP work_ln56cwsp7ffppl4wxeq7osqfuu 345 30 - - HYPH work_ln56cwsp7ffppl4wxeq7osqfuu 345 31 dominating dominate VBG work_ln56cwsp7ffppl4wxeq7osqfuu 345 32 some some DT work_ln56cwsp7ffppl4wxeq7osqfuu 345 33 other other JJ work_ln56cwsp7ffppl4wxeq7osqfuu 345 34 alternatives alternative NNS work_ln56cwsp7ffppl4wxeq7osqfuu 345 35 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 345 36 any any DT work_ln56cwsp7ffppl4wxeq7osqfuu 345 37 decision decision NN work_ln56cwsp7ffppl4wxeq7osqfuu 345 38 rule rule NN work_ln56cwsp7ffppl4wxeq7osqfuu 345 39 selecting select VBG work_ln56cwsp7ffppl4wxeq7osqfuu 345 40 this this DT work_ln56cwsp7ffppl4wxeq7osqfuu 345 41 set set NN work_ln56cwsp7ffppl4wxeq7osqfuu 345 42 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 345 43 Pareto Pareto NNP work_ln56cwsp7ffppl4wxeq7osqfuu 345 44 - - HYPH work_ln56cwsp7ffppl4wxeq7osqfuu 345 45 dominating dominate VBG work_ln56cwsp7ffppl4wxeq7osqfuu 345 46 alternatives alternative NNS work_ln56cwsp7ffppl4wxeq7osqfuu 345 47 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 345 48 optimal optimal JJ work_ln56cwsp7ffppl4wxeq7osqfuu 345 49 in in IN work_ln56cwsp7ffppl4wxeq7osqfuu 345 50 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 345 51 sense sense NN work_ln56cwsp7ffppl4wxeq7osqfuu 345 52 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 345 53 maximizing maximize VBG work_ln56cwsp7ffppl4wxeq7osqfuu 345 54 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 345 55 probability probability NN work_ln56cwsp7ffppl4wxeq7osqfuu 345 56 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 345 57 avoiding avoid VBG work_ln56cwsp7ffppl4wxeq7osqfuu 345 58 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 345 59 selection selection NN work_ln56cwsp7ffppl4wxeq7osqfuu 345 60 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 345 61 worst bad JJS work_ln56cwsp7ffppl4wxeq7osqfuu 345 62 maximax maximax NNP work_ln56cwsp7ffppl4wxeq7osqfuu 345 63 alternatives alternative NNS work_ln56cwsp7ffppl4wxeq7osqfuu 345 64 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 346 1 Clearly clearly RB work_ln56cwsp7ffppl4wxeq7osqfuu 346 2 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 346 3 plurality plurality NN work_ln56cwsp7ffppl4wxeq7osqfuu 346 4 alternatives alternative NNS work_ln56cwsp7ffppl4wxeq7osqfuu 346 5 tend tend VBP work_ln56cwsp7ffppl4wxeq7osqfuu 346 6 to to TO work_ln56cwsp7ffppl4wxeq7osqfuu 346 7 be be VB work_ln56cwsp7ffppl4wxeq7osqfuu 346 8 Pareto Pareto NNP work_ln56cwsp7ffppl4wxeq7osqfuu 346 9 - - HYPH work_ln56cwsp7ffppl4wxeq7osqfuu 346 10 dominating dominate VBG work_ln56cwsp7ffppl4wxeq7osqfuu 346 11 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 346 12 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 346 13 hence hence RB work_ln56cwsp7ffppl4wxeq7osqfuu 346 14 plurality plurality NN work_ln56cwsp7ffppl4wxeq7osqfuu 346 15 voting voting NN work_ln56cwsp7ffppl4wxeq7osqfuu 346 16 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 346 17 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 346 18 most most RBS work_ln56cwsp7ffppl4wxeq7osqfuu 346 19 obvious obvious JJ work_ln56cwsp7ffppl4wxeq7osqfuu 346 20 candidate candidate NN work_ln56cwsp7ffppl4wxeq7osqfuu 346 21 to to TO work_ln56cwsp7ffppl4wxeq7osqfuu 346 22 be be VB work_ln56cwsp7ffppl4wxeq7osqfuu 346 23 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 346 24 optimal optimal JJ work_ln56cwsp7ffppl4wxeq7osqfuu 346 25 decision decision NN work_ln56cwsp7ffppl4wxeq7osqfuu 346 26 rule rule NN work_ln56cwsp7ffppl4wxeq7osqfuu 346 27 in in IN work_ln56cwsp7ffppl4wxeq7osqfuu 346 28 terms term NNS work_ln56cwsp7ffppl4wxeq7osqfuu 346 29 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 346 30 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 346 31 γMX γmx NN work_ln56cwsp7ffppl4wxeq7osqfuu 346 32 - - HYPH work_ln56cwsp7ffppl4wxeq7osqfuu 346 33 index index NN work_ln56cwsp7ffppl4wxeq7osqfuu 346 34 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 347 1 We -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 347 2 write write VBP work_ln56cwsp7ffppl4wxeq7osqfuu 347 3 Ml Ml NNP work_ln56cwsp7ffppl4wxeq7osqfuu 347 4 > > XX work_ln56cwsp7ffppl4wxeq7osqfuu 347 5 Mh Mh NNP work_ln56cwsp7ffppl4wxeq7osqfuu 347 6 whenever whenever WRB work_ln56cwsp7ffppl4wxeq7osqfuu 347 7 mli mli NNP work_ln56cwsp7ffppl4wxeq7osqfuu 347 8 > > NNP work_ln56cwsp7ffppl4wxeq7osqfuu 347 9 m m NNP work_ln56cwsp7ffppl4wxeq7osqfuu 347 10 h h NNP work_ln56cwsp7ffppl4wxeq7osqfuu 347 11 i i PRP work_ln56cwsp7ffppl4wxeq7osqfuu 347 12 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 347 13 every every DT work_ln56cwsp7ffppl4wxeq7osqfuu 347 14 i. i. NN work_ln56cwsp7ffppl4wxeq7osqfuu 348 1 That that RB work_ln56cwsp7ffppl4wxeq7osqfuu 348 2 is is RB work_ln56cwsp7ffppl4wxeq7osqfuu 348 3 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 348 4 every every DT work_ln56cwsp7ffppl4wxeq7osqfuu 348 5 individ- individ- NN work_ln56cwsp7ffppl4wxeq7osqfuu 348 6 ual ual NNP work_ln56cwsp7ffppl4wxeq7osqfuu 348 7 i i PRP work_ln56cwsp7ffppl4wxeq7osqfuu 348 8 ranks rank VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 348 9 alternative alternative NNP work_ln56cwsp7ffppl4wxeq7osqfuu 348 10 l l NN work_ln56cwsp7ffppl4wxeq7osqfuu 348 11 higher high JJR work_ln56cwsp7ffppl4wxeq7osqfuu 348 12 than than IN work_ln56cwsp7ffppl4wxeq7osqfuu 348 13 alternative alternative JJ work_ln56cwsp7ffppl4wxeq7osqfuu 348 14 h. h. NN work_ln56cwsp7ffppl4wxeq7osqfuu 348 15 This this DT work_ln56cwsp7ffppl4wxeq7osqfuu 348 16 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 348 17 equivalent equivalent JJ work_ln56cwsp7ffppl4wxeq7osqfuu 348 18 to to IN work_ln56cwsp7ffppl4wxeq7osqfuu 348 19 Pareto- Pareto- NNP work_ln56cwsp7ffppl4wxeq7osqfuu 348 20 dominance dominance NN work_ln56cwsp7ffppl4wxeq7osqfuu 348 21 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 349 1 Then then RB work_ln56cwsp7ffppl4wxeq7osqfuu 349 2 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 349 3 consider consider VB work_ln56cwsp7ffppl4wxeq7osqfuu 349 4 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 349 5 following follow VBG work_ln56cwsp7ffppl4wxeq7osqfuu 349 6 set set NN work_ln56cwsp7ffppl4wxeq7osqfuu 349 7 P(M P(M NNP work_ln56cwsp7ffppl4wxeq7osqfuu 349 8 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 349 9 = = NFP work_ln56cwsp7ffppl4wxeq7osqfuu 349 10 { { -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 349 11 l l NN work_ln56cwsp7ffppl4wxeq7osqfuu 349 12 ∈ ∈ NNP work_ln56cwsp7ffppl4wxeq7osqfuu 349 13 K K NNP work_ln56cwsp7ffppl4wxeq7osqfuu 349 14 such such JJ work_ln56cwsp7ffppl4wxeq7osqfuu 349 15 that that IN work_ln56cwsp7ffppl4wxeq7osqfuu 349 16 there there EX work_ln56cwsp7ffppl4wxeq7osqfuu 349 17 exists exist VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 349 18 h h NN work_ln56cwsp7ffppl4wxeq7osqfuu 349 19 ∈ ∈ NNP work_ln56cwsp7ffppl4wxeq7osqfuu 349 20 K k NN work_ln56cwsp7ffppl4wxeq7osqfuu 349 21 with with IN work_ln56cwsp7ffppl4wxeq7osqfuu 349 22 Ml Ml NNP work_ln56cwsp7ffppl4wxeq7osqfuu 349 23 > > XX work_ln56cwsp7ffppl4wxeq7osqfuu 349 24 Mh Mh NNP work_ln56cwsp7ffppl4wxeq7osqfuu 349 25 } } -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 349 26 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 350 1 Proposition proposition NN work_ln56cwsp7ffppl4wxeq7osqfuu 350 2 4.6 4.6 CD work_ln56cwsp7ffppl4wxeq7osqfuu 350 3 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 351 1 For for IN work_ln56cwsp7ffppl4wxeq7osqfuu 351 2 n×k n×k JJ work_ln56cwsp7ffppl4wxeq7osqfuu 351 3 societies society NNS work_ln56cwsp7ffppl4wxeq7osqfuu 351 4 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 351 5 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 351 6 any any DT work_ln56cwsp7ffppl4wxeq7osqfuu 351 7 culture culture NN work_ln56cwsp7ffppl4wxeq7osqfuu 351 8 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 351 9 whenever whenever WRB work_ln56cwsp7ffppl4wxeq7osqfuu 351 10 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 351 11 set set NN work_ln56cwsp7ffppl4wxeq7osqfuu 351 12 P(M P(M NNP work_ln56cwsp7ffppl4wxeq7osqfuu 351 13 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 351 14 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 351 15 non non JJ work_ln56cwsp7ffppl4wxeq7osqfuu 351 16 - - JJ work_ln56cwsp7ffppl4wxeq7osqfuu 351 17 empty empty JJ work_ln56cwsp7ffppl4wxeq7osqfuu 351 18 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 351 19 P(M p(m ADD work_ln56cwsp7ffppl4wxeq7osqfuu 351 20 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 351 21 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 351 22 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 351 23 maximum maximum JJ work_ln56cwsp7ffppl4wxeq7osqfuu 351 24 γMX γmx NN work_ln56cwsp7ffppl4wxeq7osqfuu 351 25 - - HYPH work_ln56cwsp7ffppl4wxeq7osqfuu 351 26 optimal optimal JJ work_ln56cwsp7ffppl4wxeq7osqfuu 351 27 rule rule NN work_ln56cwsp7ffppl4wxeq7osqfuu 351 28 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 352 1 16 16 CD work_ln56cwsp7ffppl4wxeq7osqfuu 352 2 Finally finally RB work_ln56cwsp7ffppl4wxeq7osqfuu 352 3 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 352 4 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 352 5 simulations simulation NNS work_ln56cwsp7ffppl4wxeq7osqfuu 352 6 also also RB work_ln56cwsp7ffppl4wxeq7osqfuu 352 7 generally generally RB work_ln56cwsp7ffppl4wxeq7osqfuu 352 8 select select VBP work_ln56cwsp7ffppl4wxeq7osqfuu 352 9 plurality plurality NN work_ln56cwsp7ffppl4wxeq7osqfuu 352 10 as as IN work_ln56cwsp7ffppl4wxeq7osqfuu 352 11 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 352 12 best good JJS work_ln56cwsp7ffppl4wxeq7osqfuu 352 13 decision decision NN work_ln56cwsp7ffppl4wxeq7osqfuu 352 14 rule rule NN work_ln56cwsp7ffppl4wxeq7osqfuu 352 15 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 352 16 across across IN work_ln56cwsp7ffppl4wxeq7osqfuu 352 17 society society NN work_ln56cwsp7ffppl4wxeq7osqfuu 352 18 sizes size NNS work_ln56cwsp7ffppl4wxeq7osqfuu 352 19 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 352 20 cultures culture NNS work_ln56cwsp7ffppl4wxeq7osqfuu 352 21 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 352 22 see see VB work_ln56cwsp7ffppl4wxeq7osqfuu 352 23 Appendix Appendix NNP work_ln56cwsp7ffppl4wxeq7osqfuu 352 24 B B NNP work_ln56cwsp7ffppl4wxeq7osqfuu 352 25 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 352 26 a a DT work_ln56cwsp7ffppl4wxeq7osqfuu 352 27 discussion discussion NN work_ln56cwsp7ffppl4wxeq7osqfuu 352 28 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 352 29 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 353 1 5 5 CD work_ln56cwsp7ffppl4wxeq7osqfuu 353 2 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 354 1 Maximin Maximin NNP work_ln56cwsp7ffppl4wxeq7osqfuu 354 2 For for IN work_ln56cwsp7ffppl4wxeq7osqfuu 354 3 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 354 4 analysis analysis NN work_ln56cwsp7ffppl4wxeq7osqfuu 354 5 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 354 6 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 354 7 maximin maximin NN work_ln56cwsp7ffppl4wxeq7osqfuu 354 8 case case NN work_ln56cwsp7ffppl4wxeq7osqfuu 354 9 we -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 354 10 exploit exploit VBP work_ln56cwsp7ffppl4wxeq7osqfuu 354 11 a a DT work_ln56cwsp7ffppl4wxeq7osqfuu 354 12 symmetry symmetry NN work_ln56cwsp7ffppl4wxeq7osqfuu 354 13 between between IN work_ln56cwsp7ffppl4wxeq7osqfuu 354 14 maximin maximin NNP work_ln56cwsp7ffppl4wxeq7osqfuu 354 15 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 354 16 maximax maximax NNP work_ln56cwsp7ffppl4wxeq7osqfuu 354 17 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 355 1 This this DT work_ln56cwsp7ffppl4wxeq7osqfuu 355 2 allows allow VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 355 3 us -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 355 4 to to TO work_ln56cwsp7ffppl4wxeq7osqfuu 355 5 directly directly RB work_ln56cwsp7ffppl4wxeq7osqfuu 355 6 extrapolate extrapolate VB work_ln56cwsp7ffppl4wxeq7osqfuu 355 7 results result NNS work_ln56cwsp7ffppl4wxeq7osqfuu 355 8 that that WDT work_ln56cwsp7ffppl4wxeq7osqfuu 355 9 we -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 355 10 obtained obtain VBD work_ln56cwsp7ffppl4wxeq7osqfuu 355 11 from from IN work_ln56cwsp7ffppl4wxeq7osqfuu 355 12 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 355 13 maximax maximax NNP work_ln56cwsp7ffppl4wxeq7osqfuu 355 14 case case NN work_ln56cwsp7ffppl4wxeq7osqfuu 355 15 to to IN work_ln56cwsp7ffppl4wxeq7osqfuu 355 16 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 355 17 maximin maximin NN work_ln56cwsp7ffppl4wxeq7osqfuu 355 18 case case NN work_ln56cwsp7ffppl4wxeq7osqfuu 355 19 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 356 1 In in IN work_ln56cwsp7ffppl4wxeq7osqfuu 356 2 particular particular JJ work_ln56cwsp7ffppl4wxeq7osqfuu 356 3 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 356 4 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 356 5 results result NNS work_ln56cwsp7ffppl4wxeq7osqfuu 356 6 point point NN work_ln56cwsp7ffppl4wxeq7osqfuu 356 7 to to IN work_ln56cwsp7ffppl4wxeq7osqfuu 356 8 negative negative JJ work_ln56cwsp7ffppl4wxeq7osqfuu 356 9 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 356 10 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 356 11 symmetric symmetric JJ work_ln56cwsp7ffppl4wxeq7osqfuu 356 12 scoring scoring JJ work_ln56cwsp7ffppl4wxeq7osqfuu 356 13 rule rule NN work_ln56cwsp7ffppl4wxeq7osqfuu 356 14 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 356 15 plurality plurality NN work_ln56cwsp7ffppl4wxeq7osqfuu 356 16 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 356 17 as as IN work_ln56cwsp7ffppl4wxeq7osqfuu 356 18 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 356 19 obvious obvious JJ work_ln56cwsp7ffppl4wxeq7osqfuu 356 20 candidate candidate NN work_ln56cwsp7ffppl4wxeq7osqfuu 356 21 to to TO work_ln56cwsp7ffppl4wxeq7osqfuu 356 22 be be VB work_ln56cwsp7ffppl4wxeq7osqfuu 356 23 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 356 24 optimal optimal JJ work_ln56cwsp7ffppl4wxeq7osqfuu 356 25 decision decision NN work_ln56cwsp7ffppl4wxeq7osqfuu 356 26 rule rule NN work_ln56cwsp7ffppl4wxeq7osqfuu 356 27 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 356 28 maximin maximin NN work_ln56cwsp7ffppl4wxeq7osqfuu 356 29 in in IN work_ln56cwsp7ffppl4wxeq7osqfuu 356 30 terms term NNS work_ln56cwsp7ffppl4wxeq7osqfuu 356 31 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 356 32 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 356 33 three three CD work_ln56cwsp7ffppl4wxeq7osqfuu 356 34 indices index NNS work_ln56cwsp7ffppl4wxeq7osqfuu 356 35 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 356 36 consistency consistency NN work_ln56cwsp7ffppl4wxeq7osqfuu 356 37 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 356 38 α α NNP work_ln56cwsp7ffppl4wxeq7osqfuu 356 39 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 356 40 β β NNP work_ln56cwsp7ffppl4wxeq7osqfuu 356 41 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 356 42 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 356 43 γ γ NNP work_ln56cwsp7ffppl4wxeq7osqfuu 356 44 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 356 45 Denote Denote NNP work_ln56cwsp7ffppl4wxeq7osqfuu 356 46 by by IN work_ln56cwsp7ffppl4wxeq7osqfuu 356 47 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 356 48 an an DT work_ln56cwsp7ffppl4wxeq7osqfuu 356 49 n×k n×k NNP work_ln56cwsp7ffppl4wxeq7osqfuu 356 50 matrix matrix NN work_ln56cwsp7ffppl4wxeq7osqfuu 356 51 with with IN work_ln56cwsp7ffppl4wxeq7osqfuu 356 52 all all DT work_ln56cwsp7ffppl4wxeq7osqfuu 356 53 entries entry NNS work_ln56cwsp7ffppl4wxeq7osqfuu 356 54 equal equal JJ work_ln56cwsp7ffppl4wxeq7osqfuu 356 55 to to IN work_ln56cwsp7ffppl4wxeq7osqfuu 356 56 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 356 57 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 357 1 Then then RB work_ln56cwsp7ffppl4wxeq7osqfuu 357 2 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 357 3 consider consider VB work_ln56cwsp7ffppl4wxeq7osqfuu 357 4 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 357 5 follow- follow- JJ work_ln56cwsp7ffppl4wxeq7osqfuu 357 6 ing ing NN work_ln56cwsp7ffppl4wxeq7osqfuu 357 7 Theorem theorem NN work_ln56cwsp7ffppl4wxeq7osqfuu 357 8 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 358 1 Theorem theorem NN work_ln56cwsp7ffppl4wxeq7osqfuu 358 2 5.1 5.1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 358 3 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 359 1 For for IN work_ln56cwsp7ffppl4wxeq7osqfuu 359 2 n×k n×k NNP work_ln56cwsp7ffppl4wxeq7osqfuu 359 3 societies society NNS work_ln56cwsp7ffppl4wxeq7osqfuu 359 4 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 359 5 symmetric symmetric JJ work_ln56cwsp7ffppl4wxeq7osqfuu 359 6 cultures culture NNS work_ln56cwsp7ffppl4wxeq7osqfuu 359 7 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 359 8 every every DT work_ln56cwsp7ffppl4wxeq7osqfuu 359 9 M M NNP work_ln56cwsp7ffppl4wxeq7osqfuu 359 10 ∈M ∈M NNP work_ln56cwsp7ffppl4wxeq7osqfuu 359 11 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 359 12 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 359 13 l l NN work_ln56cwsp7ffppl4wxeq7osqfuu 359 14 ∈ ∈ NNP work_ln56cwsp7ffppl4wxeq7osqfuu 359 15 K K NNP work_ln56cwsp7ffppl4wxeq7osqfuu 359 16 : : : work_ln56cwsp7ffppl4wxeq7osqfuu 359 17 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 359 18 1 1 LS work_ln56cwsp7ffppl4wxeq7osqfuu 359 19 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 359 20 αlMN αlMN NNP work_ln56cwsp7ffppl4wxeq7osqfuu 359 21 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 359 22 M m NN work_ln56cwsp7ffppl4wxeq7osqfuu 359 23 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 359 24 = = NFP work_ln56cwsp7ffppl4wxeq7osqfuu 359 25 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 359 26 −α −α CD work_ln56cwsp7ffppl4wxeq7osqfuu 359 27 l l NN work_ln56cwsp7ffppl4wxeq7osqfuu 359 28 MX((k MX((k NNP work_ln56cwsp7ffppl4wxeq7osqfuu 359 29 + + CC work_ln56cwsp7ffppl4wxeq7osqfuu 359 30 1)1 1)1 NNP work_ln56cwsp7ffppl4wxeq7osqfuu 359 31 −M −M NNP work_ln56cwsp7ffppl4wxeq7osqfuu 359 32 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 359 33 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 359 34 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 359 35 2 2 LS work_ln56cwsp7ffppl4wxeq7osqfuu 359 36 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 359 37 βlMN βlMN NNP work_ln56cwsp7ffppl4wxeq7osqfuu 359 38 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 359 39 M M NNP work_ln56cwsp7ffppl4wxeq7osqfuu 359 40 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 359 41 = = SYM work_ln56cwsp7ffppl4wxeq7osqfuu 359 42 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 359 43 −γ −γ NN work_ln56cwsp7ffppl4wxeq7osqfuu 359 44 l l NN work_ln56cwsp7ffppl4wxeq7osqfuu 359 45 MX((k MX((k NNP work_ln56cwsp7ffppl4wxeq7osqfuu 359 46 + + CC work_ln56cwsp7ffppl4wxeq7osqfuu 359 47 1)1 1)1 NNP work_ln56cwsp7ffppl4wxeq7osqfuu 359 48 −M −M NNP work_ln56cwsp7ffppl4wxeq7osqfuu 359 49 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 359 50 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 359 51 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 359 52 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 359 53 3 3 LS work_ln56cwsp7ffppl4wxeq7osqfuu 359 54 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 359 55 γlMN γlMN NNP work_ln56cwsp7ffppl4wxeq7osqfuu 359 56 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 359 57 M M NNP work_ln56cwsp7ffppl4wxeq7osqfuu 359 58 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 359 59 = = NFP work_ln56cwsp7ffppl4wxeq7osqfuu 359 60 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 359 61 −β −β NN work_ln56cwsp7ffppl4wxeq7osqfuu 359 62 l l NN work_ln56cwsp7ffppl4wxeq7osqfuu 359 63 MX((k MX((k NNP work_ln56cwsp7ffppl4wxeq7osqfuu 359 64 + + CC work_ln56cwsp7ffppl4wxeq7osqfuu 359 65 1)1 1)1 NNP work_ln56cwsp7ffppl4wxeq7osqfuu 359 66 −M −M NNP work_ln56cwsp7ffppl4wxeq7osqfuu 359 67 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 359 68 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 360 1 Theorem theorem NN work_ln56cwsp7ffppl4wxeq7osqfuu 360 2 5.1 5.1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 360 3 allows allow VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 360 4 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 360 5 extrapolation extrapolation NN work_ln56cwsp7ffppl4wxeq7osqfuu 360 6 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 360 7 all all DT work_ln56cwsp7ffppl4wxeq7osqfuu 360 8 analytical analytical JJ work_ln56cwsp7ffppl4wxeq7osqfuu 360 9 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 360 10 simulations simulation NNS work_ln56cwsp7ffppl4wxeq7osqfuu 360 11 results result NNS work_ln56cwsp7ffppl4wxeq7osqfuu 360 12 ob- ob- RB work_ln56cwsp7ffppl4wxeq7osqfuu 360 13 tained taine VBD work_ln56cwsp7ffppl4wxeq7osqfuu 360 14 in in IN work_ln56cwsp7ffppl4wxeq7osqfuu 360 15 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 360 16 previous previous JJ work_ln56cwsp7ffppl4wxeq7osqfuu 360 17 section section NN work_ln56cwsp7ffppl4wxeq7osqfuu 360 18 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 360 19 maximax maximax NNP work_ln56cwsp7ffppl4wxeq7osqfuu 360 20 that that WDT work_ln56cwsp7ffppl4wxeq7osqfuu 360 21 involve involve VBP work_ln56cwsp7ffppl4wxeq7osqfuu 360 22 symmetric symmetric JJ work_ln56cwsp7ffppl4wxeq7osqfuu 360 23 cultures culture NNS work_ln56cwsp7ffppl4wxeq7osqfuu 360 24 to to IN work_ln56cwsp7ffppl4wxeq7osqfuu 360 25 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 360 26 case case NN work_ln56cwsp7ffppl4wxeq7osqfuu 360 27 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 360 28 maximin maximin NN work_ln56cwsp7ffppl4wxeq7osqfuu 360 29 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 361 1 This this DT work_ln56cwsp7ffppl4wxeq7osqfuu 361 2 means mean VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 361 3 that that IN work_ln56cwsp7ffppl4wxeq7osqfuu 361 4 negative negative JJ work_ln56cwsp7ffppl4wxeq7osqfuu 361 5 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 361 6 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 361 7 decision decision NN work_ln56cwsp7ffppl4wxeq7osqfuu 361 8 rule rule NN work_ln56cwsp7ffppl4wxeq7osqfuu 361 9 best best RB work_ln56cwsp7ffppl4wxeq7osqfuu 361 10 suited suit VBN work_ln56cwsp7ffppl4wxeq7osqfuu 361 11 to to TO work_ln56cwsp7ffppl4wxeq7osqfuu 361 12 optimize optimize VB work_ln56cwsp7ffppl4wxeq7osqfuu 361 13 maximin maximin NN work_ln56cwsp7ffppl4wxeq7osqfuu 361 14 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 362 1 For for IN work_ln56cwsp7ffppl4wxeq7osqfuu 362 2 asymmetric asymmetric JJ work_ln56cwsp7ffppl4wxeq7osqfuu 362 3 cultures culture NNS work_ln56cwsp7ffppl4wxeq7osqfuu 362 4 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 362 5 Theorem theorem NN work_ln56cwsp7ffppl4wxeq7osqfuu 362 6 5.1 5.1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 362 7 does do VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 362 8 not not RB work_ln56cwsp7ffppl4wxeq7osqfuu 362 9 apply apply VB work_ln56cwsp7ffppl4wxeq7osqfuu 362 10 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 363 1 To to TO work_ln56cwsp7ffppl4wxeq7osqfuu 363 2 test test VB work_ln56cwsp7ffppl4wxeq7osqfuu 363 3 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 363 4 robust- robust- NN work_ln56cwsp7ffppl4wxeq7osqfuu 363 5 ness ness NN work_ln56cwsp7ffppl4wxeq7osqfuu 363 6 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 363 7 our -PRON- PRP$ work_ln56cwsp7ffppl4wxeq7osqfuu 363 8 theoretical theoretical JJ work_ln56cwsp7ffppl4wxeq7osqfuu 363 9 findings finding NNS work_ln56cwsp7ffppl4wxeq7osqfuu 363 10 when when WRB work_ln56cwsp7ffppl4wxeq7osqfuu 363 11 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 363 12 culture culture NN work_ln56cwsp7ffppl4wxeq7osqfuu 363 13 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 363 14 asymmetric asymmetric JJ work_ln56cwsp7ffppl4wxeq7osqfuu 363 15 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 363 16 we -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 363 17 estimate estimate VBP work_ln56cwsp7ffppl4wxeq7osqfuu 363 18 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 363 19 value value NN work_ln56cwsp7ffppl4wxeq7osqfuu 363 20 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 363 21 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 363 22 three three CD work_ln56cwsp7ffppl4wxeq7osqfuu 363 23 indices index NNS work_ln56cwsp7ffppl4wxeq7osqfuu 363 24 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 363 25 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 363 26 case case NN work_ln56cwsp7ffppl4wxeq7osqfuu 363 27 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 363 28 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 363 29 exponential exponential JJ work_ln56cwsp7ffppl4wxeq7osqfuu 363 30 distribution distribution NN work_ln56cwsp7ffppl4wxeq7osqfuu 363 31 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 364 1 Table table NN work_ln56cwsp7ffppl4wxeq7osqfuu 364 2 3 3 CD work_ln56cwsp7ffppl4wxeq7osqfuu 364 3 in in IN work_ln56cwsp7ffppl4wxeq7osqfuu 364 4 Appen- Appen- NNP work_ln56cwsp7ffppl4wxeq7osqfuu 364 5 dix dix NN work_ln56cwsp7ffppl4wxeq7osqfuu 364 6 B B NNP work_ln56cwsp7ffppl4wxeq7osqfuu 364 7 reports report VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 364 8 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 364 9 results result NNS work_ln56cwsp7ffppl4wxeq7osqfuu 364 10 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 365 1 Once once RB work_ln56cwsp7ffppl4wxeq7osqfuu 365 2 more more RBR work_ln56cwsp7ffppl4wxeq7osqfuu 365 3 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 365 4 it -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 365 5 can can MD work_ln56cwsp7ffppl4wxeq7osqfuu 365 6 be be VB work_ln56cwsp7ffppl4wxeq7osqfuu 365 7 appreciated appreciate VBN work_ln56cwsp7ffppl4wxeq7osqfuu 365 8 that that IN work_ln56cwsp7ffppl4wxeq7osqfuu 365 9 negative negative JJ work_ln56cwsp7ffppl4wxeq7osqfuu 365 10 generally generally RB work_ln56cwsp7ffppl4wxeq7osqfuu 365 11 emerges emerge VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 365 12 as as IN work_ln56cwsp7ffppl4wxeq7osqfuu 365 13 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 365 14 optimal optimal JJ work_ln56cwsp7ffppl4wxeq7osqfuu 365 15 scoring score VBG work_ln56cwsp7ffppl4wxeq7osqfuu 365 16 rule rule NN work_ln56cwsp7ffppl4wxeq7osqfuu 365 17 in in IN work_ln56cwsp7ffppl4wxeq7osqfuu 365 18 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 365 19 computational computational JJ work_ln56cwsp7ffppl4wxeq7osqfuu 365 20 analysis analysis NN work_ln56cwsp7ffppl4wxeq7osqfuu 365 21 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 365 22 see see VB work_ln56cwsp7ffppl4wxeq7osqfuu 365 23 Appendix Appendix NNP work_ln56cwsp7ffppl4wxeq7osqfuu 365 24 B B NNP work_ln56cwsp7ffppl4wxeq7osqfuu 365 25 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 365 26 a a DT work_ln56cwsp7ffppl4wxeq7osqfuu 365 27 more more RBR work_ln56cwsp7ffppl4wxeq7osqfuu 365 28 detailed detailed JJ work_ln56cwsp7ffppl4wxeq7osqfuu 365 29 account account NN work_ln56cwsp7ffppl4wxeq7osqfuu 365 30 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 365 31 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 365 32 results result NNS work_ln56cwsp7ffppl4wxeq7osqfuu 365 33 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 365 34 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 365 35 simulations simulation NNS work_ln56cwsp7ffppl4wxeq7osqfuu 365 36 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 365 37 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 366 1 6 6 CD work_ln56cwsp7ffppl4wxeq7osqfuu 366 2 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 367 1 Conclusions conclusion NNS work_ln56cwsp7ffppl4wxeq7osqfuu 367 2 This this DT work_ln56cwsp7ffppl4wxeq7osqfuu 367 3 paper paper NN work_ln56cwsp7ffppl4wxeq7osqfuu 367 4 explores explore VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 367 5 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 367 6 relation relation NN work_ln56cwsp7ffppl4wxeq7osqfuu 367 7 between between IN work_ln56cwsp7ffppl4wxeq7osqfuu 367 8 ideals ideal NNS work_ln56cwsp7ffppl4wxeq7osqfuu 367 9 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 367 10 justice justice NN work_ln56cwsp7ffppl4wxeq7osqfuu 367 11 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 367 12 decision decision NN work_ln56cwsp7ffppl4wxeq7osqfuu 367 13 rules rule NNS work_ln56cwsp7ffppl4wxeq7osqfuu 367 14 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 368 1 Whereas whereas IN work_ln56cwsp7ffppl4wxeq7osqfuu 368 2 ideals ideal NNS work_ln56cwsp7ffppl4wxeq7osqfuu 368 3 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 368 4 justice justice NN work_ln56cwsp7ffppl4wxeq7osqfuu 368 5 are be VBP work_ln56cwsp7ffppl4wxeq7osqfuu 368 6 typically typically RB work_ln56cwsp7ffppl4wxeq7osqfuu 368 7 presented present VBN work_ln56cwsp7ffppl4wxeq7osqfuu 368 8 in in IN work_ln56cwsp7ffppl4wxeq7osqfuu 368 9 cardinal cardinal JJ work_ln56cwsp7ffppl4wxeq7osqfuu 368 10 terms term NNS work_ln56cwsp7ffppl4wxeq7osqfuu 368 11 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 368 12 decision decision NN work_ln56cwsp7ffppl4wxeq7osqfuu 368 13 rules rule NNS work_ln56cwsp7ffppl4wxeq7osqfuu 368 14 are be VBP work_ln56cwsp7ffppl4wxeq7osqfuu 368 15 primarily primarily RB work_ln56cwsp7ffppl4wxeq7osqfuu 368 16 constructed construct VBN work_ln56cwsp7ffppl4wxeq7osqfuu 368 17 on on IN work_ln56cwsp7ffppl4wxeq7osqfuu 368 18 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 368 19 basis basis NN work_ln56cwsp7ffppl4wxeq7osqfuu 368 20 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 368 21 ordinal ordinal JJ work_ln56cwsp7ffppl4wxeq7osqfuu 368 22 information information NN work_ln56cwsp7ffppl4wxeq7osqfuu 368 23 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 369 1 We -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 369 2 study study VBP work_ln56cwsp7ffppl4wxeq7osqfuu 369 3 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 369 4 cardinal cardinal JJ work_ln56cwsp7ffppl4wxeq7osqfuu 369 5 consequences consequence NNS work_ln56cwsp7ffppl4wxeq7osqfuu 369 6 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 369 7 using use VBG work_ln56cwsp7ffppl4wxeq7osqfuu 369 8 ordinal ordinal RB work_ln56cwsp7ffppl4wxeq7osqfuu 369 9 - - HYPH work_ln56cwsp7ffppl4wxeq7osqfuu 369 10 based base VBN work_ln56cwsp7ffppl4wxeq7osqfuu 369 11 decision decision NN work_ln56cwsp7ffppl4wxeq7osqfuu 369 12 rules rule NNS work_ln56cwsp7ffppl4wxeq7osqfuu 369 13 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 370 1 We -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 370 2 have have VBP work_ln56cwsp7ffppl4wxeq7osqfuu 370 3 shown show VBN work_ln56cwsp7ffppl4wxeq7osqfuu 370 4 that that IN work_ln56cwsp7ffppl4wxeq7osqfuu 370 5 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 370 6 optimal optimal JJ work_ln56cwsp7ffppl4wxeq7osqfuu 370 7 choice choice NN work_ln56cwsp7ffppl4wxeq7osqfuu 370 8 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 370 9 decision decision NN work_ln56cwsp7ffppl4wxeq7osqfuu 370 10 rules rule NNS work_ln56cwsp7ffppl4wxeq7osqfuu 370 11 depends depend VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 370 12 on on IN work_ln56cwsp7ffppl4wxeq7osqfuu 370 13 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 370 14 criterion criterion NN work_ln56cwsp7ffppl4wxeq7osqfuu 370 15 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 370 16 justice justice NN work_ln56cwsp7ffppl4wxeq7osqfuu 370 17 that that WDT work_ln56cwsp7ffppl4wxeq7osqfuu 370 18 one one CD work_ln56cwsp7ffppl4wxeq7osqfuu 370 19 wishes wish VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 370 20 to to TO work_ln56cwsp7ffppl4wxeq7osqfuu 370 21 follow follow VB work_ln56cwsp7ffppl4wxeq7osqfuu 370 22 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 371 1 Among among IN work_ln56cwsp7ffppl4wxeq7osqfuu 371 2 our -PRON- PRP$ work_ln56cwsp7ffppl4wxeq7osqfuu 371 3 specific specific JJ work_ln56cwsp7ffppl4wxeq7osqfuu 371 4 findings finding NNS work_ln56cwsp7ffppl4wxeq7osqfuu 371 5 we -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 371 6 emphasize emphasize VBP work_ln56cwsp7ffppl4wxeq7osqfuu 371 7 that that IN work_ln56cwsp7ffppl4wxeq7osqfuu 371 8 our -PRON- PRP$ work_ln56cwsp7ffppl4wxeq7osqfuu 371 9 results result NNS work_ln56cwsp7ffppl4wxeq7osqfuu 371 10 identify identify VBP work_ln56cwsp7ffppl4wxeq7osqfuu 371 11 a a DT work_ln56cwsp7ffppl4wxeq7osqfuu 371 12 particularly particularly RB work_ln56cwsp7ffppl4wxeq7osqfuu 371 13 prominent prominent JJ work_ln56cwsp7ffppl4wxeq7osqfuu 371 14 set set NN work_ln56cwsp7ffppl4wxeq7osqfuu 371 15 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 371 16 decision decision NN work_ln56cwsp7ffppl4wxeq7osqfuu 371 17 rules rule NNS work_ln56cwsp7ffppl4wxeq7osqfuu 371 18 as as IN work_ln56cwsp7ffppl4wxeq7osqfuu 371 19 optimal optimal NNP work_ln56cwsp7ffppl4wxeq7osqfuu 371 20 : : : work_ln56cwsp7ffppl4wxeq7osqfuu 371 21 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 371 22 set set NN work_ln56cwsp7ffppl4wxeq7osqfuu 371 23 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 371 24 scoring score VBG work_ln56cwsp7ffppl4wxeq7osqfuu 371 25 rules rule NNS work_ln56cwsp7ffppl4wxeq7osqfuu 371 26 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 372 1 Moreover moreover RB work_ln56cwsp7ffppl4wxeq7osqfuu 372 2 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 372 3 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 372 4 three three CD work_ln56cwsp7ffppl4wxeq7osqfuu 372 5 most most RBS work_ln56cwsp7ffppl4wxeq7osqfuu 372 6 prominent prominent JJ work_ln56cwsp7ffppl4wxeq7osqfuu 372 7 scoring score VBG work_ln56cwsp7ffppl4wxeq7osqfuu 372 8 rules rule NNS work_ln56cwsp7ffppl4wxeq7osqfuu 372 9 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 372 10 plurality plurality NN work_ln56cwsp7ffppl4wxeq7osqfuu 372 11 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 372 12 Borda Borda NNP work_ln56cwsp7ffppl4wxeq7osqfuu 372 13 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 372 14 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 372 15 negative negative JJ work_ln56cwsp7ffppl4wxeq7osqfuu 372 16 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 372 17 are be VBP work_ln56cwsp7ffppl4wxeq7osqfuu 372 18 optimal optimal JJ work_ln56cwsp7ffppl4wxeq7osqfuu 372 19 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 372 20 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 372 21 three three CD work_ln56cwsp7ffppl4wxeq7osqfuu 372 22 different different JJ work_ln56cwsp7ffppl4wxeq7osqfuu 372 23 ideals ideal NNS work_ln56cwsp7ffppl4wxeq7osqfuu 372 24 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 372 25 justice justice NN work_ln56cwsp7ffppl4wxeq7osqfuu 372 26 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 373 1 Maximax Maximax NNP work_ln56cwsp7ffppl4wxeq7osqfuu 373 2 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 373 3 best well RBS work_ln56cwsp7ffppl4wxeq7osqfuu 373 4 approached approach VBN work_ln56cwsp7ffppl4wxeq7osqfuu 373 5 by by IN work_ln56cwsp7ffppl4wxeq7osqfuu 373 6 plurality plurality NN work_ln56cwsp7ffppl4wxeq7osqfuu 373 7 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 373 8 any any DT work_ln56cwsp7ffppl4wxeq7osqfuu 373 9 possible possible JJ work_ln56cwsp7ffppl4wxeq7osqfuu 373 10 culture culture NN work_ln56cwsp7ffppl4wxeq7osqfuu 373 11 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 373 12 maximin maximin NN work_ln56cwsp7ffppl4wxeq7osqfuu 373 13 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 373 14 best well RBS work_ln56cwsp7ffppl4wxeq7osqfuu 373 15 approached approach VBN work_ln56cwsp7ffppl4wxeq7osqfuu 373 16 by by IN work_ln56cwsp7ffppl4wxeq7osqfuu 373 17 negative negative JJ work_ln56cwsp7ffppl4wxeq7osqfuu 373 18 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 373 19 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 373 20 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 373 21 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 373 22 a a DT work_ln56cwsp7ffppl4wxeq7osqfuu 373 23 range range NN work_ln56cwsp7ffppl4wxeq7osqfuu 373 24 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 373 25 cultures culture NNS work_ln56cwsp7ffppl4wxeq7osqfuu 373 26 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 373 27 utilitarianism utilitarianism NN work_ln56cwsp7ffppl4wxeq7osqfuu 373 28 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 373 29 best well RBS work_ln56cwsp7ffppl4wxeq7osqfuu 373 30 approached approach VBN work_ln56cwsp7ffppl4wxeq7osqfuu 373 31 by by IN work_ln56cwsp7ffppl4wxeq7osqfuu 373 32 Borda Borda NNP work_ln56cwsp7ffppl4wxeq7osqfuu 373 33 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 374 1 17 17 CD work_ln56cwsp7ffppl4wxeq7osqfuu 374 2 Moreover moreover RB work_ln56cwsp7ffppl4wxeq7osqfuu 374 3 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 374 4 in in IN work_ln56cwsp7ffppl4wxeq7osqfuu 374 5 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 374 6 latter latter JJ work_ln56cwsp7ffppl4wxeq7osqfuu 374 7 case case NN work_ln56cwsp7ffppl4wxeq7osqfuu 374 8 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 374 9 utilitarianism utilitarianism NN work_ln56cwsp7ffppl4wxeq7osqfuu 374 10 we -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 374 11 provide provide VBP work_ln56cwsp7ffppl4wxeq7osqfuu 374 12 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 374 13 mapping mapping NN work_ln56cwsp7ffppl4wxeq7osqfuu 374 14 between between IN work_ln56cwsp7ffppl4wxeq7osqfuu 374 15 cultures culture NNS work_ln56cwsp7ffppl4wxeq7osqfuu 374 16 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 374 17 optimal optimal JJ work_ln56cwsp7ffppl4wxeq7osqfuu 374 18 decision decision NN work_ln56cwsp7ffppl4wxeq7osqfuu 374 19 rules rule NNS work_ln56cwsp7ffppl4wxeq7osqfuu 374 20 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 375 1 Appendix Appendix NNP work_ln56cwsp7ffppl4wxeq7osqfuu 375 2 A. A. NNP work_ln56cwsp7ffppl4wxeq7osqfuu 376 1 Proofs Proofs NNP work_ln56cwsp7ffppl4wxeq7osqfuu 376 2 Proof Proof NNP work_ln56cwsp7ffppl4wxeq7osqfuu 376 3 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 376 4 Theorem Theorem NNP work_ln56cwsp7ffppl4wxeq7osqfuu 376 5 3.1 3.1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 376 6 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 377 1 Recall recall VB work_ln56cwsp7ffppl4wxeq7osqfuu 377 2 that that IN work_ln56cwsp7ffppl4wxeq7osqfuu 377 3 αlUT αlUT NNP work_ln56cwsp7ffppl4wxeq7osqfuu 377 4 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 377 5 M m NN work_ln56cwsp7ffppl4wxeq7osqfuu 377 6 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 377 7 = = NFP work_ln56cwsp7ffppl4wxeq7osqfuu 377 8 E e NN work_ln56cwsp7ffppl4wxeq7osqfuu 377 9 [ [ -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 377 10 ∑ ∑ . work_ln56cwsp7ffppl4wxeq7osqfuu 377 11 i i PRP work_ln56cwsp7ffppl4wxeq7osqfuu 377 12 U U NNP work_ln56cwsp7ffppl4wxeq7osqfuu 377 13 l l NN work_ln56cwsp7ffppl4wxeq7osqfuu 377 14 i i NN work_ln56cwsp7ffppl4wxeq7osqfuu 377 15 n n CC work_ln56cwsp7ffppl4wxeq7osqfuu 377 16 | | NNP work_ln56cwsp7ffppl4wxeq7osqfuu 377 17 M M NNP work_ln56cwsp7ffppl4wxeq7osqfuu 377 18 ] ] -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 377 19 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 378 1 The the DT work_ln56cwsp7ffppl4wxeq7osqfuu 378 2 independence independence NN work_ln56cwsp7ffppl4wxeq7osqfuu 378 3 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 378 4 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 378 5 random random JJ work_ln56cwsp7ffppl4wxeq7osqfuu 378 6 variables variable NNS work_ln56cwsp7ffppl4wxeq7osqfuu 378 7 Uli Uli NNP work_ln56cwsp7ffppl4wxeq7osqfuu 378 8 across across IN work_ln56cwsp7ffppl4wxeq7osqfuu 378 9 individuals individual NNS work_ln56cwsp7ffppl4wxeq7osqfuu 378 10 allows allow VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 378 11 us -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 378 12 to to TO work_ln56cwsp7ffppl4wxeq7osqfuu 378 13 write write VB work_ln56cwsp7ffppl4wxeq7osqfuu 378 14 α α IN work_ln56cwsp7ffppl4wxeq7osqfuu 378 15 l l NN work_ln56cwsp7ffppl4wxeq7osqfuu 378 16 UT UT NNP work_ln56cwsp7ffppl4wxeq7osqfuu 378 17 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 378 18 M M NNP work_ln56cwsp7ffppl4wxeq7osqfuu 378 19 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 378 20 = = NFP work_ln56cwsp7ffppl4wxeq7osqfuu 378 21 ∑ ∑ . work_ln56cwsp7ffppl4wxeq7osqfuu 378 22 i i PRP work_ln56cwsp7ffppl4wxeq7osqfuu 378 23 E[U e[u VBP work_ln56cwsp7ffppl4wxeq7osqfuu 378 24 l l NN work_ln56cwsp7ffppl4wxeq7osqfuu 378 25 i i NN work_ln56cwsp7ffppl4wxeq7osqfuu 378 26 | | NNP work_ln56cwsp7ffppl4wxeq7osqfuu 378 27 Mi]/n Mi]/n NNP work_ln56cwsp7ffppl4wxeq7osqfuu 378 28 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 379 1 In in IN work_ln56cwsp7ffppl4wxeq7osqfuu 379 2 addition addition NN work_ln56cwsp7ffppl4wxeq7osqfuu 379 3 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 379 4 since since IN work_ln56cwsp7ffppl4wxeq7osqfuu 379 5 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 379 6 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 379 7 every every DT work_ln56cwsp7ffppl4wxeq7osqfuu 379 8 individual individual NN work_ln56cwsp7ffppl4wxeq7osqfuu 379 9 i i PRP work_ln56cwsp7ffppl4wxeq7osqfuu 379 10 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 379 11 all all PDT work_ln56cwsp7ffppl4wxeq7osqfuu 379 12 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 379 13 random random JJ work_ln56cwsp7ffppl4wxeq7osqfuu 379 14 variables variable NNS work_ln56cwsp7ffppl4wxeq7osqfuu 379 15 are be VBP work_ln56cwsp7ffppl4wxeq7osqfuu 379 16 identi- identi- VBN work_ln56cwsp7ffppl4wxeq7osqfuu 379 17 cally cally RB work_ln56cwsp7ffppl4wxeq7osqfuu 379 18 distributed distribute VBN work_ln56cwsp7ffppl4wxeq7osqfuu 379 19 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 379 20 we -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 379 21 can can MD work_ln56cwsp7ffppl4wxeq7osqfuu 379 22 write write VB work_ln56cwsp7ffppl4wxeq7osqfuu 379 23 αlUT αlUT NNP work_ln56cwsp7ffppl4wxeq7osqfuu 379 24 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 379 25 M m NN work_ln56cwsp7ffppl4wxeq7osqfuu 379 26 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 379 27 = = NFP work_ln56cwsp7ffppl4wxeq7osqfuu 379 28 ∑ ∑ . work_ln56cwsp7ffppl4wxeq7osqfuu 379 29 i i PRP work_ln56cwsp7ffppl4wxeq7osqfuu 379 30 E[U e[u VBP work_ln56cwsp7ffppl4wxeq7osqfuu 379 31 l l NN work_ln56cwsp7ffppl4wxeq7osqfuu 379 32 i i NN work_ln56cwsp7ffppl4wxeq7osqfuu 379 33 | | NNP work_ln56cwsp7ffppl4wxeq7osqfuu 379 34 Mli Mli NNP work_ln56cwsp7ffppl4wxeq7osqfuu 379 35 ] ] -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 379 36 /n /n . work_ln56cwsp7ffppl4wxeq7osqfuu 379 37 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 380 1 Finally finally RB work_ln56cwsp7ffppl4wxeq7osqfuu 380 2 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 380 3 since since IN work_ln56cwsp7ffppl4wxeq7osqfuu 380 4 Ul1 ul1 NN work_ln56cwsp7ffppl4wxeq7osqfuu 380 5 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 380 6 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 381 1 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 382 1 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 383 1 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 383 2 Uln Uln NNP work_ln56cwsp7ffppl4wxeq7osqfuu 383 3 are be VBP work_ln56cwsp7ffppl4wxeq7osqfuu 383 4 also also RB work_ln56cwsp7ffppl4wxeq7osqfuu 383 5 identically identically RB work_ln56cwsp7ffppl4wxeq7osqfuu 383 6 distributed distribute VBN work_ln56cwsp7ffppl4wxeq7osqfuu 383 7 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 383 8 we -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 383 9 can can MD work_ln56cwsp7ffppl4wxeq7osqfuu 383 10 write write VB work_ln56cwsp7ffppl4wxeq7osqfuu 383 11 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 383 12 last last JJ work_ln56cwsp7ffppl4wxeq7osqfuu 383 13 expression expression NN work_ln56cwsp7ffppl4wxeq7osqfuu 383 14 in in IN work_ln56cwsp7ffppl4wxeq7osqfuu 383 15 terms term NNS work_ln56cwsp7ffppl4wxeq7osqfuu 383 16 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 383 17 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 383 18 num- num- NNP work_ln56cwsp7ffppl4wxeq7osqfuu 383 19 ber ber NN work_ln56cwsp7ffppl4wxeq7osqfuu 383 20 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 383 21 order order NN work_ln56cwsp7ffppl4wxeq7osqfuu 383 22 statistics statistic NNS work_ln56cwsp7ffppl4wxeq7osqfuu 383 23 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 384 1 First first RB work_ln56cwsp7ffppl4wxeq7osqfuu 384 2 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 384 3 note note VB work_ln56cwsp7ffppl4wxeq7osqfuu 384 4 that that IN work_ln56cwsp7ffppl4wxeq7osqfuu 384 5 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 384 6 since since IN work_ln56cwsp7ffppl4wxeq7osqfuu 384 7 U u NN work_ln56cwsp7ffppl4wxeq7osqfuu 384 8 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 384 9 h h NNP work_ln56cwsp7ffppl4wxeq7osqfuu 384 10 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 384 11 i i PRP work_ln56cwsp7ffppl4wxeq7osqfuu 384 12 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 384 13 U u NN work_ln56cwsp7ffppl4wxeq7osqfuu 384 14 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 384 15 h h NNP work_ln56cwsp7ffppl4wxeq7osqfuu 384 16 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 384 17 j j NNP work_ln56cwsp7ffppl4wxeq7osqfuu 384 18 are be VBP work_ln56cwsp7ffppl4wxeq7osqfuu 384 19 identically identically RB work_ln56cwsp7ffppl4wxeq7osqfuu 384 20 distributed distribute VBN work_ln56cwsp7ffppl4wxeq7osqfuu 384 21 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 384 22 we -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 384 23 may may MD work_ln56cwsp7ffppl4wxeq7osqfuu 384 24 simply simply RB work_ln56cwsp7ffppl4wxeq7osqfuu 384 25 write write VB work_ln56cwsp7ffppl4wxeq7osqfuu 384 26 U(h u(h CD work_ln56cwsp7ffppl4wxeq7osqfuu 384 27 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 384 28 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 385 1 Then then RB work_ln56cwsp7ffppl4wxeq7osqfuu 385 2 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 385 3 αlUT αlUT NNP work_ln56cwsp7ffppl4wxeq7osqfuu 385 4 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 385 5 M M NNP work_ln56cwsp7ffppl4wxeq7osqfuu 385 6 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 385 7 = = NFP work_ln56cwsp7ffppl4wxeq7osqfuu 385 8 ∑ ∑ . work_ln56cwsp7ffppl4wxeq7osqfuu 385 9 h h NNP work_ln56cwsp7ffppl4wxeq7osqfuu 385 10 l l NN work_ln56cwsp7ffppl4wxeq7osqfuu 385 11 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 385 12 h)E[U(h h)E[U(h NNP work_ln56cwsp7ffppl4wxeq7osqfuu 385 13 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 385 14 ] ] -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 385 15 n n XX work_ln56cwsp7ffppl4wxeq7osqfuu 385 16 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 386 1 The the DT work_ln56cwsp7ffppl4wxeq7osqfuu 386 2 value value NN work_ln56cwsp7ffppl4wxeq7osqfuu 386 3 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 386 4 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 386 5 difference difference NN work_ln56cwsp7ffppl4wxeq7osqfuu 386 6 between between IN work_ln56cwsp7ffppl4wxeq7osqfuu 386 7 two two CD work_ln56cwsp7ffppl4wxeq7osqfuu 386 8 alternatives alternative NNS work_ln56cwsp7ffppl4wxeq7osqfuu 386 9 l l NNP work_ln56cwsp7ffppl4wxeq7osqfuu 386 10 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 386 11 q q NNP work_ln56cwsp7ffppl4wxeq7osqfuu 386 12 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 386 13 αlUT αlUT NNP work_ln56cwsp7ffppl4wxeq7osqfuu 386 14 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 386 15 M)−α M)−α NNP work_ln56cwsp7ffppl4wxeq7osqfuu 386 16 q q NNP work_ln56cwsp7ffppl4wxeq7osqfuu 386 17 UT UT NNP work_ln56cwsp7ffppl4wxeq7osqfuu 386 18 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 386 19 M M NNP work_ln56cwsp7ffppl4wxeq7osqfuu 386 20 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 386 21 = = NFP work_ln56cwsp7ffppl4wxeq7osqfuu 386 22 ∑ ∑ . work_ln56cwsp7ffppl4wxeq7osqfuu 386 23 h h NNP work_ln56cwsp7ffppl4wxeq7osqfuu 386 24 l l NN work_ln56cwsp7ffppl4wxeq7osqfuu 386 25 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 386 26 h)E[U(h h)E[U(h NNP work_ln56cwsp7ffppl4wxeq7osqfuu 386 27 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 386 28 ] ] -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 386 29 n n NNP work_ln56cwsp7ffppl4wxeq7osqfuu 386 30 − − NNP work_ln56cwsp7ffppl4wxeq7osqfuu 386 31 ∑ ∑ . work_ln56cwsp7ffppl4wxeq7osqfuu 386 32 h h NNP work_ln56cwsp7ffppl4wxeq7osqfuu 386 33 q q NNP work_ln56cwsp7ffppl4wxeq7osqfuu 386 34 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 386 35 h)E[U(h h)E[U(h NNP work_ln56cwsp7ffppl4wxeq7osqfuu 386 36 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 386 37 ] ] -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 386 38 n n NN work_ln56cwsp7ffppl4wxeq7osqfuu 386 39 = = SYM work_ln56cwsp7ffppl4wxeq7osqfuu 386 40 ∑ ∑ . work_ln56cwsp7ffppl4wxeq7osqfuu 386 41 h(l h(l NNP work_ln56cwsp7ffppl4wxeq7osqfuu 386 42 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 386 43 h)−q(h))E[U(h h)−q(h))e[u(h NN work_ln56cwsp7ffppl4wxeq7osqfuu 386 44 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 386 45 ] ] -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 386 46 n n XX work_ln56cwsp7ffppl4wxeq7osqfuu 386 47 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 387 1 Note note VB work_ln56cwsp7ffppl4wxeq7osqfuu 387 2 that that IN work_ln56cwsp7ffppl4wxeq7osqfuu 387 3 ∑ ∑ . work_ln56cwsp7ffppl4wxeq7osqfuu 387 4 h h NNP work_ln56cwsp7ffppl4wxeq7osqfuu 387 5 l l NN work_ln56cwsp7ffppl4wxeq7osqfuu 387 6 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 387 7 h h NN work_ln56cwsp7ffppl4wxeq7osqfuu 387 8 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 387 9 = = NFP work_ln56cwsp7ffppl4wxeq7osqfuu 387 10 ∑ ∑ . work_ln56cwsp7ffppl4wxeq7osqfuu 387 11 h h NNP work_ln56cwsp7ffppl4wxeq7osqfuu 387 12 q q NNP work_ln56cwsp7ffppl4wxeq7osqfuu 387 13 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 387 14 h h NNP work_ln56cwsp7ffppl4wxeq7osqfuu 387 15 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 387 16 = = NFP work_ln56cwsp7ffppl4wxeq7osqfuu 387 17 n n XX work_ln56cwsp7ffppl4wxeq7osqfuu 387 18 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 387 19 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 387 20 therefore therefore RB work_ln56cwsp7ffppl4wxeq7osqfuu 387 21 ∑ ∑ . work_ln56cwsp7ffppl4wxeq7osqfuu 387 22 h h NN work_ln56cwsp7ffppl4wxeq7osqfuu 387 23 E[U e[u CD work_ln56cwsp7ffppl4wxeq7osqfuu 387 24 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 387 25 1)](l(h)−q(h 1)](l(h)−q(h CD work_ln56cwsp7ffppl4wxeq7osqfuu 387 26 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 387 27 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 387 28 n n LS work_ln56cwsp7ffppl4wxeq7osqfuu 387 29 = = SYM work_ln56cwsp7ffppl4wxeq7osqfuu 387 30 0 0 NFP work_ln56cwsp7ffppl4wxeq7osqfuu 387 31 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 388 1 We -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 388 2 then then RB work_ln56cwsp7ffppl4wxeq7osqfuu 388 3 write write VBP work_ln56cwsp7ffppl4wxeq7osqfuu 388 4 αlUT αlUT NNP work_ln56cwsp7ffppl4wxeq7osqfuu 388 5 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 388 6 M)−α M)−α NNP work_ln56cwsp7ffppl4wxeq7osqfuu 388 7 q q NNP work_ln56cwsp7ffppl4wxeq7osqfuu 388 8 UT UT NNP work_ln56cwsp7ffppl4wxeq7osqfuu 388 9 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 388 10 M M NNP work_ln56cwsp7ffppl4wxeq7osqfuu 388 11 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 388 12 = = NFP work_ln56cwsp7ffppl4wxeq7osqfuu 388 13 ∑ ∑ . work_ln56cwsp7ffppl4wxeq7osqfuu 388 14 h(l h(l NNP work_ln56cwsp7ffppl4wxeq7osqfuu 388 15 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 388 16 h)−q(h))E[U(h h)−q(h))e[u(h NN work_ln56cwsp7ffppl4wxeq7osqfuu 388 17 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 388 18 ] ] -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 388 19 n n CC work_ln56cwsp7ffppl4wxeq7osqfuu 388 20 −∑ −∑ NNP work_ln56cwsp7ffppl4wxeq7osqfuu 388 21 h h NN work_ln56cwsp7ffppl4wxeq7osqfuu 388 22 E[U e[u CD work_ln56cwsp7ffppl4wxeq7osqfuu 388 23 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 388 24 1)](l(h)−q(h 1)](l(h)−q(h CD work_ln56cwsp7ffppl4wxeq7osqfuu 388 25 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 388 26 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 388 27 n n LS work_ln56cwsp7ffppl4wxeq7osqfuu 388 28 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 388 29 hence hence RB work_ln56cwsp7ffppl4wxeq7osqfuu 388 30 αlUT αlUT NNP work_ln56cwsp7ffppl4wxeq7osqfuu 388 31 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 388 32 M M NNP work_ln56cwsp7ffppl4wxeq7osqfuu 388 33 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 388 34 − − NNP work_ln56cwsp7ffppl4wxeq7osqfuu 388 35 α α NNP work_ln56cwsp7ffppl4wxeq7osqfuu 388 36 q q NNP work_ln56cwsp7ffppl4wxeq7osqfuu 388 37 UT UT NNP work_ln56cwsp7ffppl4wxeq7osqfuu 388 38 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 388 39 M M NNP work_ln56cwsp7ffppl4wxeq7osqfuu 388 40 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 388 41 = = NFP work_ln56cwsp7ffppl4wxeq7osqfuu 388 42 ∑ ∑ . work_ln56cwsp7ffppl4wxeq7osqfuu 388 43 h(l h(l NNP work_ln56cwsp7ffppl4wxeq7osqfuu 388 44 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 388 45 h)−q(h))(E[U(h)]−E[U(1 h)−q(h))(E[U(h)]−E[U(1 NNP work_ln56cwsp7ffppl4wxeq7osqfuu 388 46 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 388 47 ] ] -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 388 48 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 388 49 n n XX work_ln56cwsp7ffppl4wxeq7osqfuu 388 50 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 389 1 Note note VB work_ln56cwsp7ffppl4wxeq7osqfuu 389 2 that that IN work_ln56cwsp7ffppl4wxeq7osqfuu 389 3 E[U(k E[U(k NNP work_ln56cwsp7ffppl4wxeq7osqfuu 389 4 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 389 5 ] ] -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 389 6 − − NNP work_ln56cwsp7ffppl4wxeq7osqfuu 389 7 E[U(1 E[U(1 NNP work_ln56cwsp7ffppl4wxeq7osqfuu 389 8 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 389 9 ] ] -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 389 10 > > XX work_ln56cwsp7ffppl4wxeq7osqfuu 389 11 0 0 CD work_ln56cwsp7ffppl4wxeq7osqfuu 389 12 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 390 1 Then then RB work_ln56cwsp7ffppl4wxeq7osqfuu 390 2 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 390 3 multiplying multiply VBG work_ln56cwsp7ffppl4wxeq7osqfuu 390 4 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 390 5 dividing divide VBG work_ln56cwsp7ffppl4wxeq7osqfuu 390 6 by by IN work_ln56cwsp7ffppl4wxeq7osqfuu 390 7 E[U(k E[U(k NNP work_ln56cwsp7ffppl4wxeq7osqfuu 390 8 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 390 9 ] ] -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 390 10 − − NNP work_ln56cwsp7ffppl4wxeq7osqfuu 390 11 E[U(1 E[U(1 . work_ln56cwsp7ffppl4wxeq7osqfuu 390 12 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 390 13 ] ] -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 390 14 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 390 15 we -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 390 16 have have VBP work_ln56cwsp7ffppl4wxeq7osqfuu 390 17 αlUT αlUT NNP work_ln56cwsp7ffppl4wxeq7osqfuu 390 18 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 390 19 M m NN work_ln56cwsp7ffppl4wxeq7osqfuu 390 20 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 390 21 −α −α . work_ln56cwsp7ffppl4wxeq7osqfuu 390 22 q q NNP work_ln56cwsp7ffppl4wxeq7osqfuu 390 23 UT UT NNP work_ln56cwsp7ffppl4wxeq7osqfuu 390 24 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 390 25 M M NNP work_ln56cwsp7ffppl4wxeq7osqfuu 390 26 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 390 27 = = NFP work_ln56cwsp7ffppl4wxeq7osqfuu 390 28 E[U(k E[U(k NNP work_ln56cwsp7ffppl4wxeq7osqfuu 390 29 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 390 30 ] ] -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 390 31 − − NNP work_ln56cwsp7ffppl4wxeq7osqfuu 390 32 E[U(1 E[U(1 NNP work_ln56cwsp7ffppl4wxeq7osqfuu 390 33 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 390 34 ] ] -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 390 35 n n NN work_ln56cwsp7ffppl4wxeq7osqfuu 390 36 ∑ ∑ NNP work_ln56cwsp7ffppl4wxeq7osqfuu 390 37 h(l h(l NN work_ln56cwsp7ffppl4wxeq7osqfuu 390 38 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 390 39 h h NN work_ln56cwsp7ffppl4wxeq7osqfuu 390 40 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 390 41 − − NNP work_ln56cwsp7ffppl4wxeq7osqfuu 390 42 q(h))(E[U(h q(h))(e[u(h ADD work_ln56cwsp7ffppl4wxeq7osqfuu 390 43 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 390 44 ] ] -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 390 45 − − NNP work_ln56cwsp7ffppl4wxeq7osqfuu 390 46 E[U(1 E[U(1 . work_ln56cwsp7ffppl4wxeq7osqfuu 390 47 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 390 48 ] ] -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 390 49 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 390 50 E[U(k E[U(k NNP work_ln56cwsp7ffppl4wxeq7osqfuu 390 51 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 390 52 ] ] -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 390 53 − − NNP work_ln56cwsp7ffppl4wxeq7osqfuu 390 54 E[U(1 E[U(1 . work_ln56cwsp7ffppl4wxeq7osqfuu 390 55 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 390 56 ] ] -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 390 57 = = NFP work_ln56cwsp7ffppl4wxeq7osqfuu 390 58 E[U(k E[U(k NNP work_ln56cwsp7ffppl4wxeq7osqfuu 390 59 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 390 60 ] ] -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 390 61 − − NNP work_ln56cwsp7ffppl4wxeq7osqfuu 390 62 E[U(1 E[U(1 NNP work_ln56cwsp7ffppl4wxeq7osqfuu 390 63 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 390 64 ] ] -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 390 65 n n NNP work_ln56cwsp7ffppl4wxeq7osqfuu 390 66 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 390 67 ∑ ∑ . work_ln56cwsp7ffppl4wxeq7osqfuu 390 68 h h NN work_ln56cwsp7ffppl4wxeq7osqfuu 390 69 [ [ -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 390 70 l(h l(h NNP work_ln56cwsp7ffppl4wxeq7osqfuu 390 71 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 390 72 − − NNP work_ln56cwsp7ffppl4wxeq7osqfuu 390 73 q(h)]S∗h q(h)]S∗h NNP work_ln56cwsp7ffppl4wxeq7osqfuu 390 74 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 390 75 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 391 1 Since since IN work_ln56cwsp7ffppl4wxeq7osqfuu 391 2 E[U(k E[U(k NNP work_ln56cwsp7ffppl4wxeq7osqfuu 391 3 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 391 4 ] ] -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 391 5 − − NNP work_ln56cwsp7ffppl4wxeq7osqfuu 391 6 E[U(1 E[U(1 NNP work_ln56cwsp7ffppl4wxeq7osqfuu 391 7 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 391 8 ] ] -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 391 9 > > NNP work_ln56cwsp7ffppl4wxeq7osqfuu 391 10 0 0 NFP work_ln56cwsp7ffppl4wxeq7osqfuu 391 11 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 391 12 it -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 391 13 follows follow VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 391 14 that that IN work_ln56cwsp7ffppl4wxeq7osqfuu 391 15 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 391 16 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 391 17 every every DT work_ln56cwsp7ffppl4wxeq7osqfuu 391 18 M M NNP work_ln56cwsp7ffppl4wxeq7osqfuu 391 19 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 391 20 S∗ s∗ NN work_ln56cwsp7ffppl4wxeq7osqfuu 391 21 gives give VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 391 22 exactly exactly RB work_ln56cwsp7ffppl4wxeq7osqfuu 391 23 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 391 24 same same JJ work_ln56cwsp7ffppl4wxeq7osqfuu 391 25 ranking ranking NN work_ln56cwsp7ffppl4wxeq7osqfuu 391 26 over over IN work_ln56cwsp7ffppl4wxeq7osqfuu 391 27 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 391 28 alternatives alternative NNS work_ln56cwsp7ffppl4wxeq7osqfuu 391 29 as as IN work_ln56cwsp7ffppl4wxeq7osqfuu 391 30 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 391 31 one one NN work_ln56cwsp7ffppl4wxeq7osqfuu 391 32 given give VBN work_ln56cwsp7ffppl4wxeq7osqfuu 391 33 by by IN work_ln56cwsp7ffppl4wxeq7osqfuu 391 34 utilitarianism utilitarianism NN work_ln56cwsp7ffppl4wxeq7osqfuu 391 35 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 392 1 Hence hence RB work_ln56cwsp7ffppl4wxeq7osqfuu 392 2 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 392 3 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 392 4 two two CD work_ln56cwsp7ffppl4wxeq7osqfuu 392 5 claims claim NNS work_ln56cwsp7ffppl4wxeq7osqfuu 392 6 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 392 7 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 392 8 theorem theorem JJ work_ln56cwsp7ffppl4wxeq7osqfuu 392 9 follow follow NN work_ln56cwsp7ffppl4wxeq7osqfuu 392 10 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 393 1 � � NNP work_ln56cwsp7ffppl4wxeq7osqfuu 393 2 Proof Proof NNP work_ln56cwsp7ffppl4wxeq7osqfuu 393 3 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 393 4 Corollary Corollary NNP work_ln56cwsp7ffppl4wxeq7osqfuu 393 5 3.2 3.2 CD work_ln56cwsp7ffppl4wxeq7osqfuu 393 6 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 394 1 The the DT work_ln56cwsp7ffppl4wxeq7osqfuu 394 2 first first JJ work_ln56cwsp7ffppl4wxeq7osqfuu 394 3 two two CD work_ln56cwsp7ffppl4wxeq7osqfuu 394 4 points point NNS work_ln56cwsp7ffppl4wxeq7osqfuu 394 5 in in IN work_ln56cwsp7ffppl4wxeq7osqfuu 394 6 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 394 7 corollary corollary JJ work_ln56cwsp7ffppl4wxeq7osqfuu 394 8 follow follow NN work_ln56cwsp7ffppl4wxeq7osqfuu 394 9 directly directly RB work_ln56cwsp7ffppl4wxeq7osqfuu 394 10 from from IN work_ln56cwsp7ffppl4wxeq7osqfuu 394 11 Theorem Theorem NNP work_ln56cwsp7ffppl4wxeq7osqfuu 394 12 3.1 3.1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 394 13 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 395 1 To to TO work_ln56cwsp7ffppl4wxeq7osqfuu 395 2 see see VB work_ln56cwsp7ffppl4wxeq7osqfuu 395 3 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 395 4 third third JJ work_ln56cwsp7ffppl4wxeq7osqfuu 395 5 claim claim NN work_ln56cwsp7ffppl4wxeq7osqfuu 395 6 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 395 7 consider consider VB work_ln56cwsp7ffppl4wxeq7osqfuu 395 8 that that IN work_ln56cwsp7ffppl4wxeq7osqfuu 395 9 a a DT work_ln56cwsp7ffppl4wxeq7osqfuu 395 10 well well RB work_ln56cwsp7ffppl4wxeq7osqfuu 395 11 known know VBN work_ln56cwsp7ffppl4wxeq7osqfuu 395 12 fact fact NN work_ln56cwsp7ffppl4wxeq7osqfuu 395 13 in in IN work_ln56cwsp7ffppl4wxeq7osqfuu 395 14 order order NN work_ln56cwsp7ffppl4wxeq7osqfuu 395 15 sta- sta- VBP work_ln56cwsp7ffppl4wxeq7osqfuu 395 16 tistics tistic NNS work_ln56cwsp7ffppl4wxeq7osqfuu 395 17 theory theory NN work_ln56cwsp7ffppl4wxeq7osqfuu 395 18 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 395 19 that that IN work_ln56cwsp7ffppl4wxeq7osqfuu 395 20 ∑ ∑ . work_ln56cwsp7ffppl4wxeq7osqfuu 395 21 l l NN work_ln56cwsp7ffppl4wxeq7osqfuu 395 22 E[U e[u CD work_ln56cwsp7ffppl4wxeq7osqfuu 395 23 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 395 24 l l NN work_ln56cwsp7ffppl4wxeq7osqfuu 395 25 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 395 26 ] ] -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 395 27 = = NFP work_ln56cwsp7ffppl4wxeq7osqfuu 395 28 kE[Uh kE[Uh NNP work_ln56cwsp7ffppl4wxeq7osqfuu 395 29 ] ] -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 395 30 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 395 31 any any DT work_ln56cwsp7ffppl4wxeq7osqfuu 395 32 alternative alternative JJ work_ln56cwsp7ffppl4wxeq7osqfuu 395 33 h. h. NN work_ln56cwsp7ffppl4wxeq7osqfuu 395 34 Consequently consequently RB work_ln56cwsp7ffppl4wxeq7osqfuu 395 35 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 395 36 since since IN work_ln56cwsp7ffppl4wxeq7osqfuu 395 37 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 395 38 symmetry symmetry NN work_ln56cwsp7ffppl4wxeq7osqfuu 395 39 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 395 40 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 395 41 density density NN work_ln56cwsp7ffppl4wxeq7osqfuu 395 42 function function NN work_ln56cwsp7ffppl4wxeq7osqfuu 395 43 implies imply VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 395 44 that that IN work_ln56cwsp7ffppl4wxeq7osqfuu 395 45 E[Uh e[uh LS work_ln56cwsp7ffppl4wxeq7osqfuu 395 46 ] ] -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 395 47 = = NFP work_ln56cwsp7ffppl4wxeq7osqfuu 395 48 E[U(2 E[U(2 NNP work_ln56cwsp7ffppl4wxeq7osqfuu 395 49 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 395 50 ] ] -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 395 51 = = NN work_ln56cwsp7ffppl4wxeq7osqfuu 395 52 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 395 53 2 2 CD work_ln56cwsp7ffppl4wxeq7osqfuu 395 54 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 395 55 it -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 395 56 follows follow VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 395 57 immediately immediately RB work_ln56cwsp7ffppl4wxeq7osqfuu 395 58 that that IN work_ln56cwsp7ffppl4wxeq7osqfuu 395 59 E[U(l+1 E[U(l+1 NFP work_ln56cwsp7ffppl4wxeq7osqfuu 395 60 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 395 61 ] ] -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 395 62 − − NNP work_ln56cwsp7ffppl4wxeq7osqfuu 395 63 E[U(l E[U(l NNP work_ln56cwsp7ffppl4wxeq7osqfuu 395 64 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 395 65 ] ] -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 395 66 = = NFP work_ln56cwsp7ffppl4wxeq7osqfuu 395 67 c c NN work_ln56cwsp7ffppl4wxeq7osqfuu 395 68 with with IN work_ln56cwsp7ffppl4wxeq7osqfuu 395 69 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 395 70 ≤ ≤ NNP work_ln56cwsp7ffppl4wxeq7osqfuu 395 71 l l NNP work_ln56cwsp7ffppl4wxeq7osqfuu 395 72 ≤ ≤ NNP work_ln56cwsp7ffppl4wxeq7osqfuu 395 73 2 2 CD work_ln56cwsp7ffppl4wxeq7osqfuu 395 74 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 396 1 Then then RB work_ln56cwsp7ffppl4wxeq7osqfuu 396 2 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 396 3 from from IN work_ln56cwsp7ffppl4wxeq7osqfuu 396 4 Theorem Theorem NNP work_ln56cwsp7ffppl4wxeq7osqfuu 396 5 3.1 3.1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 396 6 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 396 7 Borda Borda NNP work_ln56cwsp7ffppl4wxeq7osqfuu 396 8 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 396 9 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 396 10 αUT αut CD work_ln56cwsp7ffppl4wxeq7osqfuu 396 11 -optimal -optimal JJ work_ln56cwsp7ffppl4wxeq7osqfuu 396 12 decision decision NN work_ln56cwsp7ffppl4wxeq7osqfuu 396 13 rule rule NN work_ln56cwsp7ffppl4wxeq7osqfuu 396 14 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 397 1 � � JJ work_ln56cwsp7ffppl4wxeq7osqfuu 397 2 Proof Proof NNP work_ln56cwsp7ffppl4wxeq7osqfuu 397 3 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 397 4 Theorem Theorem NNP work_ln56cwsp7ffppl4wxeq7osqfuu 397 5 3.5 3.5 CD work_ln56cwsp7ffppl4wxeq7osqfuu 397 6 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 398 1 We -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 398 2 report report VBP work_ln56cwsp7ffppl4wxeq7osqfuu 398 3 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 398 4 proof proof NN work_ln56cwsp7ffppl4wxeq7osqfuu 398 5 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 398 6 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 398 7 uniform uniform JJ work_ln56cwsp7ffppl4wxeq7osqfuu 398 8 distribution distribution NN work_ln56cwsp7ffppl4wxeq7osqfuu 398 9 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 399 1 The the DT work_ln56cwsp7ffppl4wxeq7osqfuu 399 2 cor- cor- RB work_ln56cwsp7ffppl4wxeq7osqfuu 399 3 responding respond VBG work_ln56cwsp7ffppl4wxeq7osqfuu 399 4 proof proof NN work_ln56cwsp7ffppl4wxeq7osqfuu 399 5 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 399 6 any any DT work_ln56cwsp7ffppl4wxeq7osqfuu 399 7 other other JJ work_ln56cwsp7ffppl4wxeq7osqfuu 399 8 parabolic parabolic JJ work_ln56cwsp7ffppl4wxeq7osqfuu 399 9 function function NN work_ln56cwsp7ffppl4wxeq7osqfuu 399 10 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 399 11 analogous analogous JJ work_ln56cwsp7ffppl4wxeq7osqfuu 399 12 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 399 13 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 399 14 hence hence RB work_ln56cwsp7ffppl4wxeq7osqfuu 399 15 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 399 16 omitted omit VBN work_ln56cwsp7ffppl4wxeq7osqfuu 399 17 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 400 1 We -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 400 2 organize organize VBP work_ln56cwsp7ffppl4wxeq7osqfuu 400 3 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 400 4 proof proof NN work_ln56cwsp7ffppl4wxeq7osqfuu 400 5 by by IN work_ln56cwsp7ffppl4wxeq7osqfuu 400 6 types type NNS work_ln56cwsp7ffppl4wxeq7osqfuu 400 7 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 400 8 societies society NNS work_ln56cwsp7ffppl4wxeq7osqfuu 400 9 in in IN work_ln56cwsp7ffppl4wxeq7osqfuu 400 10 ordinal ordinal JJ work_ln56cwsp7ffppl4wxeq7osqfuu 400 11 terms term NNS work_ln56cwsp7ffppl4wxeq7osqfuu 400 12 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 401 1 Type type NN work_ln56cwsp7ffppl4wxeq7osqfuu 401 2 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 401 3 : : : work_ln56cwsp7ffppl4wxeq7osqfuu 401 4 Perfect perfect JJ work_ln56cwsp7ffppl4wxeq7osqfuu 401 5 correlation correlation NN work_ln56cwsp7ffppl4wxeq7osqfuu 401 6 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 402 1 This this DT work_ln56cwsp7ffppl4wxeq7osqfuu 402 2 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 402 3 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 402 4 case case NN work_ln56cwsp7ffppl4wxeq7osqfuu 402 5 when when WRB work_ln56cwsp7ffppl4wxeq7osqfuu 402 6 M1 M1 NNP work_ln56cwsp7ffppl4wxeq7osqfuu 402 7 = = SYM work_ln56cwsp7ffppl4wxeq7osqfuu 402 8 M2 M2 NNP work_ln56cwsp7ffppl4wxeq7osqfuu 402 9 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 403 1 Let let VB work_ln56cwsp7ffppl4wxeq7osqfuu 403 2 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 403 3 w.l.o.g w.l.o.g NNP work_ln56cwsp7ffppl4wxeq7osqfuu 403 4 . . NNP work_ln56cwsp7ffppl4wxeq7osqfuu 403 5 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 403 6 M1 M1 NNP work_ln56cwsp7ffppl4wxeq7osqfuu 403 7 = = NFP work_ln56cwsp7ffppl4wxeq7osqfuu 403 8 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 403 9 3 3 CD work_ln56cwsp7ffppl4wxeq7osqfuu 403 10 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 403 11 2 2 CD work_ln56cwsp7ffppl4wxeq7osqfuu 403 12 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 403 13 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 403 14 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 403 15 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 404 1 Utilitarianism Utilitarianism NNP work_ln56cwsp7ffppl4wxeq7osqfuu 404 2 always always RB work_ln56cwsp7ffppl4wxeq7osqfuu 404 3 selects select VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 404 4 alternative alternative JJ work_ln56cwsp7ffppl4wxeq7osqfuu 404 5 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 404 6 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 405 1 Hence hence RB work_ln56cwsp7ffppl4wxeq7osqfuu 405 2 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 405 3 βUT βut FW work_ln56cwsp7ffppl4wxeq7osqfuu 405 4 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 405 5 M m NN work_ln56cwsp7ffppl4wxeq7osqfuu 405 6 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 405 7 = = NFP work_ln56cwsp7ffppl4wxeq7osqfuu 405 8 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 405 9 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 405 10 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 405 11 0 0 CD work_ln56cwsp7ffppl4wxeq7osqfuu 405 12 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 405 13 0 0 CD work_ln56cwsp7ffppl4wxeq7osqfuu 405 14 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 405 15 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 406 1 18 18 CD work_ln56cwsp7ffppl4wxeq7osqfuu 406 2 Type type NN work_ln56cwsp7ffppl4wxeq7osqfuu 406 3 2 2 CD work_ln56cwsp7ffppl4wxeq7osqfuu 406 4 : : : work_ln56cwsp7ffppl4wxeq7osqfuu 406 5 Only only RB work_ln56cwsp7ffppl4wxeq7osqfuu 406 6 best good JJS work_ln56cwsp7ffppl4wxeq7osqfuu 406 7 - - HYPH work_ln56cwsp7ffppl4wxeq7osqfuu 406 8 correlation correlation NN work_ln56cwsp7ffppl4wxeq7osqfuu 406 9 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 407 1 Both both DT work_ln56cwsp7ffppl4wxeq7osqfuu 407 2 individuals individual NNS work_ln56cwsp7ffppl4wxeq7osqfuu 407 3 agree agree VBP work_ln56cwsp7ffppl4wxeq7osqfuu 407 4 on on IN work_ln56cwsp7ffppl4wxeq7osqfuu 407 5 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 407 6 best good JJS work_ln56cwsp7ffppl4wxeq7osqfuu 407 7 alternative alternative NN work_ln56cwsp7ffppl4wxeq7osqfuu 407 8 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 407 9 but but CC work_ln56cwsp7ffppl4wxeq7osqfuu 407 10 disagree disagree VB work_ln56cwsp7ffppl4wxeq7osqfuu 407 11 on on IN work_ln56cwsp7ffppl4wxeq7osqfuu 407 12 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 407 13 others other NNS work_ln56cwsp7ffppl4wxeq7osqfuu 407 14 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 408 1 Let let VB work_ln56cwsp7ffppl4wxeq7osqfuu 408 2 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 408 3 w.l.o.g w.l.o.g NNP work_ln56cwsp7ffppl4wxeq7osqfuu 408 4 . . NNP work_ln56cwsp7ffppl4wxeq7osqfuu 408 5 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 408 6 M1 M1 NNP work_ln56cwsp7ffppl4wxeq7osqfuu 408 7 = = NFP work_ln56cwsp7ffppl4wxeq7osqfuu 408 8 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 408 9 3 3 CD work_ln56cwsp7ffppl4wxeq7osqfuu 408 10 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 408 11 2 2 CD work_ln56cwsp7ffppl4wxeq7osqfuu 408 12 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 408 13 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 408 14 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 408 15 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 408 16 M2 M2 NNP work_ln56cwsp7ffppl4wxeq7osqfuu 408 17 = = NFP work_ln56cwsp7ffppl4wxeq7osqfuu 408 18 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 408 19 3 3 CD work_ln56cwsp7ffppl4wxeq7osqfuu 408 20 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 408 21 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 408 22 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 408 23 2 2 CD work_ln56cwsp7ffppl4wxeq7osqfuu 408 24 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 408 25 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 409 1 Utilitarianism Utilitarianism NNP work_ln56cwsp7ffppl4wxeq7osqfuu 409 2 selects select VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 409 3 alternative alternative JJ work_ln56cwsp7ffppl4wxeq7osqfuu 409 4 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 409 5 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 409 6 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 409 7 then then RB work_ln56cwsp7ffppl4wxeq7osqfuu 409 8 βUT βut NN work_ln56cwsp7ffppl4wxeq7osqfuu 409 9 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 409 10 M m NN work_ln56cwsp7ffppl4wxeq7osqfuu 409 11 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 409 12 = = NFP work_ln56cwsp7ffppl4wxeq7osqfuu 409 13 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 409 14 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 409 15 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 409 16 0 0 CD work_ln56cwsp7ffppl4wxeq7osqfuu 409 17 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 409 18 0 0 CD work_ln56cwsp7ffppl4wxeq7osqfuu 409 19 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 409 20 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 410 1 Type type NN work_ln56cwsp7ffppl4wxeq7osqfuu 410 2 3 3 CD work_ln56cwsp7ffppl4wxeq7osqfuu 410 3 : : : work_ln56cwsp7ffppl4wxeq7osqfuu 410 4 Only only RB work_ln56cwsp7ffppl4wxeq7osqfuu 410 5 worst bad JJS work_ln56cwsp7ffppl4wxeq7osqfuu 410 6 - - HYPH work_ln56cwsp7ffppl4wxeq7osqfuu 410 7 correlation correlation NN work_ln56cwsp7ffppl4wxeq7osqfuu 410 8 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 411 1 Both both DT work_ln56cwsp7ffppl4wxeq7osqfuu 411 2 individuals individual NNS work_ln56cwsp7ffppl4wxeq7osqfuu 411 3 coincide coincide VBP work_ln56cwsp7ffppl4wxeq7osqfuu 411 4 in in IN work_ln56cwsp7ffppl4wxeq7osqfuu 411 5 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 411 6 worst bad JJS work_ln56cwsp7ffppl4wxeq7osqfuu 411 7 alternative alternative NN work_ln56cwsp7ffppl4wxeq7osqfuu 411 8 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 411 9 but but CC work_ln56cwsp7ffppl4wxeq7osqfuu 411 10 disagree disagree VB work_ln56cwsp7ffppl4wxeq7osqfuu 411 11 on on IN work_ln56cwsp7ffppl4wxeq7osqfuu 411 12 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 411 13 others other NNS work_ln56cwsp7ffppl4wxeq7osqfuu 411 14 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 412 1 Let let VB work_ln56cwsp7ffppl4wxeq7osqfuu 412 2 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 412 3 w.l.o.g w.l.o.g NNP work_ln56cwsp7ffppl4wxeq7osqfuu 412 4 . . NNP work_ln56cwsp7ffppl4wxeq7osqfuu 412 5 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 412 6 M1 M1 NNP work_ln56cwsp7ffppl4wxeq7osqfuu 412 7 = = NFP work_ln56cwsp7ffppl4wxeq7osqfuu 412 8 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 412 9 3 3 CD work_ln56cwsp7ffppl4wxeq7osqfuu 412 10 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 412 11 2 2 CD work_ln56cwsp7ffppl4wxeq7osqfuu 412 12 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 412 13 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 412 14 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 412 15 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 412 16 M2 M2 NNP work_ln56cwsp7ffppl4wxeq7osqfuu 412 17 = = NFP work_ln56cwsp7ffppl4wxeq7osqfuu 412 18 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 412 19 2 2 CD work_ln56cwsp7ffppl4wxeq7osqfuu 412 20 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 412 21 3 3 CD work_ln56cwsp7ffppl4wxeq7osqfuu 412 22 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 412 23 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 412 24 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 412 25 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 413 1 It -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 413 2 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 413 3 straightforward straightforward JJ work_ln56cwsp7ffppl4wxeq7osqfuu 413 4 to to TO work_ln56cwsp7ffppl4wxeq7osqfuu 413 5 see see VB work_ln56cwsp7ffppl4wxeq7osqfuu 413 6 that that DT work_ln56cwsp7ffppl4wxeq7osqfuu 413 7 βUT βut NN work_ln56cwsp7ffppl4wxeq7osqfuu 413 8 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 413 9 M m NN work_ln56cwsp7ffppl4wxeq7osqfuu 413 10 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 413 11 = = NFP work_ln56cwsp7ffppl4wxeq7osqfuu 413 12 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 413 13 1/2 1/2 CD work_ln56cwsp7ffppl4wxeq7osqfuu 413 14 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 413 15 1/2 1/2 CD work_ln56cwsp7ffppl4wxeq7osqfuu 413 16 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 413 17 0 0 CD work_ln56cwsp7ffppl4wxeq7osqfuu 413 18 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 413 19 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 414 1 Type type NN work_ln56cwsp7ffppl4wxeq7osqfuu 414 2 4 4 CD work_ln56cwsp7ffppl4wxeq7osqfuu 414 3 : : : work_ln56cwsp7ffppl4wxeq7osqfuu 414 4 Only only RB work_ln56cwsp7ffppl4wxeq7osqfuu 414 5 middle middle NN work_ln56cwsp7ffppl4wxeq7osqfuu 414 6 - - HYPH work_ln56cwsp7ffppl4wxeq7osqfuu 414 7 correlation correlation NN work_ln56cwsp7ffppl4wxeq7osqfuu 414 8 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 415 1 Both both DT work_ln56cwsp7ffppl4wxeq7osqfuu 415 2 individuals individual NNS work_ln56cwsp7ffppl4wxeq7osqfuu 415 3 agree agree VBP work_ln56cwsp7ffppl4wxeq7osqfuu 415 4 on on IN work_ln56cwsp7ffppl4wxeq7osqfuu 415 5 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 415 6 middle middle JJ work_ln56cwsp7ffppl4wxeq7osqfuu 415 7 alternative alternative NN work_ln56cwsp7ffppl4wxeq7osqfuu 415 8 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 415 9 but but CC work_ln56cwsp7ffppl4wxeq7osqfuu 415 10 disagree disagree VB work_ln56cwsp7ffppl4wxeq7osqfuu 415 11 on on IN work_ln56cwsp7ffppl4wxeq7osqfuu 415 12 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 415 13 others.7 others.7 CD work_ln56cwsp7ffppl4wxeq7osqfuu 415 14 Let Let NNP work_ln56cwsp7ffppl4wxeq7osqfuu 415 15 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 415 16 w.l.o.g w.l.o.g NNP work_ln56cwsp7ffppl4wxeq7osqfuu 415 17 . . NNP work_ln56cwsp7ffppl4wxeq7osqfuu 415 18 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 415 19 M1 M1 NNP work_ln56cwsp7ffppl4wxeq7osqfuu 415 20 = = NFP work_ln56cwsp7ffppl4wxeq7osqfuu 415 21 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 415 22 3 3 CD work_ln56cwsp7ffppl4wxeq7osqfuu 415 23 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 415 24 2 2 CD work_ln56cwsp7ffppl4wxeq7osqfuu 415 25 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 415 26 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 415 27 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 415 28 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 415 29 M2 M2 NNP work_ln56cwsp7ffppl4wxeq7osqfuu 415 30 = = NFP work_ln56cwsp7ffppl4wxeq7osqfuu 415 31 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 415 32 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 415 33 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 415 34 2 2 CD work_ln56cwsp7ffppl4wxeq7osqfuu 415 35 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 415 36 3 3 CD work_ln56cwsp7ffppl4wxeq7osqfuu 415 37 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 415 38 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 416 1 To to TO work_ln56cwsp7ffppl4wxeq7osqfuu 416 2 compute compute VB work_ln56cwsp7ffppl4wxeq7osqfuu 416 3 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 416 4 selection selection NN work_ln56cwsp7ffppl4wxeq7osqfuu 416 5 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 416 6 utilitarianism utilitarianism NN work_ln56cwsp7ffppl4wxeq7osqfuu 416 7 we -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 416 8 first first RB work_ln56cwsp7ffppl4wxeq7osqfuu 416 9 need need VBP work_ln56cwsp7ffppl4wxeq7osqfuu 416 10 to to TO work_ln56cwsp7ffppl4wxeq7osqfuu 416 11 derive derive VB work_ln56cwsp7ffppl4wxeq7osqfuu 416 12 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 416 13 joint joint JJ work_ln56cwsp7ffppl4wxeq7osqfuu 416 14 probability probability NN work_ln56cwsp7ffppl4wxeq7osqfuu 416 15 distribution distribution NN work_ln56cwsp7ffppl4wxeq7osqfuu 416 16 associated associate VBN work_ln56cwsp7ffppl4wxeq7osqfuu 416 17 to to IN work_ln56cwsp7ffppl4wxeq7osqfuu 416 18 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 416 19 continuous continuous JJ work_ln56cwsp7ffppl4wxeq7osqfuu 416 20 random random JJ work_ln56cwsp7ffppl4wxeq7osqfuu 416 21 variables variable NNS work_ln56cwsp7ffppl4wxeq7osqfuu 416 22 U u NN work_ln56cwsp7ffppl4wxeq7osqfuu 416 23 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 416 24 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 416 25 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 416 26 i i PRP work_ln56cwsp7ffppl4wxeq7osqfuu 416 27 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 416 28 U u NN work_ln56cwsp7ffppl4wxeq7osqfuu 416 29 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 416 30 2 2 CD work_ln56cwsp7ffppl4wxeq7osqfuu 416 31 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 416 32 i i PRP work_ln56cwsp7ffppl4wxeq7osqfuu 416 33 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 416 34 U u NN work_ln56cwsp7ffppl4wxeq7osqfuu 416 35 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 416 36 3 3 CD work_ln56cwsp7ffppl4wxeq7osqfuu 416 37 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 416 38 i i PRP work_ln56cwsp7ffppl4wxeq7osqfuu 416 39 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 417 1 The the DT work_ln56cwsp7ffppl4wxeq7osqfuu 417 2 joint joint JJ work_ln56cwsp7ffppl4wxeq7osqfuu 417 3 probability probability NN work_ln56cwsp7ffppl4wxeq7osqfuu 417 4 density density NN work_ln56cwsp7ffppl4wxeq7osqfuu 417 5 function function NN work_ln56cwsp7ffppl4wxeq7osqfuu 417 6 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 417 7 f(u f(u NNP work_ln56cwsp7ffppl4wxeq7osqfuu 417 8 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 417 9 1 1 LS work_ln56cwsp7ffppl4wxeq7osqfuu 417 10 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 417 11 i i PRP work_ln56cwsp7ffppl4wxeq7osqfuu 417 12 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 417 13 u u NNP work_ln56cwsp7ffppl4wxeq7osqfuu 417 14 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 417 15 2 2 CD work_ln56cwsp7ffppl4wxeq7osqfuu 417 16 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 417 17 i i PRP work_ln56cwsp7ffppl4wxeq7osqfuu 417 18 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 417 19 u u NNP work_ln56cwsp7ffppl4wxeq7osqfuu 417 20 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 417 21 3 3 CD work_ln56cwsp7ffppl4wxeq7osqfuu 417 22 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 417 23 i i NN work_ln56cwsp7ffppl4wxeq7osqfuu 417 24 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 417 25 = = NFP work_ln56cwsp7ffppl4wxeq7osqfuu 417 26 { { -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 417 27 6 6 CD work_ln56cwsp7ffppl4wxeq7osqfuu 417 28 if if IN work_ln56cwsp7ffppl4wxeq7osqfuu 417 29 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 417 30 ≥ ≥ CD work_ln56cwsp7ffppl4wxeq7osqfuu 417 31 u(3)i u(3)i UH work_ln56cwsp7ffppl4wxeq7osqfuu 417 32 ≥ ≥ UH work_ln56cwsp7ffppl4wxeq7osqfuu 417 33 u u NN work_ln56cwsp7ffppl4wxeq7osqfuu 417 34 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 417 35 2 2 CD work_ln56cwsp7ffppl4wxeq7osqfuu 417 36 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 417 37 i i PRP work_ln56cwsp7ffppl4wxeq7osqfuu 417 38 ≥ ≥ VBP work_ln56cwsp7ffppl4wxeq7osqfuu 417 39 u u NNP work_ln56cwsp7ffppl4wxeq7osqfuu 417 40 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 417 41 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 417 42 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 417 43 i i PRP work_ln56cwsp7ffppl4wxeq7osqfuu 417 44 ≥ ≥ VBP work_ln56cwsp7ffppl4wxeq7osqfuu 417 45 0 0 NFP work_ln56cwsp7ffppl4wxeq7osqfuu 417 46 0 0 CD work_ln56cwsp7ffppl4wxeq7osqfuu 417 47 otherwise otherwise RB work_ln56cwsp7ffppl4wxeq7osqfuu 417 48 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 418 1 Hence hence RB work_ln56cwsp7ffppl4wxeq7osqfuu 418 2 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 418 3 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 418 4 density density NN work_ln56cwsp7ffppl4wxeq7osqfuu 418 5 function function NN work_ln56cwsp7ffppl4wxeq7osqfuu 418 6 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 418 7 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 418 8 two two CD work_ln56cwsp7ffppl4wxeq7osqfuu 418 9 agents agent NNS work_ln56cwsp7ffppl4wxeq7osqfuu 418 10 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 418 11 f(u f(u NNP work_ln56cwsp7ffppl4wxeq7osqfuu 418 12 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 418 13 1 1 LS work_ln56cwsp7ffppl4wxeq7osqfuu 418 14 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 418 15 i i PRP work_ln56cwsp7ffppl4wxeq7osqfuu 418 16 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 418 17 u u NNP work_ln56cwsp7ffppl4wxeq7osqfuu 418 18 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 418 19 2 2 CD work_ln56cwsp7ffppl4wxeq7osqfuu 418 20 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 418 21 i i PRP work_ln56cwsp7ffppl4wxeq7osqfuu 418 22 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 418 23 u u NNP work_ln56cwsp7ffppl4wxeq7osqfuu 418 24 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 418 25 3 3 CD work_ln56cwsp7ffppl4wxeq7osqfuu 418 26 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 418 27 i i PRP work_ln56cwsp7ffppl4wxeq7osqfuu 418 28 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 418 29 u u NNP work_ln56cwsp7ffppl4wxeq7osqfuu 418 30 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 418 31 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 418 32 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 418 33 j j NNP work_ln56cwsp7ffppl4wxeq7osqfuu 418 34 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 418 35 u u NNP work_ln56cwsp7ffppl4wxeq7osqfuu 418 36 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 418 37 2 2 CD work_ln56cwsp7ffppl4wxeq7osqfuu 418 38 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 418 39 j j NNP work_ln56cwsp7ffppl4wxeq7osqfuu 418 40 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 418 41 u u NNP work_ln56cwsp7ffppl4wxeq7osqfuu 418 42 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 418 43 3 3 CD work_ln56cwsp7ffppl4wxeq7osqfuu 418 44 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 418 45 j j NN work_ln56cwsp7ffppl4wxeq7osqfuu 418 46 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 418 47 = = NFP work_ln56cwsp7ffppl4wxeq7osqfuu 418 48   NN work_ln56cwsp7ffppl4wxeq7osqfuu 418 49   VBD work_ln56cwsp7ffppl4wxeq7osqfuu 418 50 36 36 CD work_ln56cwsp7ffppl4wxeq7osqfuu 418 51 if if IN work_ln56cwsp7ffppl4wxeq7osqfuu 418 52 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 418 53 ≥ ≥ CD work_ln56cwsp7ffppl4wxeq7osqfuu 418 54 u(3)i u(3)i UH work_ln56cwsp7ffppl4wxeq7osqfuu 418 55 ≥ ≥ UH work_ln56cwsp7ffppl4wxeq7osqfuu 418 56 u u NN work_ln56cwsp7ffppl4wxeq7osqfuu 418 57 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 418 58 2 2 CD work_ln56cwsp7ffppl4wxeq7osqfuu 418 59 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 418 60 i i PRP work_ln56cwsp7ffppl4wxeq7osqfuu 418 61 ≥ ≥ VBP work_ln56cwsp7ffppl4wxeq7osqfuu 418 62 u u NNP work_ln56cwsp7ffppl4wxeq7osqfuu 418 63 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 418 64 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 418 65 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 418 66 i i PRP work_ln56cwsp7ffppl4wxeq7osqfuu 418 67 ≥ ≥ UH work_ln56cwsp7ffppl4wxeq7osqfuu 418 68 0 0 NFP work_ln56cwsp7ffppl4wxeq7osqfuu 418 69 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 418 70 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 418 71 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 418 72 ≥ ≥ CD work_ln56cwsp7ffppl4wxeq7osqfuu 418 73 u(3)j u(3)j JJ work_ln56cwsp7ffppl4wxeq7osqfuu 418 74 ≥ ≥ UH work_ln56cwsp7ffppl4wxeq7osqfuu 418 75 u u NN work_ln56cwsp7ffppl4wxeq7osqfuu 418 76 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 418 77 2 2 CD work_ln56cwsp7ffppl4wxeq7osqfuu 418 78 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 418 79 j j NNP work_ln56cwsp7ffppl4wxeq7osqfuu 418 80 ≥ ≥ NN work_ln56cwsp7ffppl4wxeq7osqfuu 418 81 u u NNP work_ln56cwsp7ffppl4wxeq7osqfuu 418 82 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 418 83 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 418 84 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 418 85 j j NNP work_ln56cwsp7ffppl4wxeq7osqfuu 418 86 ≥ ≥ CD work_ln56cwsp7ffppl4wxeq7osqfuu 418 87 0 0 CD work_ln56cwsp7ffppl4wxeq7osqfuu 418 88 0 0 CD work_ln56cwsp7ffppl4wxeq7osqfuu 418 89 otherwise otherwise RB work_ln56cwsp7ffppl4wxeq7osqfuu 418 90 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 419 1 We -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 419 2 can can MD work_ln56cwsp7ffppl4wxeq7osqfuu 419 3 now now RB work_ln56cwsp7ffppl4wxeq7osqfuu 419 4 calculate calculate VB work_ln56cwsp7ffppl4wxeq7osqfuu 419 5 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 419 6 probability probability NN work_ln56cwsp7ffppl4wxeq7osqfuu 419 7 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 419 8 utilitarianism utilitarianism NN work_ln56cwsp7ffppl4wxeq7osqfuu 419 9 resulting result VBG work_ln56cwsp7ffppl4wxeq7osqfuu 419 10 in in IN work_ln56cwsp7ffppl4wxeq7osqfuu 419 11 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 419 12 selection selection NN work_ln56cwsp7ffppl4wxeq7osqfuu 419 13 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 419 14 alternative alternative JJ work_ln56cwsp7ffppl4wxeq7osqfuu 419 15 2 2 CD work_ln56cwsp7ffppl4wxeq7osqfuu 419 16 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 420 1 Alternative alternative JJ work_ln56cwsp7ffppl4wxeq7osqfuu 420 2 2 2 CD work_ln56cwsp7ffppl4wxeq7osqfuu 420 3 will will MD work_ln56cwsp7ffppl4wxeq7osqfuu 420 4 be be VB work_ln56cwsp7ffppl4wxeq7osqfuu 420 5 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 420 6 utilitarian utilitarian JJ work_ln56cwsp7ffppl4wxeq7osqfuu 420 7 winner winner NN work_ln56cwsp7ffppl4wxeq7osqfuu 420 8 whenever whenever WRB work_ln56cwsp7ffppl4wxeq7osqfuu 420 9 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 420 10 sum sum NN work_ln56cwsp7ffppl4wxeq7osqfuu 420 11 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 420 12 U u NN work_ln56cwsp7ffppl4wxeq7osqfuu 420 13 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 420 14 2 2 CD work_ln56cwsp7ffppl4wxeq7osqfuu 420 15 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 420 16 i i PRP work_ln56cwsp7ffppl4wxeq7osqfuu 420 17 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 420 18 U u NN work_ln56cwsp7ffppl4wxeq7osqfuu 420 19 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 420 20 2 2 CD work_ln56cwsp7ffppl4wxeq7osqfuu 420 21 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 420 22 j j NNP work_ln56cwsp7ffppl4wxeq7osqfuu 420 23 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 420 24 greater great JJR work_ln56cwsp7ffppl4wxeq7osqfuu 420 25 than than IN work_ln56cwsp7ffppl4wxeq7osqfuu 420 26 U u NN work_ln56cwsp7ffppl4wxeq7osqfuu 420 27 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 420 28 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 420 29 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 420 30 i i NN work_ln56cwsp7ffppl4wxeq7osqfuu 420 31 + + CC work_ln56cwsp7ffppl4wxeq7osqfuu 420 32 U u NN work_ln56cwsp7ffppl4wxeq7osqfuu 420 33 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 420 34 3 3 CD work_ln56cwsp7ffppl4wxeq7osqfuu 420 35 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 420 36 j j NN work_ln56cwsp7ffppl4wxeq7osqfuu 420 37 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 420 38 U U NNP work_ln56cwsp7ffppl4wxeq7osqfuu 420 39 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 420 40 3 3 CD work_ln56cwsp7ffppl4wxeq7osqfuu 420 41 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 420 42 i i NN work_ln56cwsp7ffppl4wxeq7osqfuu 420 43 + + CC work_ln56cwsp7ffppl4wxeq7osqfuu 420 44 U u NN work_ln56cwsp7ffppl4wxeq7osqfuu 420 45 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 420 46 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 420 47 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 420 48 j j NN work_ln56cwsp7ffppl4wxeq7osqfuu 420 49 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 421 1 Equivalently equivalently RB work_ln56cwsp7ffppl4wxeq7osqfuu 421 2 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 421 3 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 421 4 A.1)∫ A.1)∫ NNP work_ln56cwsp7ffppl4wxeq7osqfuu 421 5 R R NNP work_ln56cwsp7ffppl4wxeq7osqfuu 421 6 ∫ ∫ : work_ln56cwsp7ffppl4wxeq7osqfuu 421 7 R r NN work_ln56cwsp7ffppl4wxeq7osqfuu 421 8 ∫ ∫ : work_ln56cwsp7ffppl4wxeq7osqfuu 421 9 R r NN work_ln56cwsp7ffppl4wxeq7osqfuu 421 10 ∫ ∫ . work_ln56cwsp7ffppl4wxeq7osqfuu 421 11 R r NN work_ln56cwsp7ffppl4wxeq7osqfuu 421 12 ∫ ∫ . work_ln56cwsp7ffppl4wxeq7osqfuu 421 13 Ha ha UH work_ln56cwsp7ffppl4wxeq7osqfuu 421 14 ∫ ∫ . work_ln56cwsp7ffppl4wxeq7osqfuu 421 15 Hb Hb NNP work_ln56cwsp7ffppl4wxeq7osqfuu 421 16 f(u f(u NNP work_ln56cwsp7ffppl4wxeq7osqfuu 421 17 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 421 18 1 1 LS work_ln56cwsp7ffppl4wxeq7osqfuu 421 19 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 421 20 i i PRP work_ln56cwsp7ffppl4wxeq7osqfuu 421 21 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 421 22 u u NNP work_ln56cwsp7ffppl4wxeq7osqfuu 421 23 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 421 24 2 2 CD work_ln56cwsp7ffppl4wxeq7osqfuu 421 25 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 421 26 i i PRP work_ln56cwsp7ffppl4wxeq7osqfuu 421 27 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 421 28 u u NNP work_ln56cwsp7ffppl4wxeq7osqfuu 421 29 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 421 30 3 3 CD work_ln56cwsp7ffppl4wxeq7osqfuu 421 31 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 421 32 i i PRP work_ln56cwsp7ffppl4wxeq7osqfuu 421 33 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 421 34 u u NNP work_ln56cwsp7ffppl4wxeq7osqfuu 421 35 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 421 36 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 421 37 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 421 38 j j NNP work_ln56cwsp7ffppl4wxeq7osqfuu 421 39 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 421 40 u u NNP work_ln56cwsp7ffppl4wxeq7osqfuu 421 41 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 421 42 2 2 CD work_ln56cwsp7ffppl4wxeq7osqfuu 421 43 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 421 44 j j NNP work_ln56cwsp7ffppl4wxeq7osqfuu 421 45 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 421 46 u u NNP work_ln56cwsp7ffppl4wxeq7osqfuu 421 47 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 421 48 3 3 CD work_ln56cwsp7ffppl4wxeq7osqfuu 421 49 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 421 50 j j NNP work_ln56cwsp7ffppl4wxeq7osqfuu 421 51 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 421 52 du du NNP work_ln56cwsp7ffppl4wxeq7osqfuu 421 53 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 421 54 3 3 CD work_ln56cwsp7ffppl4wxeq7osqfuu 421 55 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 421 56 i i PRP work_ln56cwsp7ffppl4wxeq7osqfuu 421 57 du du VBP work_ln56cwsp7ffppl4wxeq7osqfuu 421 58 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 421 59 3 3 CD work_ln56cwsp7ffppl4wxeq7osqfuu 421 60 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 421 61 j j NNP work_ln56cwsp7ffppl4wxeq7osqfuu 421 62 du du NN work_ln56cwsp7ffppl4wxeq7osqfuu 421 63 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 421 64 2 2 CD work_ln56cwsp7ffppl4wxeq7osqfuu 421 65 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 421 66 i i PRP work_ln56cwsp7ffppl4wxeq7osqfuu 421 67 du du VBP work_ln56cwsp7ffppl4wxeq7osqfuu 421 68 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 421 69 2 2 CD work_ln56cwsp7ffppl4wxeq7osqfuu 421 70 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 421 71 j j NNP work_ln56cwsp7ffppl4wxeq7osqfuu 421 72 du du NNP work_ln56cwsp7ffppl4wxeq7osqfuu 421 73 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 421 74 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 421 75 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 421 76 i i PRP work_ln56cwsp7ffppl4wxeq7osqfuu 421 77 du du VBP work_ln56cwsp7ffppl4wxeq7osqfuu 421 78 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 421 79 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 421 80 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 421 81 j j NNP work_ln56cwsp7ffppl4wxeq7osqfuu 421 82 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 421 83 where where WRB work_ln56cwsp7ffppl4wxeq7osqfuu 421 84 Ha ha UH work_ln56cwsp7ffppl4wxeq7osqfuu 421 85 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 421 86 Hb Hb NNP work_ln56cwsp7ffppl4wxeq7osqfuu 421 87 are be VBP work_ln56cwsp7ffppl4wxeq7osqfuu 421 88 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 421 89 sets set NNS work_ln56cwsp7ffppl4wxeq7osqfuu 421 90 Ha ha XX work_ln56cwsp7ffppl4wxeq7osqfuu 421 91 = = NFP work_ln56cwsp7ffppl4wxeq7osqfuu 421 92 { { -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 421 93 t t NN work_ln56cwsp7ffppl4wxeq7osqfuu 421 94 : : : work_ln56cwsp7ffppl4wxeq7osqfuu 421 95 t t NNP work_ln56cwsp7ffppl4wxeq7osqfuu 421 96 ≤ ≤ NNP work_ln56cwsp7ffppl4wxeq7osqfuu 421 97 u u NNP work_ln56cwsp7ffppl4wxeq7osqfuu 421 98 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 421 99 2 2 CD work_ln56cwsp7ffppl4wxeq7osqfuu 421 100 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 421 101 i i NN work_ln56cwsp7ffppl4wxeq7osqfuu 421 102 + + CC work_ln56cwsp7ffppl4wxeq7osqfuu 421 103 u u NN work_ln56cwsp7ffppl4wxeq7osqfuu 421 104 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 421 105 2 2 CD work_ln56cwsp7ffppl4wxeq7osqfuu 421 106 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 421 107 j j NNP work_ln56cwsp7ffppl4wxeq7osqfuu 421 108 − − NNP work_ln56cwsp7ffppl4wxeq7osqfuu 421 109 u u NNP work_ln56cwsp7ffppl4wxeq7osqfuu 421 110 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 421 111 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 421 112 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 421 113 i i PRP work_ln56cwsp7ffppl4wxeq7osqfuu 421 114 } } -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 421 115 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 421 116 Hb Hb NNP work_ln56cwsp7ffppl4wxeq7osqfuu 421 117 = = SYM work_ln56cwsp7ffppl4wxeq7osqfuu 421 118 { { -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 421 119 t t NN work_ln56cwsp7ffppl4wxeq7osqfuu 421 120 : : : work_ln56cwsp7ffppl4wxeq7osqfuu 421 121 t t NNP work_ln56cwsp7ffppl4wxeq7osqfuu 421 122 ≤ ≤ NNP work_ln56cwsp7ffppl4wxeq7osqfuu 421 123 u u NNP work_ln56cwsp7ffppl4wxeq7osqfuu 421 124 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 421 125 2 2 CD work_ln56cwsp7ffppl4wxeq7osqfuu 421 126 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 421 127 i i NN work_ln56cwsp7ffppl4wxeq7osqfuu 421 128 + + CC work_ln56cwsp7ffppl4wxeq7osqfuu 421 129 u u NN work_ln56cwsp7ffppl4wxeq7osqfuu 421 130 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 421 131 2 2 CD work_ln56cwsp7ffppl4wxeq7osqfuu 421 132 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 421 133 j j NNP work_ln56cwsp7ffppl4wxeq7osqfuu 421 134 −u −u CD work_ln56cwsp7ffppl4wxeq7osqfuu 421 135 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 421 136 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 421 137 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 421 138 j j NNP work_ln56cwsp7ffppl4wxeq7osqfuu 421 139 } } -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 421 140 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 422 1 Then then RB work_ln56cwsp7ffppl4wxeq7osqfuu 422 2 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 422 3 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 422 4 A.1 a.1 NN work_ln56cwsp7ffppl4wxeq7osqfuu 422 5 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 422 6 can can MD work_ln56cwsp7ffppl4wxeq7osqfuu 422 7 be be VB work_ln56cwsp7ffppl4wxeq7osqfuu 422 8 expressed express VBN work_ln56cwsp7ffppl4wxeq7osqfuu 422 9 as as IN work_ln56cwsp7ffppl4wxeq7osqfuu 422 10 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 422 11 A.2)∫ A.2)∫ NNP work_ln56cwsp7ffppl4wxeq7osqfuu 422 12 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 422 13 0 0 CD work_ln56cwsp7ffppl4wxeq7osqfuu 422 14 ∫ ∫ CD work_ln56cwsp7ffppl4wxeq7osqfuu 422 15 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 422 16 0 0 CD work_ln56cwsp7ffppl4wxeq7osqfuu 422 17 ∫ ∫ CD work_ln56cwsp7ffppl4wxeq7osqfuu 422 18 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 422 19 u u NNP work_ln56cwsp7ffppl4wxeq7osqfuu 422 20 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 422 21 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 422 22 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 422 23 j j NNP work_ln56cwsp7ffppl4wxeq7osqfuu 422 24 ∫ ∫ CD work_ln56cwsp7ffppl4wxeq7osqfuu 422 25 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 422 26 u u NNP work_ln56cwsp7ffppl4wxeq7osqfuu 422 27 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 422 28 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 422 29 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 422 30 i i PRP work_ln56cwsp7ffppl4wxeq7osqfuu 422 31 ∫ ∫ : work_ln56cwsp7ffppl4wxeq7osqfuu 422 32 min{1,u(2)i min{1,u(2)i UH work_ln56cwsp7ffppl4wxeq7osqfuu 422 33 + + CC work_ln56cwsp7ffppl4wxeq7osqfuu 422 34 u(2)j u(2)j NNP work_ln56cwsp7ffppl4wxeq7osqfuu 422 35 −u(1)i −u(1)i NNP work_ln56cwsp7ffppl4wxeq7osqfuu 422 36 } } -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 422 37 u u NNP work_ln56cwsp7ffppl4wxeq7osqfuu 422 38 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 422 39 2 2 CD work_ln56cwsp7ffppl4wxeq7osqfuu 422 40 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 422 41 j j NNP work_ln56cwsp7ffppl4wxeq7osqfuu 422 42 ∫ ∫ XX work_ln56cwsp7ffppl4wxeq7osqfuu 422 43 min{1,u(2)i min{1,u(2)i UH work_ln56cwsp7ffppl4wxeq7osqfuu 422 44 + + CC work_ln56cwsp7ffppl4wxeq7osqfuu 422 45 u(2)j u(2)j NNP work_ln56cwsp7ffppl4wxeq7osqfuu 422 46 −u(1)j −u(1)j NNP work_ln56cwsp7ffppl4wxeq7osqfuu 422 47 } } -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 422 48 u u NNP work_ln56cwsp7ffppl4wxeq7osqfuu 422 49 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 422 50 2 2 CD work_ln56cwsp7ffppl4wxeq7osqfuu 422 51 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 422 52 i i PRP work_ln56cwsp7ffppl4wxeq7osqfuu 422 53 36du 36du RB work_ln56cwsp7ffppl4wxeq7osqfuu 422 54 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 422 55 3 3 CD work_ln56cwsp7ffppl4wxeq7osqfuu 422 56 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 422 57 i i PRP work_ln56cwsp7ffppl4wxeq7osqfuu 422 58 du du VBP work_ln56cwsp7ffppl4wxeq7osqfuu 422 59 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 422 60 3 3 CD work_ln56cwsp7ffppl4wxeq7osqfuu 422 61 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 422 62 j j NNP work_ln56cwsp7ffppl4wxeq7osqfuu 422 63 du du NN work_ln56cwsp7ffppl4wxeq7osqfuu 422 64 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 422 65 2 2 CD work_ln56cwsp7ffppl4wxeq7osqfuu 422 66 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 422 67 i i PRP work_ln56cwsp7ffppl4wxeq7osqfuu 422 68 du du VBP work_ln56cwsp7ffppl4wxeq7osqfuu 422 69 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 422 70 2 2 CD work_ln56cwsp7ffppl4wxeq7osqfuu 422 71 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 422 72 j j NNP work_ln56cwsp7ffppl4wxeq7osqfuu 422 73 du du NNP work_ln56cwsp7ffppl4wxeq7osqfuu 422 74 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 422 75 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 422 76 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 422 77 i i PRP work_ln56cwsp7ffppl4wxeq7osqfuu 422 78 du du VBP work_ln56cwsp7ffppl4wxeq7osqfuu 422 79 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 422 80 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 422 81 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 422 82 j j NN work_ln56cwsp7ffppl4wxeq7osqfuu 422 83 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 423 1 It -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 423 2 can can MD work_ln56cwsp7ffppl4wxeq7osqfuu 423 3 be be VB work_ln56cwsp7ffppl4wxeq7osqfuu 423 4 shown show VBN work_ln56cwsp7ffppl4wxeq7osqfuu 423 5 that that IN work_ln56cwsp7ffppl4wxeq7osqfuu 423 6 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 423 7 above above JJ work_ln56cwsp7ffppl4wxeq7osqfuu 423 8 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 423 9 .3 .3 NN work_ln56cwsp7ffppl4wxeq7osqfuu 423 10 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 423 11 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 423 12 any any DT work_ln56cwsp7ffppl4wxeq7osqfuu 423 13 parabolic parabolic JJ work_ln56cwsp7ffppl4wxeq7osqfuu 423 14 distribution distribution NN work_ln56cwsp7ffppl4wxeq7osqfuu 423 15 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 423 16 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 423 17 value value NN work_ln56cwsp7ffppl4wxeq7osqfuu 423 18 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 423 19 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 423 20 integral integral NN work_ln56cwsp7ffppl4wxeq7osqfuu 423 21 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 423 22 strictly strictly RB work_ln56cwsp7ffppl4wxeq7osqfuu 423 23 lower low JJR work_ln56cwsp7ffppl4wxeq7osqfuu 423 24 than than IN work_ln56cwsp7ffppl4wxeq7osqfuu 423 25 1/3 1/3 CD work_ln56cwsp7ffppl4wxeq7osqfuu 423 26 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 423 27 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 424 1 Clearly clearly RB work_ln56cwsp7ffppl4wxeq7osqfuu 424 2 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 424 3 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 424 4 utilitarian utilitarian JJ work_ln56cwsp7ffppl4wxeq7osqfuu 424 5 choice choice NN work_ln56cwsp7ffppl4wxeq7osqfuu 424 6 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 424 7 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 424 8 with with IN work_ln56cwsp7ffppl4wxeq7osqfuu 424 9 equal equal JJ work_ln56cwsp7ffppl4wxeq7osqfuu 424 10 probability probability NN work_ln56cwsp7ffppl4wxeq7osqfuu 424 11 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 424 12 either either CC work_ln56cwsp7ffppl4wxeq7osqfuu 424 13 alternative alternative JJ work_ln56cwsp7ffppl4wxeq7osqfuu 424 14 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 424 15 or or CC work_ln56cwsp7ffppl4wxeq7osqfuu 424 16 3 3 CD work_ln56cwsp7ffppl4wxeq7osqfuu 424 17 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 425 1 Then then RB work_ln56cwsp7ffppl4wxeq7osqfuu 425 2 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 425 3 βUT βut FW work_ln56cwsp7ffppl4wxeq7osqfuu 425 4 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 425 5 M m NN work_ln56cwsp7ffppl4wxeq7osqfuu 425 6 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 425 7 = = NFP work_ln56cwsp7ffppl4wxeq7osqfuu 425 8 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 425 9 .35 .35 NN work_ln56cwsp7ffppl4wxeq7osqfuu 425 10 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 425 11 .3 .3 NN work_ln56cwsp7ffppl4wxeq7osqfuu 425 12 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 425 13 .35 .35 CD work_ln56cwsp7ffppl4wxeq7osqfuu 425 14 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 425 15 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 425 16 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 425 17 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 425 18 remaining remain VBG work_ln56cwsp7ffppl4wxeq7osqfuu 425 19 parabolic parabolic JJ work_ln56cwsp7ffppl4wxeq7osqfuu 425 20 functions function NNS work_ln56cwsp7ffppl4wxeq7osqfuu 425 21 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 425 22 β1UT β1UT '' work_ln56cwsp7ffppl4wxeq7osqfuu 425 23 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 425 24 M m NN work_ln56cwsp7ffppl4wxeq7osqfuu 425 25 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 425 26 = = NFP work_ln56cwsp7ffppl4wxeq7osqfuu 425 27 β β NNP work_ln56cwsp7ffppl4wxeq7osqfuu 425 28 3 3 CD work_ln56cwsp7ffppl4wxeq7osqfuu 425 29 UT UT NNP work_ln56cwsp7ffppl4wxeq7osqfuu 425 30 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 425 31 M M NNP work_ln56cwsp7ffppl4wxeq7osqfuu 425 32 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 425 33 > > XX work_ln56cwsp7ffppl4wxeq7osqfuu 425 34 β β NNP work_ln56cwsp7ffppl4wxeq7osqfuu 425 35 2 2 CD work_ln56cwsp7ffppl4wxeq7osqfuu 425 36 UT UT NNP work_ln56cwsp7ffppl4wxeq7osqfuu 425 37 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 425 38 M M NNP work_ln56cwsp7ffppl4wxeq7osqfuu 425 39 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 425 40 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 426 1 7This 7this DT work_ln56cwsp7ffppl4wxeq7osqfuu 426 2 type type NN work_ln56cwsp7ffppl4wxeq7osqfuu 426 3 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 426 4 societies society NNS work_ln56cwsp7ffppl4wxeq7osqfuu 426 5 has have VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 426 6 attracted attract VBN work_ln56cwsp7ffppl4wxeq7osqfuu 426 7 a a DT work_ln56cwsp7ffppl4wxeq7osqfuu 426 8 good good JJ work_ln56cwsp7ffppl4wxeq7osqfuu 426 9 deal deal NN work_ln56cwsp7ffppl4wxeq7osqfuu 426 10 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 426 11 attention attention NN work_ln56cwsp7ffppl4wxeq7osqfuu 426 12 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 427 1 Interestingly interestingly RB work_ln56cwsp7ffppl4wxeq7osqfuu 427 2 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 427 3 Börgers Börgers NNP work_ln56cwsp7ffppl4wxeq7osqfuu 427 4 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 427 5 Postl Postl NNP work_ln56cwsp7ffppl4wxeq7osqfuu 427 6 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 427 7 2007 2007 CD work_ln56cwsp7ffppl4wxeq7osqfuu 427 8 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 427 9 study study VB work_ln56cwsp7ffppl4wxeq7osqfuu 427 10 whether whether IN work_ln56cwsp7ffppl4wxeq7osqfuu 427 11 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 427 12 this this DT work_ln56cwsp7ffppl4wxeq7osqfuu 427 13 class class NN work_ln56cwsp7ffppl4wxeq7osqfuu 427 14 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 427 15 societies society NNS work_ln56cwsp7ffppl4wxeq7osqfuu 427 16 there there EX work_ln56cwsp7ffppl4wxeq7osqfuu 427 17 are be VBP work_ln56cwsp7ffppl4wxeq7osqfuu 427 18 incentive incentive NN work_ln56cwsp7ffppl4wxeq7osqfuu 427 19 - - HYPH work_ln56cwsp7ffppl4wxeq7osqfuu 427 20 compatible compatible JJ work_ln56cwsp7ffppl4wxeq7osqfuu 427 21 rules rule NNS work_ln56cwsp7ffppl4wxeq7osqfuu 427 22 which which WDT work_ln56cwsp7ffppl4wxeq7osqfuu 427 23 elicit elicit VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 427 24 utilities utility NNS work_ln56cwsp7ffppl4wxeq7osqfuu 427 25 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 427 26 implement implement VB work_ln56cwsp7ffppl4wxeq7osqfuu 427 27 efficient efficient JJ work_ln56cwsp7ffppl4wxeq7osqfuu 427 28 decisions decision NNS work_ln56cwsp7ffppl4wxeq7osqfuu 427 29 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 428 1 19 19 CD work_ln56cwsp7ffppl4wxeq7osqfuu 428 2 Type type NN work_ln56cwsp7ffppl4wxeq7osqfuu 428 3 5 5 CD work_ln56cwsp7ffppl4wxeq7osqfuu 428 4 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 429 1 No no DT work_ln56cwsp7ffppl4wxeq7osqfuu 429 2 correlation correlation NN work_ln56cwsp7ffppl4wxeq7osqfuu 429 3 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 430 1 Individuals individual NNS work_ln56cwsp7ffppl4wxeq7osqfuu 430 2 do do VBP work_ln56cwsp7ffppl4wxeq7osqfuu 430 3 not not RB work_ln56cwsp7ffppl4wxeq7osqfuu 430 4 agree agree VB work_ln56cwsp7ffppl4wxeq7osqfuu 430 5 on on IN work_ln56cwsp7ffppl4wxeq7osqfuu 430 6 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 430 7 ranking ranking NN work_ln56cwsp7ffppl4wxeq7osqfuu 430 8 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 430 9 any any DT work_ln56cwsp7ffppl4wxeq7osqfuu 430 10 alternative alternative NN work_ln56cwsp7ffppl4wxeq7osqfuu 430 11 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 431 1 Let let VB work_ln56cwsp7ffppl4wxeq7osqfuu 431 2 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 431 3 w.l.o.g w.l.o.g NNP work_ln56cwsp7ffppl4wxeq7osqfuu 431 4 . . NNP work_ln56cwsp7ffppl4wxeq7osqfuu 431 5 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 431 6 M1 M1 NNP work_ln56cwsp7ffppl4wxeq7osqfuu 431 7 = = NFP work_ln56cwsp7ffppl4wxeq7osqfuu 431 8 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 431 9 3 3 CD work_ln56cwsp7ffppl4wxeq7osqfuu 431 10 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 431 11 2 2 CD work_ln56cwsp7ffppl4wxeq7osqfuu 431 12 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 431 13 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 431 14 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 431 15 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 431 16 M1 M1 NNP work_ln56cwsp7ffppl4wxeq7osqfuu 431 17 = = NFP work_ln56cwsp7ffppl4wxeq7osqfuu 431 18 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 431 19 2 2 CD work_ln56cwsp7ffppl4wxeq7osqfuu 431 20 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 431 21 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 431 22 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 431 23 3 3 CD work_ln56cwsp7ffppl4wxeq7osqfuu 431 24 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 431 25 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 432 1 Hence hence RB work_ln56cwsp7ffppl4wxeq7osqfuu 432 2 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 432 3 alternative alternative JJ work_ln56cwsp7ffppl4wxeq7osqfuu 432 4 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 432 5 dominates dominate NNS work_ln56cwsp7ffppl4wxeq7osqfuu 432 6 alternative alternative JJ work_ln56cwsp7ffppl4wxeq7osqfuu 432 7 2 2 CD work_ln56cwsp7ffppl4wxeq7osqfuu 432 8 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 432 9 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 432 10 consequently consequently RB work_ln56cwsp7ffppl4wxeq7osqfuu 432 11 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 432 12 utilitarian utilitarian JJ work_ln56cwsp7ffppl4wxeq7osqfuu 432 13 choice choice NN work_ln56cwsp7ffppl4wxeq7osqfuu 432 14 will will MD work_ln56cwsp7ffppl4wxeq7osqfuu 432 15 never never RB work_ln56cwsp7ffppl4wxeq7osqfuu 432 16 be be VB work_ln56cwsp7ffppl4wxeq7osqfuu 432 17 alternative alternative JJ work_ln56cwsp7ffppl4wxeq7osqfuu 432 18 2 2 CD work_ln56cwsp7ffppl4wxeq7osqfuu 432 19 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 433 1 We -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 433 2 now now RB work_ln56cwsp7ffppl4wxeq7osqfuu 433 3 show show VBP work_ln56cwsp7ffppl4wxeq7osqfuu 433 4 that that IN work_ln56cwsp7ffppl4wxeq7osqfuu 433 5 alternative alternative NN work_ln56cwsp7ffppl4wxeq7osqfuu 433 6 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 433 7 has have VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 433 8 a a DT work_ln56cwsp7ffppl4wxeq7osqfuu 433 9 higher high JJR work_ln56cwsp7ffppl4wxeq7osqfuu 433 10 probability probability NN work_ln56cwsp7ffppl4wxeq7osqfuu 433 11 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 433 12 being be VBG work_ln56cwsp7ffppl4wxeq7osqfuu 433 13 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 433 14 utilitarian utilitarian JJ work_ln56cwsp7ffppl4wxeq7osqfuu 433 15 choice choice NN work_ln56cwsp7ffppl4wxeq7osqfuu 433 16 than than IN work_ln56cwsp7ffppl4wxeq7osqfuu 433 17 alternative alternative JJ work_ln56cwsp7ffppl4wxeq7osqfuu 433 18 3 3 CD work_ln56cwsp7ffppl4wxeq7osqfuu 433 19 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 434 1 For for IN work_ln56cwsp7ffppl4wxeq7osqfuu 434 2 any any DT work_ln56cwsp7ffppl4wxeq7osqfuu 434 3 society society NN work_ln56cwsp7ffppl4wxeq7osqfuu 434 4 where where WRB work_ln56cwsp7ffppl4wxeq7osqfuu 434 5 alternative alternative JJ work_ln56cwsp7ffppl4wxeq7osqfuu 434 6 3 3 CD work_ln56cwsp7ffppl4wxeq7osqfuu 434 7 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 434 8 better well JJR work_ln56cwsp7ffppl4wxeq7osqfuu 434 9 in in IN work_ln56cwsp7ffppl4wxeq7osqfuu 434 10 utilitarian utilitarian JJ work_ln56cwsp7ffppl4wxeq7osqfuu 434 11 terms term NNS work_ln56cwsp7ffppl4wxeq7osqfuu 434 12 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 434 13 a a DT work_ln56cwsp7ffppl4wxeq7osqfuu 434 14 society society NN work_ln56cwsp7ffppl4wxeq7osqfuu 434 15 can can MD work_ln56cwsp7ffppl4wxeq7osqfuu 434 16 be be VB work_ln56cwsp7ffppl4wxeq7osqfuu 434 17 injectively injectively RB work_ln56cwsp7ffppl4wxeq7osqfuu 434 18 constructed construct VBN work_ln56cwsp7ffppl4wxeq7osqfuu 434 19 such such JJ work_ln56cwsp7ffppl4wxeq7osqfuu 434 20 that that DT work_ln56cwsp7ffppl4wxeq7osqfuu 434 21 : : : work_ln56cwsp7ffppl4wxeq7osqfuu 434 22 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 434 23 i i NN work_ln56cwsp7ffppl4wxeq7osqfuu 434 24 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 434 25 it -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 434 26 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 434 27 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 434 28 type type NN work_ln56cwsp7ffppl4wxeq7osqfuu 434 29 5 5 CD work_ln56cwsp7ffppl4wxeq7osqfuu 434 30 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 434 31 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 434 32 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 434 33 ii ii LS work_ln56cwsp7ffppl4wxeq7osqfuu 434 34 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 434 35 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 434 36 utilitarian utilitarian JJ work_ln56cwsp7ffppl4wxeq7osqfuu 434 37 choice choice NN work_ln56cwsp7ffppl4wxeq7osqfuu 434 38 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 434 39 alternative alternative JJ work_ln56cwsp7ffppl4wxeq7osqfuu 434 40 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 434 41 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 435 1 Simply simply RB work_ln56cwsp7ffppl4wxeq7osqfuu 435 2 write write VB work_ln56cwsp7ffppl4wxeq7osqfuu 435 3 u u NNP work_ln56cwsp7ffppl4wxeq7osqfuu 435 4 ′1 ′1 NNP work_ln56cwsp7ffppl4wxeq7osqfuu 435 5 1 1 NNP work_ln56cwsp7ffppl4wxeq7osqfuu 435 6 = = SYM work_ln56cwsp7ffppl4wxeq7osqfuu 435 7 u u NNP work_ln56cwsp7ffppl4wxeq7osqfuu 435 8 3 3 CD work_ln56cwsp7ffppl4wxeq7osqfuu 435 9 2 2 CD work_ln56cwsp7ffppl4wxeq7osqfuu 435 10 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 435 11 u u NNP work_ln56cwsp7ffppl4wxeq7osqfuu 435 12 ′2 ′2 NN work_ln56cwsp7ffppl4wxeq7osqfuu 435 13 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 435 14 = = SYM work_ln56cwsp7ffppl4wxeq7osqfuu 435 15 u u NNP work_ln56cwsp7ffppl4wxeq7osqfuu 435 16 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 435 17 2 2 CD work_ln56cwsp7ffppl4wxeq7osqfuu 435 18 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 435 19 u u NNP work_ln56cwsp7ffppl4wxeq7osqfuu 435 20 ′3 ′3 NNP work_ln56cwsp7ffppl4wxeq7osqfuu 435 21 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 435 22 = = SYM work_ln56cwsp7ffppl4wxeq7osqfuu 435 23 u u NNP work_ln56cwsp7ffppl4wxeq7osqfuu 435 24 2 2 CD work_ln56cwsp7ffppl4wxeq7osqfuu 435 25 2 2 CD work_ln56cwsp7ffppl4wxeq7osqfuu 435 26 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 435 27 u u NNP work_ln56cwsp7ffppl4wxeq7osqfuu 435 28 ′1 ′1 NNP work_ln56cwsp7ffppl4wxeq7osqfuu 435 29 2 2 NNP work_ln56cwsp7ffppl4wxeq7osqfuu 435 30 = = SYM work_ln56cwsp7ffppl4wxeq7osqfuu 435 31 u u NNP work_ln56cwsp7ffppl4wxeq7osqfuu 435 32 2 2 CD work_ln56cwsp7ffppl4wxeq7osqfuu 435 33 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 435 34 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 435 35 u u NNP work_ln56cwsp7ffppl4wxeq7osqfuu 435 36 ′2 ′2 NN work_ln56cwsp7ffppl4wxeq7osqfuu 435 37 2 2 CD work_ln56cwsp7ffppl4wxeq7osqfuu 435 38 = = SYM work_ln56cwsp7ffppl4wxeq7osqfuu 435 39 u u NNP work_ln56cwsp7ffppl4wxeq7osqfuu 435 40 3 3 CD work_ln56cwsp7ffppl4wxeq7osqfuu 435 41 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 435 42 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 435 43 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 435 44 u u NNP work_ln56cwsp7ffppl4wxeq7osqfuu 435 45 ′3 ′3 NNP work_ln56cwsp7ffppl4wxeq7osqfuu 435 46 2 2 CD work_ln56cwsp7ffppl4wxeq7osqfuu 435 47 = = SYM work_ln56cwsp7ffppl4wxeq7osqfuu 435 48 u u NNP work_ln56cwsp7ffppl4wxeq7osqfuu 435 49 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 435 50 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 435 51 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 436 1 8 8 CD work_ln56cwsp7ffppl4wxeq7osqfuu 436 2 Clearly clearly RB work_ln56cwsp7ffppl4wxeq7osqfuu 436 3 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 436 4 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 436 5 constructed construct VBN work_ln56cwsp7ffppl4wxeq7osqfuu 436 6 society society NN work_ln56cwsp7ffppl4wxeq7osqfuu 436 7 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 436 8 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 436 9 type type NN work_ln56cwsp7ffppl4wxeq7osqfuu 436 10 5 5 CD work_ln56cwsp7ffppl4wxeq7osqfuu 436 11 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 436 12 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 436 13 to to TO work_ln56cwsp7ffppl4wxeq7osqfuu 436 14 see see VB work_ln56cwsp7ffppl4wxeq7osqfuu 436 15 that that IN work_ln56cwsp7ffppl4wxeq7osqfuu 436 16 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 436 17 utilitarian utilitarian JJ work_ln56cwsp7ffppl4wxeq7osqfuu 436 18 choice choice NN work_ln56cwsp7ffppl4wxeq7osqfuu 436 19 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 436 20 alternative alternative JJ work_ln56cwsp7ffppl4wxeq7osqfuu 436 21 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 436 22 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 436 23 notice notice VB work_ln56cwsp7ffppl4wxeq7osqfuu 436 24 that that IN work_ln56cwsp7ffppl4wxeq7osqfuu 436 25 u u NNP work_ln56cwsp7ffppl4wxeq7osqfuu 436 26 ′1 ′1 NNP work_ln56cwsp7ffppl4wxeq7osqfuu 436 27 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 436 28 + + CC work_ln56cwsp7ffppl4wxeq7osqfuu 436 29 u u NNP work_ln56cwsp7ffppl4wxeq7osqfuu 436 30 ′1 ′1 NNP work_ln56cwsp7ffppl4wxeq7osqfuu 436 31 2 2 NNP work_ln56cwsp7ffppl4wxeq7osqfuu 436 32 = = SYM work_ln56cwsp7ffppl4wxeq7osqfuu 436 33 u u NNP work_ln56cwsp7ffppl4wxeq7osqfuu 436 34 3 3 CD work_ln56cwsp7ffppl4wxeq7osqfuu 436 35 2 2 CD work_ln56cwsp7ffppl4wxeq7osqfuu 436 36 + + CC work_ln56cwsp7ffppl4wxeq7osqfuu 436 37 u u CD work_ln56cwsp7ffppl4wxeq7osqfuu 436 38 2 2 CD work_ln56cwsp7ffppl4wxeq7osqfuu 436 39 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 436 40 > > NN work_ln56cwsp7ffppl4wxeq7osqfuu 436 41 u u NNP work_ln56cwsp7ffppl4wxeq7osqfuu 436 42 3 3 CD work_ln56cwsp7ffppl4wxeq7osqfuu 436 43 2 2 CD work_ln56cwsp7ffppl4wxeq7osqfuu 436 44 + + SYM work_ln56cwsp7ffppl4wxeq7osqfuu 436 45 u u NN work_ln56cwsp7ffppl4wxeq7osqfuu 436 46 3 3 CD work_ln56cwsp7ffppl4wxeq7osqfuu 436 47 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 436 48 > > CD work_ln56cwsp7ffppl4wxeq7osqfuu 436 49 u11 u11 NN work_ln56cwsp7ffppl4wxeq7osqfuu 436 50 + + CC work_ln56cwsp7ffppl4wxeq7osqfuu 436 51 u u NN work_ln56cwsp7ffppl4wxeq7osqfuu 436 52 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 436 53 2 2 CD work_ln56cwsp7ffppl4wxeq7osqfuu 436 54 > > NN work_ln56cwsp7ffppl4wxeq7osqfuu 436 55 u u NNP work_ln56cwsp7ffppl4wxeq7osqfuu 436 56 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 436 57 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 436 58 + + SYM work_ln56cwsp7ffppl4wxeq7osqfuu 436 59 u u CD work_ln56cwsp7ffppl4wxeq7osqfuu 436 60 2 2 CD work_ln56cwsp7ffppl4wxeq7osqfuu 436 61 2 2 CD work_ln56cwsp7ffppl4wxeq7osqfuu 436 62 = = SYM work_ln56cwsp7ffppl4wxeq7osqfuu 436 63 u u NN work_ln56cwsp7ffppl4wxeq7osqfuu 436 64 ′3 ′3 NN work_ln56cwsp7ffppl4wxeq7osqfuu 436 65 2 2 CD work_ln56cwsp7ffppl4wxeq7osqfuu 436 66 + + CC work_ln56cwsp7ffppl4wxeq7osqfuu 436 67 u u CD work_ln56cwsp7ffppl4wxeq7osqfuu 436 68 ′3 ′3 NN work_ln56cwsp7ffppl4wxeq7osqfuu 436 69 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 436 70 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 437 1 Then then RB work_ln56cwsp7ffppl4wxeq7osqfuu 437 2 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 437 3 β β NNP work_ln56cwsp7ffppl4wxeq7osqfuu 437 4 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 437 5 UT UT NNP work_ln56cwsp7ffppl4wxeq7osqfuu 437 6 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 437 7 M M NNP work_ln56cwsp7ffppl4wxeq7osqfuu 437 8 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 437 9 > > XX work_ln56cwsp7ffppl4wxeq7osqfuu 437 10 β β NNP work_ln56cwsp7ffppl4wxeq7osqfuu 437 11 3 3 CD work_ln56cwsp7ffppl4wxeq7osqfuu 437 12 UT UT NNP work_ln56cwsp7ffppl4wxeq7osqfuu 437 13 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 437 14 M M NNP work_ln56cwsp7ffppl4wxeq7osqfuu 437 15 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 437 16 > > XX work_ln56cwsp7ffppl4wxeq7osqfuu 437 17 β β NNP work_ln56cwsp7ffppl4wxeq7osqfuu 437 18 2 2 CD work_ln56cwsp7ffppl4wxeq7osqfuu 437 19 UT UT NNP work_ln56cwsp7ffppl4wxeq7osqfuu 437 20 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 437 21 M M NNP work_ln56cwsp7ffppl4wxeq7osqfuu 437 22 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 437 23 = = SYM work_ln56cwsp7ffppl4wxeq7osqfuu 437 24 0 0 NFP work_ln56cwsp7ffppl4wxeq7osqfuu 437 25 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 438 1 Taking take VBG work_ln56cwsp7ffppl4wxeq7osqfuu 438 2 into into IN work_ln56cwsp7ffppl4wxeq7osqfuu 438 3 consideration consideration NN work_ln56cwsp7ffppl4wxeq7osqfuu 438 4 all all DT work_ln56cwsp7ffppl4wxeq7osqfuu 438 5 five five CD work_ln56cwsp7ffppl4wxeq7osqfuu 438 6 cases case NNS work_ln56cwsp7ffppl4wxeq7osqfuu 438 7 together together RB work_ln56cwsp7ffppl4wxeq7osqfuu 438 8 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 438 9 implosion implosion NN work_ln56cwsp7ffppl4wxeq7osqfuu 438 10 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 438 11 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 438 12 βUT βut NN work_ln56cwsp7ffppl4wxeq7osqfuu 438 13 -optimal -optimal JJ work_ln56cwsp7ffppl4wxeq7osqfuu 438 14 gen- gen- NN work_ln56cwsp7ffppl4wxeq7osqfuu 438 15 erator erator NN work_ln56cwsp7ffppl4wxeq7osqfuu 438 16 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 439 1 This this DT work_ln56cwsp7ffppl4wxeq7osqfuu 439 2 proves prove VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 439 3 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 439 4 first first JJ work_ln56cwsp7ffppl4wxeq7osqfuu 439 5 part part NN work_ln56cwsp7ffppl4wxeq7osqfuu 439 6 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 439 7 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 439 8 theorem theorem NN work_ln56cwsp7ffppl4wxeq7osqfuu 439 9 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 440 1 The the DT work_ln56cwsp7ffppl4wxeq7osqfuu 440 2 second second JJ work_ln56cwsp7ffppl4wxeq7osqfuu 440 3 part part NN work_ln56cwsp7ffppl4wxeq7osqfuu 440 4 follows follow VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 440 5 immediately immediately RB work_ln56cwsp7ffppl4wxeq7osqfuu 440 6 from from IN work_ln56cwsp7ffppl4wxeq7osqfuu 440 7 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 440 8 above above JJ work_ln56cwsp7ffppl4wxeq7osqfuu 440 9 analysis analysis NN work_ln56cwsp7ffppl4wxeq7osqfuu 440 10 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 440 11 � � : work_ln56cwsp7ffppl4wxeq7osqfuu 440 12 Proof Proof NNP work_ln56cwsp7ffppl4wxeq7osqfuu 440 13 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 440 14 Theorem Theorem NNP work_ln56cwsp7ffppl4wxeq7osqfuu 440 15 4.1 4.1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 440 16 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 441 1 First first RB work_ln56cwsp7ffppl4wxeq7osqfuu 441 2 note note VB work_ln56cwsp7ffppl4wxeq7osqfuu 441 3 that that IN work_ln56cwsp7ffppl4wxeq7osqfuu 441 4 only only RB work_ln56cwsp7ffppl4wxeq7osqfuu 441 5 alternatives alternative NNS work_ln56cwsp7ffppl4wxeq7osqfuu 441 6 ranked rank VBD work_ln56cwsp7ffppl4wxeq7osqfuu 441 7 best well RBS work_ln56cwsp7ffppl4wxeq7osqfuu 441 8 by by IN work_ln56cwsp7ffppl4wxeq7osqfuu 441 9 some some DT work_ln56cwsp7ffppl4wxeq7osqfuu 441 10 agents agent NNS work_ln56cwsp7ffppl4wxeq7osqfuu 441 11 can can MD work_ln56cwsp7ffppl4wxeq7osqfuu 441 12 provide provide VB work_ln56cwsp7ffppl4wxeq7osqfuu 441 13 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 441 14 highest high JJS work_ln56cwsp7ffppl4wxeq7osqfuu 441 15 maximax maximax NNP work_ln56cwsp7ffppl4wxeq7osqfuu 441 16 value value NN work_ln56cwsp7ffppl4wxeq7osqfuu 441 17 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 442 1 In in IN work_ln56cwsp7ffppl4wxeq7osqfuu 442 2 fact fact NN work_ln56cwsp7ffppl4wxeq7osqfuu 442 3 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 442 4 due due IN work_ln56cwsp7ffppl4wxeq7osqfuu 442 5 to to IN work_ln56cwsp7ffppl4wxeq7osqfuu 442 6 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 442 7 i.i.d i.i.d NN work_ln56cwsp7ffppl4wxeq7osqfuu 442 8 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 443 1 nature nature NN work_ln56cwsp7ffppl4wxeq7osqfuu 443 2 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 443 3 utility utility NN work_ln56cwsp7ffppl4wxeq7osqfuu 443 4 realizations realization NNS work_ln56cwsp7ffppl4wxeq7osqfuu 443 5 across across IN work_ln56cwsp7ffppl4wxeq7osqfuu 443 6 individuals individual NNS work_ln56cwsp7ffppl4wxeq7osqfuu 443 7 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 443 8 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 443 9 all all DT work_ln56cwsp7ffppl4wxeq7osqfuu 443 10 M M NNP work_ln56cwsp7ffppl4wxeq7osqfuu 443 11 ∈M ∈M NNP work_ln56cwsp7ffppl4wxeq7osqfuu 443 12 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 443 13 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 443 14 all all DT work_ln56cwsp7ffppl4wxeq7osqfuu 443 15 h h NN work_ln56cwsp7ffppl4wxeq7osqfuu 443 16 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 443 17 l l NN work_ln56cwsp7ffppl4wxeq7osqfuu 443 18 ∈ ∈ NNP work_ln56cwsp7ffppl4wxeq7osqfuu 443 19 K K NNP work_ln56cwsp7ffppl4wxeq7osqfuu 443 20 βlMX(M βlMX(M NNP work_ln56cwsp7ffppl4wxeq7osqfuu 443 21 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 443 22 ≥ ≥ UH work_ln56cwsp7ffppl4wxeq7osqfuu 443 23 β β NN work_ln56cwsp7ffppl4wxeq7osqfuu 443 24 h h NNP work_ln56cwsp7ffppl4wxeq7osqfuu 443 25 MX(M MX(M NNP work_ln56cwsp7ffppl4wxeq7osqfuu 443 26 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 443 27 ⇔ ⇔ NNP work_ln56cwsp7ffppl4wxeq7osqfuu 443 28 l l NN work_ln56cwsp7ffppl4wxeq7osqfuu 443 29 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 443 30 k k NNP work_ln56cwsp7ffppl4wxeq7osqfuu 443 31 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 443 32 ≥ ≥ UH work_ln56cwsp7ffppl4wxeq7osqfuu 443 33 h(k h(k NN work_ln56cwsp7ffppl4wxeq7osqfuu 443 34 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 443 35 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 444 1 It -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 444 2 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 444 3 immediate immediate JJ work_ln56cwsp7ffppl4wxeq7osqfuu 444 4 that that IN work_ln56cwsp7ffppl4wxeq7osqfuu 444 5 every every DT work_ln56cwsp7ffppl4wxeq7osqfuu 444 6 decision decision NN work_ln56cwsp7ffppl4wxeq7osqfuu 444 7 rule rule NN work_ln56cwsp7ffppl4wxeq7osqfuu 444 8 f f NNP work_ln56cwsp7ffppl4wxeq7osqfuu 444 9 in in IN work_ln56cwsp7ffppl4wxeq7osqfuu 444 10 δ(SPl δ(SPl NNP work_ln56cwsp7ffppl4wxeq7osqfuu 444 11 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 444 12 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 444 13 a a DT work_ln56cwsp7ffppl4wxeq7osqfuu 444 14 βMX βmx NN work_ln56cwsp7ffppl4wxeq7osqfuu 444 15 - - HYPH work_ln56cwsp7ffppl4wxeq7osqfuu 444 16 optimal optimal JJ work_ln56cwsp7ffppl4wxeq7osqfuu 444 17 decision decision NN work_ln56cwsp7ffppl4wxeq7osqfuu 444 18 rule rule NN work_ln56cwsp7ffppl4wxeq7osqfuu 444 19 since since IN work_ln56cwsp7ffppl4wxeq7osqfuu 444 20 it -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 444 21 selects select VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 444 22 precisely precisely RB work_ln56cwsp7ffppl4wxeq7osqfuu 444 23 that that DT work_ln56cwsp7ffppl4wxeq7osqfuu 444 24 subset subset NN work_ln56cwsp7ffppl4wxeq7osqfuu 444 25 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 444 26 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 444 27 alternatives alternative NNS work_ln56cwsp7ffppl4wxeq7osqfuu 444 28 that that WDT work_ln56cwsp7ffppl4wxeq7osqfuu 444 29 are be VBP work_ln56cwsp7ffppl4wxeq7osqfuu 444 30 ranked rank VBN work_ln56cwsp7ffppl4wxeq7osqfuu 444 31 best well RBS work_ln56cwsp7ffppl4wxeq7osqfuu 444 32 by by IN work_ln56cwsp7ffppl4wxeq7osqfuu 444 33 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 444 34 largest large JJS work_ln56cwsp7ffppl4wxeq7osqfuu 444 35 number number NN work_ln56cwsp7ffppl4wxeq7osqfuu 444 36 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 444 37 individuals individual NNS work_ln56cwsp7ffppl4wxeq7osqfuu 444 38 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 445 1 Furthermore furthermore RB work_ln56cwsp7ffppl4wxeq7osqfuu 445 2 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 445 3 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 445 4 every every DT work_ln56cwsp7ffppl4wxeq7osqfuu 445 5 f f NN work_ln56cwsp7ffppl4wxeq7osqfuu 445 6 6∈ 6∈ CD work_ln56cwsp7ffppl4wxeq7osqfuu 445 7 δ(SPl δ(SPl NNP work_ln56cwsp7ffppl4wxeq7osqfuu 445 8 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 445 9 there there EX work_ln56cwsp7ffppl4wxeq7osqfuu 445 10 exists exist VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 445 11 an an DT work_ln56cwsp7ffppl4wxeq7osqfuu 445 12 M M NNP work_ln56cwsp7ffppl4wxeq7osqfuu 445 13 ∈ ∈ NNP work_ln56cwsp7ffppl4wxeq7osqfuu 445 14 M M NNP work_ln56cwsp7ffppl4wxeq7osqfuu 445 15 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 445 16 an an DT work_ln56cwsp7ffppl4wxeq7osqfuu 445 17 alternative alternative JJ work_ln56cwsp7ffppl4wxeq7osqfuu 445 18 h h NN work_ln56cwsp7ffppl4wxeq7osqfuu 445 19 ∈ ∈ NNP work_ln56cwsp7ffppl4wxeq7osqfuu 445 20 K k NN work_ln56cwsp7ffppl4wxeq7osqfuu 445 21 such such JJ work_ln56cwsp7ffppl4wxeq7osqfuu 445 22 that that IN work_ln56cwsp7ffppl4wxeq7osqfuu 445 23 h h VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 445 24 ∈ ∈ IN work_ln56cwsp7ffppl4wxeq7osqfuu 445 25 f(M f(m NN work_ln56cwsp7ffppl4wxeq7osqfuu 445 26 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 445 27 \ \ NN work_ln56cwsp7ffppl4wxeq7osqfuu 445 28 SPl(M SPl(M . work_ln56cwsp7ffppl4wxeq7osqfuu 445 29 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 445 30 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 446 1 Consequently consequently RB work_ln56cwsp7ffppl4wxeq7osqfuu 446 2 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 446 3 there there EX work_ln56cwsp7ffppl4wxeq7osqfuu 446 4 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 446 5 an an DT work_ln56cwsp7ffppl4wxeq7osqfuu 446 6 l l NN work_ln56cwsp7ffppl4wxeq7osqfuu 446 7 ∈ ∈ NNP work_ln56cwsp7ffppl4wxeq7osqfuu 446 8 K k NN work_ln56cwsp7ffppl4wxeq7osqfuu 446 9 such such JJ work_ln56cwsp7ffppl4wxeq7osqfuu 446 10 that that IN work_ln56cwsp7ffppl4wxeq7osqfuu 446 11 l(k l(k NNP work_ln56cwsp7ffppl4wxeq7osqfuu 446 12 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 446 13 > > XX work_ln56cwsp7ffppl4wxeq7osqfuu 446 14 h(k h(k NNP work_ln56cwsp7ffppl4wxeq7osqfuu 446 15 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 446 16 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 446 17 hence hence RB work_ln56cwsp7ffppl4wxeq7osqfuu 446 18 f f NNP work_ln56cwsp7ffppl4wxeq7osqfuu 446 19 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 446 20 not not RB work_ln56cwsp7ffppl4wxeq7osqfuu 446 21 a a DT work_ln56cwsp7ffppl4wxeq7osqfuu 446 22 βMX βmx NN work_ln56cwsp7ffppl4wxeq7osqfuu 446 23 - - HYPH work_ln56cwsp7ffppl4wxeq7osqfuu 446 24 optimal optimal JJ work_ln56cwsp7ffppl4wxeq7osqfuu 446 25 decision decision NN work_ln56cwsp7ffppl4wxeq7osqfuu 446 26 rule rule NN work_ln56cwsp7ffppl4wxeq7osqfuu 446 27 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 446 28 � � : work_ln56cwsp7ffppl4wxeq7osqfuu 446 29 Proof Proof NNP work_ln56cwsp7ffppl4wxeq7osqfuu 446 30 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 446 31 Corollary Corollary NNP work_ln56cwsp7ffppl4wxeq7osqfuu 446 32 4.2 4.2 CD work_ln56cwsp7ffppl4wxeq7osqfuu 446 33 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 447 1 We -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 447 2 prove prove VBP work_ln56cwsp7ffppl4wxeq7osqfuu 447 3 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 447 4 corollary corollary NN work_ln56cwsp7ffppl4wxeq7osqfuu 447 5 by by IN work_ln56cwsp7ffppl4wxeq7osqfuu 447 6 showing show VBG work_ln56cwsp7ffppl4wxeq7osqfuu 447 7 that that DT work_ln56cwsp7ffppl4wxeq7osqfuu 447 8 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 447 9 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 447 10 any any DT work_ln56cwsp7ffppl4wxeq7osqfuu 447 11 given give VBN work_ln56cwsp7ffppl4wxeq7osqfuu 447 12 K K NNP work_ln56cwsp7ffppl4wxeq7osqfuu 447 13 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 447 14 when when WRB work_ln56cwsp7ffppl4wxeq7osqfuu 447 15 n n DT work_ln56cwsp7ffppl4wxeq7osqfuu 447 16 tends tend VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 447 17 to to IN work_ln56cwsp7ffppl4wxeq7osqfuu 447 18 infinity infinity NN work_ln56cwsp7ffppl4wxeq7osqfuu 447 19 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 447 20 plurality plurality NN work_ln56cwsp7ffppl4wxeq7osqfuu 447 21 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 447 22 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 447 23 only only JJ work_ln56cwsp7ffppl4wxeq7osqfuu 447 24 scoring score VBG work_ln56cwsp7ffppl4wxeq7osqfuu 447 25 rule rule NN work_ln56cwsp7ffppl4wxeq7osqfuu 447 26 in in IN work_ln56cwsp7ffppl4wxeq7osqfuu 447 27 δ(SPl δ(SPl NNP work_ln56cwsp7ffppl4wxeq7osqfuu 447 28 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 447 29 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 448 1 Take take VB work_ln56cwsp7ffppl4wxeq7osqfuu 448 2 a a DT work_ln56cwsp7ffppl4wxeq7osqfuu 448 3 scoring scoring JJ work_ln56cwsp7ffppl4wxeq7osqfuu 448 4 rule rule NN work_ln56cwsp7ffppl4wxeq7osqfuu 448 5 f f NNP work_ln56cwsp7ffppl4wxeq7osqfuu 448 6 different different RB work_ln56cwsp7ffppl4wxeq7osqfuu 448 7 from from IN work_ln56cwsp7ffppl4wxeq7osqfuu 448 8 plurality plurality NN work_ln56cwsp7ffppl4wxeq7osqfuu 448 9 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 449 1 We -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 449 2 now now RB work_ln56cwsp7ffppl4wxeq7osqfuu 449 3 find find VBP work_ln56cwsp7ffppl4wxeq7osqfuu 449 4 a a DT work_ln56cwsp7ffppl4wxeq7osqfuu 449 5 real real JJ work_ln56cwsp7ffppl4wxeq7osqfuu 449 6 number number NN work_ln56cwsp7ffppl4wxeq7osqfuu 449 7 nf nf IN work_ln56cwsp7ffppl4wxeq7osqfuu 449 8 such such JJ work_ln56cwsp7ffppl4wxeq7osqfuu 449 9 that that DT work_ln56cwsp7ffppl4wxeq7osqfuu 449 10 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 449 11 every every DT work_ln56cwsp7ffppl4wxeq7osqfuu 449 12 positive positive JJ work_ln56cwsp7ffppl4wxeq7osqfuu 449 13 integer integer NN work_ln56cwsp7ffppl4wxeq7osqfuu 449 14 n n CC work_ln56cwsp7ffppl4wxeq7osqfuu 449 15 with with IN work_ln56cwsp7ffppl4wxeq7osqfuu 449 16 n n NN work_ln56cwsp7ffppl4wxeq7osqfuu 449 17 > > XX work_ln56cwsp7ffppl4wxeq7osqfuu 449 18 nf nf NN work_ln56cwsp7ffppl4wxeq7osqfuu 449 19 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 449 20 there there EX work_ln56cwsp7ffppl4wxeq7osqfuu 449 21 exists exist VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 449 22 a a DT work_ln56cwsp7ffppl4wxeq7osqfuu 449 23 profile profile NN work_ln56cwsp7ffppl4wxeq7osqfuu 449 24 M m NN work_ln56cwsp7ffppl4wxeq7osqfuu 449 25 ∈M ∈m NN work_ln56cwsp7ffppl4wxeq7osqfuu 449 26 with with IN work_ln56cwsp7ffppl4wxeq7osqfuu 449 27 f(M f(m NN work_ln56cwsp7ffppl4wxeq7osqfuu 449 28 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 449 29 6⊆ 6⊆ CD work_ln56cwsp7ffppl4wxeq7osqfuu 449 30 SPl(M SPl(M NFP work_ln56cwsp7ffppl4wxeq7osqfuu 449 31 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 449 32 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 450 1 Given give VBN work_ln56cwsp7ffppl4wxeq7osqfuu 450 2 that that IN work_ln56cwsp7ffppl4wxeq7osqfuu 450 3 f f NNP work_ln56cwsp7ffppl4wxeq7osqfuu 450 4 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 450 5 not not RB work_ln56cwsp7ffppl4wxeq7osqfuu 450 6 plurality plurality NN work_ln56cwsp7ffppl4wxeq7osqfuu 450 7 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 450 8 Sk−1 sk−1 VB work_ln56cwsp7ffppl4wxeq7osqfuu 450 9 > > XX work_ln56cwsp7ffppl4wxeq7osqfuu 450 10 0 0 CD work_ln56cwsp7ffppl4wxeq7osqfuu 450 11 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 451 1 Take take VB work_ln56cwsp7ffppl4wxeq7osqfuu 451 2 nf nf FW work_ln56cwsp7ffppl4wxeq7osqfuu 451 3 = = DT work_ln56cwsp7ffppl4wxeq7osqfuu 451 4 2 2 CD work_ln56cwsp7ffppl4wxeq7osqfuu 451 5 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 451 6 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 451 7 Sk−1 Sk−1 NNP work_ln56cwsp7ffppl4wxeq7osqfuu 451 8 − − NNP work_ln56cwsp7ffppl4wxeq7osqfuu 451 9 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 451 10 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 451 11 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 451 12 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 451 13 n n JJ work_ln56cwsp7ffppl4wxeq7osqfuu 451 14 > > XX work_ln56cwsp7ffppl4wxeq7osqfuu 451 15 nf nf NN work_ln56cwsp7ffppl4wxeq7osqfuu 451 16 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 452 1 If if IN work_ln56cwsp7ffppl4wxeq7osqfuu 452 2 n n DT work_ln56cwsp7ffppl4wxeq7osqfuu 452 3 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 452 4 odd odd JJ work_ln56cwsp7ffppl4wxeq7osqfuu 452 5 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 452 6 consider consider VB work_ln56cwsp7ffppl4wxeq7osqfuu 452 7 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 452 8 following follow VBG work_ln56cwsp7ffppl4wxeq7osqfuu 452 9 matrix matrix NN work_ln56cwsp7ffppl4wxeq7osqfuu 452 10 M M NNP work_ln56cwsp7ffppl4wxeq7osqfuu 452 11 : : : work_ln56cwsp7ffppl4wxeq7osqfuu 452 12 Mi Mi NNP work_ln56cwsp7ffppl4wxeq7osqfuu 452 13 = = NFP work_ln56cwsp7ffppl4wxeq7osqfuu 452 14 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 452 15 k k NN work_ln56cwsp7ffppl4wxeq7osqfuu 452 16 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 452 17 k k NNP work_ln56cwsp7ffppl4wxeq7osqfuu 452 18 − − NNP work_ln56cwsp7ffppl4wxeq7osqfuu 452 19 1,k 1,k CD work_ln56cwsp7ffppl4wxeq7osqfuu 452 20 − − NNP work_ln56cwsp7ffppl4wxeq7osqfuu 452 21 2 2 CD work_ln56cwsp7ffppl4wxeq7osqfuu 452 22 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 452 23 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 453 1 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 454 1 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 455 1 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 455 2 2 2 CD work_ln56cwsp7ffppl4wxeq7osqfuu 455 3 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 455 4 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 455 5 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 455 6 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 455 7 all all DT work_ln56cwsp7ffppl4wxeq7osqfuu 455 8 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 455 9 ≤ ≤ NNP work_ln56cwsp7ffppl4wxeq7osqfuu 455 10 i i PRP work_ln56cwsp7ffppl4wxeq7osqfuu 455 11 ≤ ≤ VBP work_ln56cwsp7ffppl4wxeq7osqfuu 455 12 n+1 n+1 NNP work_ln56cwsp7ffppl4wxeq7osqfuu 455 13 2 2 CD work_ln56cwsp7ffppl4wxeq7osqfuu 455 14 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 455 15 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 455 16 Mj Mj NNP work_ln56cwsp7ffppl4wxeq7osqfuu 455 17 = = NFP work_ln56cwsp7ffppl4wxeq7osqfuu 455 18 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 455 19 1,k 1,k CD work_ln56cwsp7ffppl4wxeq7osqfuu 455 20 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 455 21 k k NNP work_ln56cwsp7ffppl4wxeq7osqfuu 455 22 − − NNP work_ln56cwsp7ffppl4wxeq7osqfuu 455 23 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 455 24 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 455 25 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 456 1 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 457 1 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 458 1 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 458 2 3 3 CD work_ln56cwsp7ffppl4wxeq7osqfuu 458 3 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 458 4 2 2 CD work_ln56cwsp7ffppl4wxeq7osqfuu 458 5 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 458 6 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 458 7 all all DT work_ln56cwsp7ffppl4wxeq7osqfuu 458 8 n+32 n+32 NNPS work_ln56cwsp7ffppl4wxeq7osqfuu 458 9 ≤ ≤ NNP work_ln56cwsp7ffppl4wxeq7osqfuu 458 10 j j NNP work_ln56cwsp7ffppl4wxeq7osqfuu 458 11 ≤ ≤ NNP work_ln56cwsp7ffppl4wxeq7osqfuu 458 12 n. n. NNP work_ln56cwsp7ffppl4wxeq7osqfuu 458 13 Plurality Plurality NNP work_ln56cwsp7ffppl4wxeq7osqfuu 458 14 selects select NNS work_ln56cwsp7ffppl4wxeq7osqfuu 458 15 alternative alternative VBP work_ln56cwsp7ffppl4wxeq7osqfuu 458 16 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 458 17 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 459 1 Scoring score VBG work_ln56cwsp7ffppl4wxeq7osqfuu 459 2 rule rule NN work_ln56cwsp7ffppl4wxeq7osqfuu 459 3 f f NNP work_ln56cwsp7ffppl4wxeq7osqfuu 459 4 assigns assign VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 459 5 to to TO work_ln56cwsp7ffppl4wxeq7osqfuu 459 6 alternative alternative VB work_ln56cwsp7ffppl4wxeq7osqfuu 459 7 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 459 8 a a DT work_ln56cwsp7ffppl4wxeq7osqfuu 459 9 total total JJ work_ln56cwsp7ffppl4wxeq7osqfuu 459 10 score score NN work_ln56cwsp7ffppl4wxeq7osqfuu 459 11 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 459 12 n+1 n+1 NN work_ln56cwsp7ffppl4wxeq7osqfuu 459 13 2 2 CD work_ln56cwsp7ffppl4wxeq7osqfuu 459 14 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 459 15 while while IN work_ln56cwsp7ffppl4wxeq7osqfuu 459 16 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 459 17 total total JJ work_ln56cwsp7ffppl4wxeq7osqfuu 459 18 score score NN work_ln56cwsp7ffppl4wxeq7osqfuu 459 19 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 459 20 alternative alternative JJ work_ln56cwsp7ffppl4wxeq7osqfuu 459 21 2 2 CD work_ln56cwsp7ffppl4wxeq7osqfuu 459 22 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 459 23 n−1 n−1 NNP work_ln56cwsp7ffppl4wxeq7osqfuu 459 24 2 2 CD work_ln56cwsp7ffppl4wxeq7osqfuu 459 25 + + CC work_ln56cwsp7ffppl4wxeq7osqfuu 459 26 n+1 n+1 NN work_ln56cwsp7ffppl4wxeq7osqfuu 459 27 2 2 CD work_ln56cwsp7ffppl4wxeq7osqfuu 459 28 Sk−1 sk−1 NN work_ln56cwsp7ffppl4wxeq7osqfuu 459 29 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 460 1 We -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 460 2 now now RB work_ln56cwsp7ffppl4wxeq7osqfuu 460 3 show show VBP work_ln56cwsp7ffppl4wxeq7osqfuu 460 4 that that IN work_ln56cwsp7ffppl4wxeq7osqfuu 460 5 n−1 n−1 NNP work_ln56cwsp7ffppl4wxeq7osqfuu 460 6 2 2 CD work_ln56cwsp7ffppl4wxeq7osqfuu 460 7 + + CC work_ln56cwsp7ffppl4wxeq7osqfuu 460 8 n+1 n+1 NN work_ln56cwsp7ffppl4wxeq7osqfuu 460 9 2 2 CD work_ln56cwsp7ffppl4wxeq7osqfuu 460 10 Sk−1 sk−1 NN work_ln56cwsp7ffppl4wxeq7osqfuu 460 11 > > XX work_ln56cwsp7ffppl4wxeq7osqfuu 460 12 n+1 n+1 NN work_ln56cwsp7ffppl4wxeq7osqfuu 460 13 2 2 CD work_ln56cwsp7ffppl4wxeq7osqfuu 460 14 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 460 15 or or CC work_ln56cwsp7ffppl4wxeq7osqfuu 460 16 equivalently equivalently RB work_ln56cwsp7ffppl4wxeq7osqfuu 460 17 n+1 n+1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 460 18 2 2 CD work_ln56cwsp7ffppl4wxeq7osqfuu 460 19 Sk−1 sk−1 NN work_ln56cwsp7ffppl4wxeq7osqfuu 460 20 > > XX work_ln56cwsp7ffppl4wxeq7osqfuu 460 21 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 460 22 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 461 1 Our -PRON- PRP$ work_ln56cwsp7ffppl4wxeq7osqfuu 461 2 original original JJ work_ln56cwsp7ffppl4wxeq7osqfuu 461 3 assumption assumption NN work_ln56cwsp7ffppl4wxeq7osqfuu 461 4 that that IN work_ln56cwsp7ffppl4wxeq7osqfuu 461 5 n n JJ work_ln56cwsp7ffppl4wxeq7osqfuu 461 6 > > XX work_ln56cwsp7ffppl4wxeq7osqfuu 461 7 nf nf FW work_ln56cwsp7ffppl4wxeq7osqfuu 461 8 = = SYM work_ln56cwsp7ffppl4wxeq7osqfuu 461 9 2 2 CD work_ln56cwsp7ffppl4wxeq7osqfuu 461 10 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 461 11 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 461 12 Sk−1 sk−1 NN work_ln56cwsp7ffppl4wxeq7osqfuu 461 13 − − NNP work_ln56cwsp7ffppl4wxeq7osqfuu 461 14 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 461 15 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 461 16 guarantees guarantee VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 461 17 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 461 18 latter latter JJ work_ln56cwsp7ffppl4wxeq7osqfuu 461 19 inequality inequality NN work_ln56cwsp7ffppl4wxeq7osqfuu 461 20 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 462 1 If if IN work_ln56cwsp7ffppl4wxeq7osqfuu 462 2 n n DT work_ln56cwsp7ffppl4wxeq7osqfuu 462 3 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 462 4 even even RB work_ln56cwsp7ffppl4wxeq7osqfuu 462 5 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 462 6 consider consider VB work_ln56cwsp7ffppl4wxeq7osqfuu 462 7 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 462 8 matrix matrix NN work_ln56cwsp7ffppl4wxeq7osqfuu 462 9 M M NNP work_ln56cwsp7ffppl4wxeq7osqfuu 462 10 with with IN work_ln56cwsp7ffppl4wxeq7osqfuu 462 11 Mi Mi NNP work_ln56cwsp7ffppl4wxeq7osqfuu 462 12 = = NFP work_ln56cwsp7ffppl4wxeq7osqfuu 462 13 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 462 14 k k NN work_ln56cwsp7ffppl4wxeq7osqfuu 462 15 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 462 16 k k NNP work_ln56cwsp7ffppl4wxeq7osqfuu 462 17 − − NNP work_ln56cwsp7ffppl4wxeq7osqfuu 462 18 1,k 1,k CD work_ln56cwsp7ffppl4wxeq7osqfuu 462 19 − − NNP work_ln56cwsp7ffppl4wxeq7osqfuu 462 20 2 2 CD work_ln56cwsp7ffppl4wxeq7osqfuu 462 21 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 462 22 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 463 1 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 464 1 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 465 1 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 465 2 2 2 CD work_ln56cwsp7ffppl4wxeq7osqfuu 465 3 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 465 4 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 465 5 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 465 6 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 465 7 all all DT work_ln56cwsp7ffppl4wxeq7osqfuu 465 8 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 465 9 ≤ ≤ NNP work_ln56cwsp7ffppl4wxeq7osqfuu 465 10 i i PRP work_ln56cwsp7ffppl4wxeq7osqfuu 465 11 ≤ ≤ VBP work_ln56cwsp7ffppl4wxeq7osqfuu 465 12 n n CC work_ln56cwsp7ffppl4wxeq7osqfuu 465 13 2 2 CD work_ln56cwsp7ffppl4wxeq7osqfuu 465 14 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 465 15 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 465 16 Mj Mj NNP work_ln56cwsp7ffppl4wxeq7osqfuu 465 17 = = NFP work_ln56cwsp7ffppl4wxeq7osqfuu 465 18 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 465 19 1,k 1,k CD work_ln56cwsp7ffppl4wxeq7osqfuu 465 20 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 465 21 k k NNP work_ln56cwsp7ffppl4wxeq7osqfuu 465 22 − − NNP work_ln56cwsp7ffppl4wxeq7osqfuu 465 23 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 465 24 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 465 25 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 466 1 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 467 1 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 468 1 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 468 2 3 3 CD work_ln56cwsp7ffppl4wxeq7osqfuu 468 3 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 468 4 2 2 CD work_ln56cwsp7ffppl4wxeq7osqfuu 468 5 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 468 6 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 468 7 all all DT work_ln56cwsp7ffppl4wxeq7osqfuu 468 8 n+22 n+22 CD work_ln56cwsp7ffppl4wxeq7osqfuu 468 9 ≤ ≤ NNP work_ln56cwsp7ffppl4wxeq7osqfuu 468 10 j j NNP work_ln56cwsp7ffppl4wxeq7osqfuu 468 11 ≤ ≤ NNP work_ln56cwsp7ffppl4wxeq7osqfuu 468 12 n n NNP work_ln56cwsp7ffppl4wxeq7osqfuu 468 13 − − NNP work_ln56cwsp7ffppl4wxeq7osqfuu 468 14 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 468 15 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 468 16 Mn Mn NNP work_ln56cwsp7ffppl4wxeq7osqfuu 468 17 = = SYM work_ln56cwsp7ffppl4wxeq7osqfuu 468 18 8Note 8note CD work_ln56cwsp7ffppl4wxeq7osqfuu 468 19 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 468 20 that that IN work_ln56cwsp7ffppl4wxeq7osqfuu 468 21 under under IN work_ln56cwsp7ffppl4wxeq7osqfuu 468 22 i.i.d i.i.d NNP work_ln56cwsp7ffppl4wxeq7osqfuu 468 23 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 468 24 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 468 25 this this DT work_ln56cwsp7ffppl4wxeq7osqfuu 468 26 argument argument NN work_ln56cwsp7ffppl4wxeq7osqfuu 468 27 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 468 28 distribution distribution NN work_ln56cwsp7ffppl4wxeq7osqfuu 468 29 free free JJ work_ln56cwsp7ffppl4wxeq7osqfuu 468 30 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 469 1 20 20 CD work_ln56cwsp7ffppl4wxeq7osqfuu 469 2 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 469 3 1,k 1,k CD work_ln56cwsp7ffppl4wxeq7osqfuu 469 4 − − NNP work_ln56cwsp7ffppl4wxeq7osqfuu 469 5 1,k 1,k CD work_ln56cwsp7ffppl4wxeq7osqfuu 469 6 − − NNP work_ln56cwsp7ffppl4wxeq7osqfuu 469 7 2 2 CD work_ln56cwsp7ffppl4wxeq7osqfuu 469 8 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 469 9 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 470 1 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 471 1 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 472 1 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 472 2 2,k 2,k CD work_ln56cwsp7ffppl4wxeq7osqfuu 472 3 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 472 4 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 473 1 An an DT work_ln56cwsp7ffppl4wxeq7osqfuu 473 2 argument argument NN work_ln56cwsp7ffppl4wxeq7osqfuu 473 3 analogous analogous JJ work_ln56cwsp7ffppl4wxeq7osqfuu 473 4 to to IN work_ln56cwsp7ffppl4wxeq7osqfuu 473 5 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 473 6 one one NN work_ln56cwsp7ffppl4wxeq7osqfuu 473 7 above above RB work_ln56cwsp7ffppl4wxeq7osqfuu 473 8 shows show VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 473 9 that that IN work_ln56cwsp7ffppl4wxeq7osqfuu 473 10 plurality plurality NN work_ln56cwsp7ffppl4wxeq7osqfuu 473 11 selects select NNS work_ln56cwsp7ffppl4wxeq7osqfuu 473 12 alternative alternative VBP work_ln56cwsp7ffppl4wxeq7osqfuu 473 13 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 473 14 while while IN work_ln56cwsp7ffppl4wxeq7osqfuu 473 15 f f NNP work_ln56cwsp7ffppl4wxeq7osqfuu 473 16 selects select VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 473 17 alternative alternative JJ work_ln56cwsp7ffppl4wxeq7osqfuu 473 18 2 2 CD work_ln56cwsp7ffppl4wxeq7osqfuu 473 19 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 474 1 Then then RB work_ln56cwsp7ffppl4wxeq7osqfuu 474 2 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 474 3 we -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 474 4 have have VBP work_ln56cwsp7ffppl4wxeq7osqfuu 474 5 shown show VBN work_ln56cwsp7ffppl4wxeq7osqfuu 474 6 that that IN work_ln56cwsp7ffppl4wxeq7osqfuu 474 7 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 474 8 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 474 9 n n DT work_ln56cwsp7ffppl4wxeq7osqfuu 474 10 > > NN work_ln56cwsp7ffppl4wxeq7osqfuu 474 11 nf nf NN work_ln56cwsp7ffppl4wxeq7osqfuu 474 12 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 474 13 decision decision NN work_ln56cwsp7ffppl4wxeq7osqfuu 474 14 rule rule NN work_ln56cwsp7ffppl4wxeq7osqfuu 474 15 f f NNP work_ln56cwsp7ffppl4wxeq7osqfuu 474 16 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 474 17 not not RB work_ln56cwsp7ffppl4wxeq7osqfuu 474 18 a a DT work_ln56cwsp7ffppl4wxeq7osqfuu 474 19 βMX βmx NN work_ln56cwsp7ffppl4wxeq7osqfuu 474 20 - - HYPH work_ln56cwsp7ffppl4wxeq7osqfuu 474 21 optimal optimal JJ work_ln56cwsp7ffppl4wxeq7osqfuu 474 22 scoring score VBG work_ln56cwsp7ffppl4wxeq7osqfuu 474 23 rule rule NN work_ln56cwsp7ffppl4wxeq7osqfuu 474 24 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 474 25 which which WDT work_ln56cwsp7ffppl4wxeq7osqfuu 474 26 proves prove VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 474 27 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 474 28 result result NN work_ln56cwsp7ffppl4wxeq7osqfuu 474 29 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 474 30 � � : work_ln56cwsp7ffppl4wxeq7osqfuu 474 31 Proof Proof NNP work_ln56cwsp7ffppl4wxeq7osqfuu 474 32 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 474 33 Lemma Lemma NNP work_ln56cwsp7ffppl4wxeq7osqfuu 474 34 4.3 4.3 CD work_ln56cwsp7ffppl4wxeq7osqfuu 474 35 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 475 1 The the DT work_ln56cwsp7ffppl4wxeq7osqfuu 475 2 distribution distribution NN work_ln56cwsp7ffppl4wxeq7osqfuu 475 3 function function NN work_ln56cwsp7ffppl4wxeq7osqfuu 475 4 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 475 5 a a DT work_ln56cwsp7ffppl4wxeq7osqfuu 475 6 uniform uniform JJ work_ln56cwsp7ffppl4wxeq7osqfuu 475 7 k k NN work_ln56cwsp7ffppl4wxeq7osqfuu 475 8 order order NN work_ln56cwsp7ffppl4wxeq7osqfuu 475 9 statistic statistic NN work_ln56cwsp7ffppl4wxeq7osqfuu 475 10 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 475 11 F F NNP work_ln56cwsp7ffppl4wxeq7osqfuu 475 12 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 475 13 k)(t k)(t NNP work_ln56cwsp7ffppl4wxeq7osqfuu 475 14 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 475 15 = = NFP work_ln56cwsp7ffppl4wxeq7osqfuu 475 16 tk tk NN work_ln56cwsp7ffppl4wxeq7osqfuu 475 17 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 475 18 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 475 19 a a DT work_ln56cwsp7ffppl4wxeq7osqfuu 475 20 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 475 21 k−1 k−1 NNP work_ln56cwsp7ffppl4wxeq7osqfuu 475 22 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 475 23 order order NN work_ln56cwsp7ffppl4wxeq7osqfuu 475 24 statistic statistic NN work_ln56cwsp7ffppl4wxeq7osqfuu 475 25 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 475 26 F F NNP work_ln56cwsp7ffppl4wxeq7osqfuu 475 27 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 475 28 k−1)(t k−1)(t NNP work_ln56cwsp7ffppl4wxeq7osqfuu 475 29 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 475 30 = = NFP work_ln56cwsp7ffppl4wxeq7osqfuu 475 31 tk+ktk−1(1−t tk+ktk−1(1−t UH work_ln56cwsp7ffppl4wxeq7osqfuu 475 32 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 475 33 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 476 1 Now now RB work_ln56cwsp7ffppl4wxeq7osqfuu 476 2 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 476 3 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 476 4 dis- dis- NN work_ln56cwsp7ffppl4wxeq7osqfuu 476 5 tribution tribution NN work_ln56cwsp7ffppl4wxeq7osqfuu 476 6 function function NN work_ln56cwsp7ffppl4wxeq7osqfuu 476 7 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 476 8 Ul(n Ul(n NNP work_ln56cwsp7ffppl4wxeq7osqfuu 476 9 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 476 10 when when WRB work_ln56cwsp7ffppl4wxeq7osqfuu 476 11 M M NNP work_ln56cwsp7ffppl4wxeq7osqfuu 476 12 l l NN work_ln56cwsp7ffppl4wxeq7osqfuu 476 13 such such JJ work_ln56cwsp7ffppl4wxeq7osqfuu 476 14 that that IN work_ln56cwsp7ffppl4wxeq7osqfuu 476 15 mli mli NNP work_ln56cwsp7ffppl4wxeq7osqfuu 476 16 = = NFP work_ln56cwsp7ffppl4wxeq7osqfuu 476 17 k k XX work_ln56cwsp7ffppl4wxeq7osqfuu 476 18 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 476 19 every every DT work_ln56cwsp7ffppl4wxeq7osqfuu 476 20 i i PRP work_ln56cwsp7ffppl4wxeq7osqfuu 476 21 ∈{1 ∈{1 PRP work_ln56cwsp7ffppl4wxeq7osqfuu 476 22 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 476 23 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 477 1 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 478 1 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 479 1 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 479 2 n n NNP work_ln56cwsp7ffppl4wxeq7osqfuu 479 3 } } -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 479 4 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 479 5 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 479 6 F(t F(t NNP work_ln56cwsp7ffppl4wxeq7osqfuu 479 7 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 479 8 = = NFP work_ln56cwsp7ffppl4wxeq7osqfuu 479 9 tnk tnk FW work_ln56cwsp7ffppl4wxeq7osqfuu 479 10 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 480 1 Then then RB work_ln56cwsp7ffppl4wxeq7osqfuu 480 2 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 480 3 E[Ul(n E[Ul(n NNP work_ln56cwsp7ffppl4wxeq7osqfuu 480 4 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 480 5 | | NNP work_ln56cwsp7ffppl4wxeq7osqfuu 480 6 M M NNP work_ln56cwsp7ffppl4wxeq7osqfuu 480 7 ] ] -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 480 8 = = NFP work_ln56cwsp7ffppl4wxeq7osqfuu 480 9 ∫ ∫ NFP work_ln56cwsp7ffppl4wxeq7osqfuu 480 10 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 480 11 0 0 CD work_ln56cwsp7ffppl4wxeq7osqfuu 480 12 t t NN work_ln56cwsp7ffppl4wxeq7osqfuu 480 13 dF(t dF(t NNP work_ln56cwsp7ffppl4wxeq7osqfuu 480 14 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 480 15 dt dt NNP work_ln56cwsp7ffppl4wxeq7osqfuu 480 16 dt dt NNP work_ln56cwsp7ffppl4wxeq7osqfuu 480 17 = = SYM work_ln56cwsp7ffppl4wxeq7osqfuu 480 18 nk nk NNP work_ln56cwsp7ffppl4wxeq7osqfuu 480 19 nk+1 nk+1 NNP work_ln56cwsp7ffppl4wxeq7osqfuu 480 20 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 481 1 Analogously analogously RB work_ln56cwsp7ffppl4wxeq7osqfuu 481 2 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 481 3 E[Ul(n+1 e[ul(n+1 ADD work_ln56cwsp7ffppl4wxeq7osqfuu 481 4 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 481 5 | | NNP work_ln56cwsp7ffppl4wxeq7osqfuu 481 6 M M NNP work_ln56cwsp7ffppl4wxeq7osqfuu 481 7 ′ ′ ADD work_ln56cwsp7ffppl4wxeq7osqfuu 481 8 ] ] -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 481 9 = = FW work_ln56cwsp7ffppl4wxeq7osqfuu 481 10 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 481 11 n+1)k n+1)k NNP work_ln56cwsp7ffppl4wxeq7osqfuu 481 12 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 481 13 n+1)k+1 n+1)k+1 UH work_ln56cwsp7ffppl4wxeq7osqfuu 481 14 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 481 15 where where WRB work_ln56cwsp7ffppl4wxeq7osqfuu 481 16 m m NNP work_ln56cwsp7ffppl4wxeq7osqfuu 481 17 ′l ′l NNP work_ln56cwsp7ffppl4wxeq7osqfuu 481 18 i i NN work_ln56cwsp7ffppl4wxeq7osqfuu 481 19 = = SYM work_ln56cwsp7ffppl4wxeq7osqfuu 481 20 k k XX work_ln56cwsp7ffppl4wxeq7osqfuu 481 21 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 481 22 every every DT work_ln56cwsp7ffppl4wxeq7osqfuu 481 23 i i NN work_ln56cwsp7ffppl4wxeq7osqfuu 481 24 ∈ ∈ IN work_ln56cwsp7ffppl4wxeq7osqfuu 481 25 { { -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 481 26 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 481 27 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 481 28 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 482 1 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 483 1 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 484 1 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 484 2 n n NNP work_ln56cwsp7ffppl4wxeq7osqfuu 484 3 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 484 4 n n NN work_ln56cwsp7ffppl4wxeq7osqfuu 484 5 + + CC work_ln56cwsp7ffppl4wxeq7osqfuu 484 6 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 484 7 } } -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 484 8 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 485 1 Finally finally RB work_ln56cwsp7ffppl4wxeq7osqfuu 485 2 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 485 3 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 485 4 distribution distribution NN work_ln56cwsp7ffppl4wxeq7osqfuu 485 5 function function NN work_ln56cwsp7ffppl4wxeq7osqfuu 485 6 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 485 7 Ul(n+1 Ul(n+1 NNP work_ln56cwsp7ffppl4wxeq7osqfuu 485 8 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 485 9 when when WRB work_ln56cwsp7ffppl4wxeq7osqfuu 485 10 M M NNP work_ln56cwsp7ffppl4wxeq7osqfuu 485 11 l l NN work_ln56cwsp7ffppl4wxeq7osqfuu 485 12 with with IN work_ln56cwsp7ffppl4wxeq7osqfuu 485 13 mli mli NNP work_ln56cwsp7ffppl4wxeq7osqfuu 485 14 = = SYM work_ln56cwsp7ffppl4wxeq7osqfuu 485 15 k k NNP work_ln56cwsp7ffppl4wxeq7osqfuu 485 16 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 485 17 every every DT work_ln56cwsp7ffppl4wxeq7osqfuu 485 18 i i PRP work_ln56cwsp7ffppl4wxeq7osqfuu 485 19 ∈{1 ∈{1 PRP work_ln56cwsp7ffppl4wxeq7osqfuu 485 20 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 485 21 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 486 1 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 487 1 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 488 1 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 488 2 n n NNP work_ln56cwsp7ffppl4wxeq7osqfuu 488 3 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 488 4 n n NN work_ln56cwsp7ffppl4wxeq7osqfuu 488 5 + + CC work_ln56cwsp7ffppl4wxeq7osqfuu 488 6 1}\{j 1}\{j NNP work_ln56cwsp7ffppl4wxeq7osqfuu 488 7 } } -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 488 8 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 488 9 mlj mlj NN work_ln56cwsp7ffppl4wxeq7osqfuu 488 10 = = SYM work_ln56cwsp7ffppl4wxeq7osqfuu 488 11 k k NN work_ln56cwsp7ffppl4wxeq7osqfuu 488 12 − − NNP work_ln56cwsp7ffppl4wxeq7osqfuu 488 13 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 488 14 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 488 15 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 488 16 F(t F(t NNP work_ln56cwsp7ffppl4wxeq7osqfuu 488 17 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 488 18 = = SYM work_ln56cwsp7ffppl4wxeq7osqfuu 488 19 tnk(tk+ktk−1(1−t tnk(tk+ktk−1(1−t NN work_ln56cwsp7ffppl4wxeq7osqfuu 488 20 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 488 21 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 488 22 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 489 1 Then then RB work_ln56cwsp7ffppl4wxeq7osqfuu 489 2 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 489 3 E[Ul(n+1 e[ul(n+1 ADD work_ln56cwsp7ffppl4wxeq7osqfuu 489 4 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 489 5 | | NNP work_ln56cwsp7ffppl4wxeq7osqfuu 489 6 M M NNP work_ln56cwsp7ffppl4wxeq7osqfuu 489 7 ] ] -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 489 8 = = NFP work_ln56cwsp7ffppl4wxeq7osqfuu 489 9 ∫ ∫ NFP work_ln56cwsp7ffppl4wxeq7osqfuu 489 10 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 489 11 0 0 CD work_ln56cwsp7ffppl4wxeq7osqfuu 489 12 t t NN work_ln56cwsp7ffppl4wxeq7osqfuu 489 13 dF(t dF(t NNP work_ln56cwsp7ffppl4wxeq7osqfuu 489 14 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 489 15 dt dt NNP work_ln56cwsp7ffppl4wxeq7osqfuu 489 16 dt dt NNP work_ln56cwsp7ffppl4wxeq7osqfuu 489 17 = = -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 489 18 k(n2k+2nk+k−1 k(n2k+2nk+k−1 NNP work_ln56cwsp7ffppl4wxeq7osqfuu 489 19 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 489 20 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 489 21 nk+k)(nk+k+1 nk+k)(nk+k+1 NN work_ln56cwsp7ffppl4wxeq7osqfuu 489 22 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 489 23 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 490 1 Con- Con- NNP work_ln56cwsp7ffppl4wxeq7osqfuu 490 2 sequently sequently RB work_ln56cwsp7ffppl4wxeq7osqfuu 490 3 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 490 4 E[Ul(n+1)|M E[Ul(n+1)|M NNP work_ln56cwsp7ffppl4wxeq7osqfuu 490 5 ′l ′l NNP work_ln56cwsp7ffppl4wxeq7osqfuu 490 6 ] ] -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 490 7 − − NNP work_ln56cwsp7ffppl4wxeq7osqfuu 490 8 E[Ul(n)|M E[Ul(n)|M NNP work_ln56cwsp7ffppl4wxeq7osqfuu 490 9 l l NN work_ln56cwsp7ffppl4wxeq7osqfuu 490 10 ] ] -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 490 11 = = SYM work_ln56cwsp7ffppl4wxeq7osqfuu 490 12 k k NNP work_ln56cwsp7ffppl4wxeq7osqfuu 490 13 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 490 14 nk+1)(nk+k+1 nk+1)(nk+k+1 NNP work_ln56cwsp7ffppl4wxeq7osqfuu 490 15 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 490 16 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 490 17 ∆ ∆ NNP work_ln56cwsp7ffppl4wxeq7osqfuu 490 18 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 490 19 k−1 k−1 NNP work_ln56cwsp7ffppl4wxeq7osqfuu 490 20 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 490 21 n n NNP work_ln56cwsp7ffppl4wxeq7osqfuu 490 22 = = SYM work_ln56cwsp7ffppl4wxeq7osqfuu 490 23 E[Ul(n+1)|M E[Ul(n+1)|M NNP work_ln56cwsp7ffppl4wxeq7osqfuu 490 24 l l NN work_ln56cwsp7ffppl4wxeq7osqfuu 490 25 ] ] -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 490 26 − − NNP work_ln56cwsp7ffppl4wxeq7osqfuu 490 27 E[Ul(n)|M E[Ul(n)|M NNP work_ln56cwsp7ffppl4wxeq7osqfuu 490 28 l l NN work_ln56cwsp7ffppl4wxeq7osqfuu 490 29 ] ] -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 490 30 = = SYM work_ln56cwsp7ffppl4wxeq7osqfuu 490 31 k(k−1 k(k−1 NN work_ln56cwsp7ffppl4wxeq7osqfuu 490 32 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 490 33 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 490 34 nk+1)(nk+k)(nk+k+1 nk+1)(nk+k)(nk+k+1 NN work_ln56cwsp7ffppl4wxeq7osqfuu 490 35 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 490 36 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 491 1 Then then RB work_ln56cwsp7ffppl4wxeq7osqfuu 491 2 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 491 3 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 491 4 result result NN work_ln56cwsp7ffppl4wxeq7osqfuu 491 5 follows follow VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 491 6 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 491 7 � � : work_ln56cwsp7ffppl4wxeq7osqfuu 491 8 Proof Proof NNP work_ln56cwsp7ffppl4wxeq7osqfuu 491 9 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 491 10 Proposition Proposition NNP work_ln56cwsp7ffppl4wxeq7osqfuu 491 11 4.4 4.4 CD work_ln56cwsp7ffppl4wxeq7osqfuu 491 12 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 492 1 We -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 492 2 start start VBP work_ln56cwsp7ffppl4wxeq7osqfuu 492 3 by by IN work_ln56cwsp7ffppl4wxeq7osqfuu 492 4 proving proving NN work_ln56cwsp7ffppl4wxeq7osqfuu 492 5 point point NN work_ln56cwsp7ffppl4wxeq7osqfuu 492 6 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 492 7 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 492 8 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 492 9 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 493 1 For for IN work_ln56cwsp7ffppl4wxeq7osqfuu 493 2 every every DT work_ln56cwsp7ffppl4wxeq7osqfuu 493 3 individual individual NN work_ln56cwsp7ffppl4wxeq7osqfuu 493 4 i i PRP work_ln56cwsp7ffppl4wxeq7osqfuu 493 5 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 493 6 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 493 7 distribution distribution NN work_ln56cwsp7ffppl4wxeq7osqfuu 493 8 functions function NNS work_ln56cwsp7ffppl4wxeq7osqfuu 493 9 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 493 10 her -PRON- PRP$ work_ln56cwsp7ffppl4wxeq7osqfuu 493 11 best good JJS work_ln56cwsp7ffppl4wxeq7osqfuu 493 12 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 493 13 medium medium JJ work_ln56cwsp7ffppl4wxeq7osqfuu 493 14 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 493 15 worst bad JJS work_ln56cwsp7ffppl4wxeq7osqfuu 493 16 random random JJ work_ln56cwsp7ffppl4wxeq7osqfuu 493 17 variables variable NNS work_ln56cwsp7ffppl4wxeq7osqfuu 493 18 are be VBP work_ln56cwsp7ffppl4wxeq7osqfuu 493 19 F F NNP work_ln56cwsp7ffppl4wxeq7osqfuu 493 20 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 493 21 3)(t 3)(t CD work_ln56cwsp7ffppl4wxeq7osqfuu 493 22 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 493 23 = = NFP work_ln56cwsp7ffppl4wxeq7osqfuu 493 24 t3 t3 UH work_ln56cwsp7ffppl4wxeq7osqfuu 493 25 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 493 26 F F NNP work_ln56cwsp7ffppl4wxeq7osqfuu 493 27 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 493 28 2)(t 2)(t CD work_ln56cwsp7ffppl4wxeq7osqfuu 493 29 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 493 30 = = SYM work_ln56cwsp7ffppl4wxeq7osqfuu 493 31 t3 t3 NN work_ln56cwsp7ffppl4wxeq7osqfuu 493 32 + + SYM work_ln56cwsp7ffppl4wxeq7osqfuu 493 33 3t2(1 3t2(1 NN work_ln56cwsp7ffppl4wxeq7osqfuu 493 34 − − NNP work_ln56cwsp7ffppl4wxeq7osqfuu 493 35 t t NNP work_ln56cwsp7ffppl4wxeq7osqfuu 493 36 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 493 37 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 493 38 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 493 39 F F NNP work_ln56cwsp7ffppl4wxeq7osqfuu 493 40 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 493 41 1)(t 1)(t CD work_ln56cwsp7ffppl4wxeq7osqfuu 493 42 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 493 43 = = SYM work_ln56cwsp7ffppl4wxeq7osqfuu 493 44 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 493 45 − − NNP work_ln56cwsp7ffppl4wxeq7osqfuu 493 46 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 493 47 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 493 48 − − NNP work_ln56cwsp7ffppl4wxeq7osqfuu 493 49 t)3 t)3 VBG work_ln56cwsp7ffppl4wxeq7osqfuu 493 50 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 493 51 respectively respectively RB work_ln56cwsp7ffppl4wxeq7osqfuu 493 52 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 494 1 The the DT work_ln56cwsp7ffppl4wxeq7osqfuu 494 2 distribution distribution NN work_ln56cwsp7ffppl4wxeq7osqfuu 494 3 function function NN work_ln56cwsp7ffppl4wxeq7osqfuu 494 4 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 494 5 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 494 6 maximum maximum NN work_ln56cwsp7ffppl4wxeq7osqfuu 494 7 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 494 8 l(3 l(3 NNP work_ln56cwsp7ffppl4wxeq7osqfuu 494 9 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 494 10 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 494 11 l(2 l(2 NNP work_ln56cwsp7ffppl4wxeq7osqfuu 494 12 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 494 13 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 494 14 n−l(3)−l(2 n−l(3)−l(2 CD work_ln56cwsp7ffppl4wxeq7osqfuu 494 15 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 494 16 = = NFP work_ln56cwsp7ffppl4wxeq7osqfuu 494 17 l(1 l(1 NFP work_ln56cwsp7ffppl4wxeq7osqfuu 494 18 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 494 19 best good JJS work_ln56cwsp7ffppl4wxeq7osqfuu 494 20 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 494 21 medium medium JJ work_ln56cwsp7ffppl4wxeq7osqfuu 494 22 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 494 23 worst bad JJS work_ln56cwsp7ffppl4wxeq7osqfuu 494 24 random random JJ work_ln56cwsp7ffppl4wxeq7osqfuu 494 25 variables variable NNS work_ln56cwsp7ffppl4wxeq7osqfuu 494 26 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 494 27 F(t F(t NNP work_ln56cwsp7ffppl4wxeq7osqfuu 494 28 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 494 29 = = NFP work_ln56cwsp7ffppl4wxeq7osqfuu 494 30 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 494 31 t3)l t3)l FW work_ln56cwsp7ffppl4wxeq7osqfuu 494 32 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 494 33 3 3 CD work_ln56cwsp7ffppl4wxeq7osqfuu 494 34 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 494 35 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 494 36 t3 t3 NN work_ln56cwsp7ffppl4wxeq7osqfuu 494 37 + + SYM work_ln56cwsp7ffppl4wxeq7osqfuu 494 38 3t2(1 3t2(1 NN work_ln56cwsp7ffppl4wxeq7osqfuu 494 39 − − NNP work_ln56cwsp7ffppl4wxeq7osqfuu 494 40 t))l t))l NN work_ln56cwsp7ffppl4wxeq7osqfuu 494 41 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 494 42 2 2 CD work_ln56cwsp7ffppl4wxeq7osqfuu 494 43 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 494 44 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 494 45 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 494 46 − − NNP work_ln56cwsp7ffppl4wxeq7osqfuu 494 47 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 494 48 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 494 49 − − NNP work_ln56cwsp7ffppl4wxeq7osqfuu 494 50 t)3)l t)3)l NN work_ln56cwsp7ffppl4wxeq7osqfuu 494 51 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 494 52 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 494 53 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 494 54 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 495 1 The the DT work_ln56cwsp7ffppl4wxeq7osqfuu 495 2 polynomial polynomial JJ work_ln56cwsp7ffppl4wxeq7osqfuu 495 3 decomposition decomposition NN work_ln56cwsp7ffppl4wxeq7osqfuu 495 4 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 495 5 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 495 6 latter latter JJ work_ln56cwsp7ffppl4wxeq7osqfuu 495 7 expression expression NN work_ln56cwsp7ffppl4wxeq7osqfuu 495 8 gives give VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 495 9 F(t F(t NNP work_ln56cwsp7ffppl4wxeq7osqfuu 495 10 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 495 11 = = NFP work_ln56cwsp7ffppl4wxeq7osqfuu 495 12 l(2)∑ l(2)∑ VBN work_ln56cwsp7ffppl4wxeq7osqfuu 495 13 a=0 a=0 HYPH work_ln56cwsp7ffppl4wxeq7osqfuu 495 14 l(1)∑ l(1)∑ NNP work_ln56cwsp7ffppl4wxeq7osqfuu 495 15 b=0 b=0 IN work_ln56cwsp7ffppl4wxeq7osqfuu 495 16 3b∑ 3b∑ NNP work_ln56cwsp7ffppl4wxeq7osqfuu 495 17 c=0 c=0 NN work_ln56cwsp7ffppl4wxeq7osqfuu 495 18 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 495 19 l(2 l(2 NNP work_ln56cwsp7ffppl4wxeq7osqfuu 495 20 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 495 21 a a LS work_ln56cwsp7ffppl4wxeq7osqfuu 495 22 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 495 23 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 495 24 l(1 l(1 NNP work_ln56cwsp7ffppl4wxeq7osqfuu 495 25 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 495 26 b b LS work_ln56cwsp7ffppl4wxeq7osqfuu 495 27 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 495 28 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 495 29 3b 3b NNP work_ln56cwsp7ffppl4wxeq7osqfuu 495 30 c c NN work_ln56cwsp7ffppl4wxeq7osqfuu 495 31 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 495 32 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 495 33 −1)a+b+c3l −1)a+b+c3l NN work_ln56cwsp7ffppl4wxeq7osqfuu 495 34 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 495 35 2)−a2at3l 2)−a2at3l CD work_ln56cwsp7ffppl4wxeq7osqfuu 495 36 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 495 37 3)+2l(2)+a+c 3)+2l(2)+a+c CD work_ln56cwsp7ffppl4wxeq7osqfuu 495 38 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 496 1 The the DT work_ln56cwsp7ffppl4wxeq7osqfuu 496 2 density density NN work_ln56cwsp7ffppl4wxeq7osqfuu 496 3 function function NN work_ln56cwsp7ffppl4wxeq7osqfuu 496 4 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 496 5 f(t f(t NN work_ln56cwsp7ffppl4wxeq7osqfuu 496 6 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 496 7 = = NFP work_ln56cwsp7ffppl4wxeq7osqfuu 496 8 l(2)∑ l(2)∑ VBN work_ln56cwsp7ffppl4wxeq7osqfuu 496 9 a=0 a=0 HYPH work_ln56cwsp7ffppl4wxeq7osqfuu 496 10 l(1)∑ l(1)∑ NNP work_ln56cwsp7ffppl4wxeq7osqfuu 496 11 b=0 b=0 IN work_ln56cwsp7ffppl4wxeq7osqfuu 496 12 3b∑ 3b∑ NNP work_ln56cwsp7ffppl4wxeq7osqfuu 496 13 c=0 c=0 NN work_ln56cwsp7ffppl4wxeq7osqfuu 496 14 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 496 15 l(2 l(2 NNP work_ln56cwsp7ffppl4wxeq7osqfuu 496 16 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 496 17 a a LS work_ln56cwsp7ffppl4wxeq7osqfuu 496 18 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 496 19 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 496 20 l(1 l(1 NNP work_ln56cwsp7ffppl4wxeq7osqfuu 496 21 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 496 22 b b LS work_ln56cwsp7ffppl4wxeq7osqfuu 496 23 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 496 24 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 496 25 3b 3b NNP work_ln56cwsp7ffppl4wxeq7osqfuu 496 26 c c NN work_ln56cwsp7ffppl4wxeq7osqfuu 496 27 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 496 28 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 496 29 −1)a+b+c3l −1)a+b+c3l NNP work_ln56cwsp7ffppl4wxeq7osqfuu 496 30 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 496 31 2)−a2a(3l(3)+2l(2)+a+c)t3l 2)−a2a(3l(3)+2l(2)+a+c)t3l CD work_ln56cwsp7ffppl4wxeq7osqfuu 496 32 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 496 33 3)+2l(2)+a+c−1 3)+2l(2)+a+c−1 NNP work_ln56cwsp7ffppl4wxeq7osqfuu 496 34 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 497 1 Finally finally RB work_ln56cwsp7ffppl4wxeq7osqfuu 497 2 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 497 3 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 497 4 expected expect VBN work_ln56cwsp7ffppl4wxeq7osqfuu 497 5 value value NN work_ln56cwsp7ffppl4wxeq7osqfuu 497 6 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 497 7 E[Ul(n)|M e[ul(n)|m FW work_ln56cwsp7ffppl4wxeq7osqfuu 497 8 ] ] -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 497 9 = = SYM work_ln56cwsp7ffppl4wxeq7osqfuu 497 10 l(2)∑ l(2)∑ NNP work_ln56cwsp7ffppl4wxeq7osqfuu 497 11 a=0 a=0 HYPH work_ln56cwsp7ffppl4wxeq7osqfuu 497 12 l(1)∑ l(1)∑ NNP work_ln56cwsp7ffppl4wxeq7osqfuu 497 13 b=0 b=0 IN work_ln56cwsp7ffppl4wxeq7osqfuu 497 14 3b∑ 3b∑ NNP work_ln56cwsp7ffppl4wxeq7osqfuu 497 15 c=0 c=0 NN work_ln56cwsp7ffppl4wxeq7osqfuu 497 16 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 497 17 l(2 l(2 NNP work_ln56cwsp7ffppl4wxeq7osqfuu 497 18 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 497 19 a a LS work_ln56cwsp7ffppl4wxeq7osqfuu 497 20 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 497 21 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 497 22 l(1 l(1 NNP work_ln56cwsp7ffppl4wxeq7osqfuu 497 23 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 497 24 b b LS work_ln56cwsp7ffppl4wxeq7osqfuu 497 25 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 497 26 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 497 27 3b 3b NNP work_ln56cwsp7ffppl4wxeq7osqfuu 497 28 c c NN work_ln56cwsp7ffppl4wxeq7osqfuu 497 29 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 497 30 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 497 31 −1)a+b+c3l −1)a+b+c3l NN work_ln56cwsp7ffppl4wxeq7osqfuu 497 32 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 497 33 2)−a2a 2)−a2a CD work_ln56cwsp7ffppl4wxeq7osqfuu 497 34 3l(3 3l(3 CD work_ln56cwsp7ffppl4wxeq7osqfuu 497 35 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 497 36 + + SYM work_ln56cwsp7ffppl4wxeq7osqfuu 497 37 2l(2 2l(2 CD work_ln56cwsp7ffppl4wxeq7osqfuu 497 38 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 497 39 + + CC work_ln56cwsp7ffppl4wxeq7osqfuu 497 40 a a NN work_ln56cwsp7ffppl4wxeq7osqfuu 497 41 + + SYM work_ln56cwsp7ffppl4wxeq7osqfuu 497 42 c c NN work_ln56cwsp7ffppl4wxeq7osqfuu 497 43 3l(3 3l(3 CD work_ln56cwsp7ffppl4wxeq7osqfuu 497 44 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 497 45 + + SYM work_ln56cwsp7ffppl4wxeq7osqfuu 497 46 2l(2 2l(2 CD work_ln56cwsp7ffppl4wxeq7osqfuu 497 47 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 497 48 + + CC work_ln56cwsp7ffppl4wxeq7osqfuu 497 49 a a NN work_ln56cwsp7ffppl4wxeq7osqfuu 497 50 + + SYM work_ln56cwsp7ffppl4wxeq7osqfuu 497 51 c c NN work_ln56cwsp7ffppl4wxeq7osqfuu 497 52 + + SYM work_ln56cwsp7ffppl4wxeq7osqfuu 497 53 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 497 54 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 498 1 We -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 498 2 start start VBP work_ln56cwsp7ffppl4wxeq7osqfuu 498 3 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 498 4 proof proof NN work_ln56cwsp7ffppl4wxeq7osqfuu 498 5 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 498 6 part part NN work_ln56cwsp7ffppl4wxeq7osqfuu 498 7 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 498 8 2 2 CD work_ln56cwsp7ffppl4wxeq7osqfuu 498 9 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 498 10 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 498 11 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 498 12 theorem theorem NN work_ln56cwsp7ffppl4wxeq7osqfuu 498 13 by by IN work_ln56cwsp7ffppl4wxeq7osqfuu 498 14 stating state VBG work_ln56cwsp7ffppl4wxeq7osqfuu 498 15 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 498 16 following follow VBG work_ln56cwsp7ffppl4wxeq7osqfuu 498 17 lemma lemma NN work_ln56cwsp7ffppl4wxeq7osqfuu 498 18 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 499 1 Lemma Lemma NNP work_ln56cwsp7ffppl4wxeq7osqfuu 499 2 A.1 A.1 NNP work_ln56cwsp7ffppl4wxeq7osqfuu 499 3 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 500 1 Let let VB work_ln56cwsp7ffppl4wxeq7osqfuu 500 2 { { -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 500 3 xa}a∈T∪{b xa}a∈T∪{b NNP work_ln56cwsp7ffppl4wxeq7osqfuu 500 4 } } -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 500 5 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 500 6 b b LS work_ln56cwsp7ffppl4wxeq7osqfuu 500 7 /∈ /∈ . work_ln56cwsp7ffppl4wxeq7osqfuu 500 8 T t NN work_ln56cwsp7ffppl4wxeq7osqfuu 500 9 6= 6= CD work_ln56cwsp7ffppl4wxeq7osqfuu 500 10 ∅ ∅ NNP work_ln56cwsp7ffppl4wxeq7osqfuu 500 11 be be VB work_ln56cwsp7ffppl4wxeq7osqfuu 500 12 a a DT work_ln56cwsp7ffppl4wxeq7osqfuu 500 13 set set NN work_ln56cwsp7ffppl4wxeq7osqfuu 500 14 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 500 15 independent independent JJ work_ln56cwsp7ffppl4wxeq7osqfuu 500 16 random random JJ work_ln56cwsp7ffppl4wxeq7osqfuu 500 17 variables variable NNS work_ln56cwsp7ffppl4wxeq7osqfuu 500 18 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 501 1 Then then RB work_ln56cwsp7ffppl4wxeq7osqfuu 501 2 E[max{xa}a∈T∪{b}]−E[max{xa}a∈T E[max{xa}a∈T∪{b}]−E[max{xa}a∈T NNP work_ln56cwsp7ffppl4wxeq7osqfuu 501 3 ] ] -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 501 4 ≤ ≤ JJ work_ln56cwsp7ffppl4wxeq7osqfuu 501 5 E[max{xa}a∈S∪{b}]−E[max{xa}a∈S E[max{xa}a∈S∪{b}]−E[max{xa}a∈S NNP work_ln56cwsp7ffppl4wxeq7osqfuu 501 6 ] ] -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 501 7 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 501 8 all all DT work_ln56cwsp7ffppl4wxeq7osqfuu 501 9 S s NN work_ln56cwsp7ffppl4wxeq7osqfuu 501 10 ⊆ ⊆ : work_ln56cwsp7ffppl4wxeq7osqfuu 501 11 T t NN work_ln56cwsp7ffppl4wxeq7osqfuu 501 12 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 502 1 21 21 CD work_ln56cwsp7ffppl4wxeq7osqfuu 502 2 The the DT work_ln56cwsp7ffppl4wxeq7osqfuu 502 3 lemma lemma NN work_ln56cwsp7ffppl4wxeq7osqfuu 502 4 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 502 5 straightforward straightforward JJ work_ln56cwsp7ffppl4wxeq7osqfuu 502 6 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 502 7 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 502 8 hence hence RB work_ln56cwsp7ffppl4wxeq7osqfuu 502 9 we -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 502 10 omit omit VBP work_ln56cwsp7ffppl4wxeq7osqfuu 502 11 its -PRON- PRP$ work_ln56cwsp7ffppl4wxeq7osqfuu 502 12 proof proof NN work_ln56cwsp7ffppl4wxeq7osqfuu 502 13 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 503 1 Since since IN work_ln56cwsp7ffppl4wxeq7osqfuu 503 2 p p NN work_ln56cwsp7ffppl4wxeq7osqfuu 503 3 ∈ ∈ NNP work_ln56cwsp7ffppl4wxeq7osqfuu 503 4 SPl(M spl(m NN work_ln56cwsp7ffppl4wxeq7osqfuu 503 5 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 503 6 it -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 503 7 must must MD work_ln56cwsp7ffppl4wxeq7osqfuu 503 8 be be VB work_ln56cwsp7ffppl4wxeq7osqfuu 503 9 that that IN work_ln56cwsp7ffppl4wxeq7osqfuu 503 10 p(3 p(3 NN work_ln56cwsp7ffppl4wxeq7osqfuu 503 11 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 503 12 ≥ ≥ UH work_ln56cwsp7ffppl4wxeq7osqfuu 503 13 h(3 h(3 NN work_ln56cwsp7ffppl4wxeq7osqfuu 503 14 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 503 15 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 504 1 Let let VB work_ln56cwsp7ffppl4wxeq7osqfuu 504 2 h(3 h(3 NNP work_ln56cwsp7ffppl4wxeq7osqfuu 504 3 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 504 4 < < XX work_ln56cwsp7ffppl4wxeq7osqfuu 504 5 p(3 p(3 NFP work_ln56cwsp7ffppl4wxeq7osqfuu 504 6 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 504 7 − − NNP work_ln56cwsp7ffppl4wxeq7osqfuu 504 8 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 504 9 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 505 1 Vector Vector NNP work_ln56cwsp7ffppl4wxeq7osqfuu 505 2 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 505 3 x x NNP work_ln56cwsp7ffppl4wxeq7osqfuu 505 4 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 505 5 y y NNP work_ln56cwsp7ffppl4wxeq7osqfuu 505 6 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 505 7 z z NNP work_ln56cwsp7ffppl4wxeq7osqfuu 505 8 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 505 9 represents represent VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 505 10 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 505 11 case case NN work_ln56cwsp7ffppl4wxeq7osqfuu 505 12 where where WRB work_ln56cwsp7ffppl4wxeq7osqfuu 505 13 x x NN work_ln56cwsp7ffppl4wxeq7osqfuu 505 14 = = SYM work_ln56cwsp7ffppl4wxeq7osqfuu 505 15 p(3 p(3 NN work_ln56cwsp7ffppl4wxeq7osqfuu 505 16 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 505 17 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 505 18 y y NNP work_ln56cwsp7ffppl4wxeq7osqfuu 505 19 = = SYM work_ln56cwsp7ffppl4wxeq7osqfuu 505 20 p(2 p(2 NNP work_ln56cwsp7ffppl4wxeq7osqfuu 505 21 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 505 22 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 505 23 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 505 24 z z NN work_ln56cwsp7ffppl4wxeq7osqfuu 505 25 = = SYM work_ln56cwsp7ffppl4wxeq7osqfuu 505 26 p(1 p(1 FW work_ln56cwsp7ffppl4wxeq7osqfuu 505 27 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 505 28 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 506 1 Then then RB work_ln56cwsp7ffppl4wxeq7osqfuu 506 2 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 506 3 it -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 506 4 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 506 5 immediate immediate JJ work_ln56cwsp7ffppl4wxeq7osqfuu 506 6 that that IN work_ln56cwsp7ffppl4wxeq7osqfuu 506 7 E[Up e[up NN work_ln56cwsp7ffppl4wxeq7osqfuu 506 8 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 506 9 n n NN work_ln56cwsp7ffppl4wxeq7osqfuu 506 10 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 506 11 | | NNP work_ln56cwsp7ffppl4wxeq7osqfuu 506 12 M M NNP work_ln56cwsp7ffppl4wxeq7osqfuu 506 13 ] ] -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 506 14 ≥ ≥ NNP work_ln56cwsp7ffppl4wxeq7osqfuu 506 15 E[(p(3 e[(p(3 NN work_ln56cwsp7ffppl4wxeq7osqfuu 506 16 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 506 17 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 506 18 0 0 CD work_ln56cwsp7ffppl4wxeq7osqfuu 506 19 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 506 20 0)].9 0)].9 CD work_ln56cwsp7ffppl4wxeq7osqfuu 506 21 Since since IN work_ln56cwsp7ffppl4wxeq7osqfuu 506 22 h(3 h(3 NNP work_ln56cwsp7ffppl4wxeq7osqfuu 506 23 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 506 24 < < XX work_ln56cwsp7ffppl4wxeq7osqfuu 506 25 p(3)−1 p(3)−1 NNP work_ln56cwsp7ffppl4wxeq7osqfuu 506 26 it -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 506 27 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 506 28 immediate immediate JJ work_ln56cwsp7ffppl4wxeq7osqfuu 506 29 that that IN work_ln56cwsp7ffppl4wxeq7osqfuu 506 30 E[Uh(n E[Uh(n NNP work_ln56cwsp7ffppl4wxeq7osqfuu 506 31 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 506 32 | | NNP work_ln56cwsp7ffppl4wxeq7osqfuu 506 33 M M NNP work_ln56cwsp7ffppl4wxeq7osqfuu 506 34 ] ] -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 506 35 ≤ ≤ NNP work_ln56cwsp7ffppl4wxeq7osqfuu 506 36 E[(p E[(p NNP work_ln56cwsp7ffppl4wxeq7osqfuu 506 37 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 506 38 3)−2,n− 3)−2,n− CD work_ln56cwsp7ffppl4wxeq7osqfuu 506 39 p(3 p(3 NNP work_ln56cwsp7ffppl4wxeq7osqfuu 506 40 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 506 41 + + CC work_ln56cwsp7ffppl4wxeq7osqfuu 506 42 2 2 CD work_ln56cwsp7ffppl4wxeq7osqfuu 506 43 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 506 44 0 0 CD work_ln56cwsp7ffppl4wxeq7osqfuu 506 45 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 506 46 ] ] -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 506 47 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 507 1 By by IN work_ln56cwsp7ffppl4wxeq7osqfuu 507 2 Lemma Lemma NNP work_ln56cwsp7ffppl4wxeq7osqfuu 507 3 A.1 A.1 NNP work_ln56cwsp7ffppl4wxeq7osqfuu 507 4 E[(p(3 E[(p(3 NNP work_ln56cwsp7ffppl4wxeq7osqfuu 507 5 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 507 6 − − NNP work_ln56cwsp7ffppl4wxeq7osqfuu 507 7 2,n− 2,n− CD work_ln56cwsp7ffppl4wxeq7osqfuu 507 8 p(3 p(3 NNP work_ln56cwsp7ffppl4wxeq7osqfuu 507 9 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 507 10 + + CC work_ln56cwsp7ffppl4wxeq7osqfuu 507 11 2 2 CD work_ln56cwsp7ffppl4wxeq7osqfuu 507 12 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 507 13 0 0 CD work_ln56cwsp7ffppl4wxeq7osqfuu 507 14 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 507 15 ] ] -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 507 16 ≤ ≤ NNP work_ln56cwsp7ffppl4wxeq7osqfuu 507 17 E[(p(3 E[(p(3 NNP work_ln56cwsp7ffppl4wxeq7osqfuu 507 18 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 507 19 − − NNP work_ln56cwsp7ffppl4wxeq7osqfuu 507 20 2 2 CD work_ln56cwsp7ffppl4wxeq7osqfuu 507 21 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 507 22 0 0 CD work_ln56cwsp7ffppl4wxeq7osqfuu 507 23 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 507 24 0 0 CD work_ln56cwsp7ffppl4wxeq7osqfuu 507 25 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 507 26 ] ] -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 507 27 + + CC work_ln56cwsp7ffppl4wxeq7osqfuu 507 28 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 507 29 n− n− NNP work_ln56cwsp7ffppl4wxeq7osqfuu 507 30 p(3 p(3 NFP work_ln56cwsp7ffppl4wxeq7osqfuu 507 31 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 507 32 + + CC work_ln56cwsp7ffppl4wxeq7osqfuu 507 33 2)∆ 2)∆ CD work_ln56cwsp7ffppl4wxeq7osqfuu 507 34 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 507 35 2 2 CD work_ln56cwsp7ffppl4wxeq7osqfuu 507 36 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 507 37 p(3)−2 p(3)−2 CD work_ln56cwsp7ffppl4wxeq7osqfuu 507 38 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 508 1 We -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 508 2 now now RB work_ln56cwsp7ffppl4wxeq7osqfuu 508 3 prove prove VBP work_ln56cwsp7ffppl4wxeq7osqfuu 508 4 that that DT work_ln56cwsp7ffppl4wxeq7osqfuu 508 5 E[(p E[(p NNP work_ln56cwsp7ffppl4wxeq7osqfuu 508 6 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 508 7 3 3 CD work_ln56cwsp7ffppl4wxeq7osqfuu 508 8 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 508 9 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 508 10 0 0 CD work_ln56cwsp7ffppl4wxeq7osqfuu 508 11 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 508 12 0 0 CD work_ln56cwsp7ffppl4wxeq7osqfuu 508 13 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 508 14 ] ] -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 508 15 > > XX work_ln56cwsp7ffppl4wxeq7osqfuu 508 16 E[(p(3 e[(p(3 NN work_ln56cwsp7ffppl4wxeq7osqfuu 508 17 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 508 18 − − NNP work_ln56cwsp7ffppl4wxeq7osqfuu 508 19 2,n− 2,n− CD work_ln56cwsp7ffppl4wxeq7osqfuu 508 20 p(3 p(3 NNP work_ln56cwsp7ffppl4wxeq7osqfuu 508 21 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 508 22 + + CC work_ln56cwsp7ffppl4wxeq7osqfuu 508 23 2 2 CD work_ln56cwsp7ffppl4wxeq7osqfuu 508 24 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 508 25 0 0 CD work_ln56cwsp7ffppl4wxeq7osqfuu 508 26 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 508 27 ] ] -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 508 28 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 509 1 By by IN work_ln56cwsp7ffppl4wxeq7osqfuu 509 2 showing show VBG work_ln56cwsp7ffppl4wxeq7osqfuu 509 3 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 509 4 latter latter JJ work_ln56cwsp7ffppl4wxeq7osqfuu 509 5 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 509 6 we -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 509 7 are be VBP work_ln56cwsp7ffppl4wxeq7osqfuu 509 8 excluding exclude VBG work_ln56cwsp7ffppl4wxeq7osqfuu 509 9 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 509 10 possibility possibility NN work_ln56cwsp7ffppl4wxeq7osqfuu 509 11 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 509 12 h h NN work_ln56cwsp7ffppl4wxeq7osqfuu 509 13 being be VBG work_ln56cwsp7ffppl4wxeq7osqfuu 509 14 an an DT work_ln56cwsp7ffppl4wxeq7osqfuu 509 15 optimal optimal JJ work_ln56cwsp7ffppl4wxeq7osqfuu 509 16 alternative alternative NN work_ln56cwsp7ffppl4wxeq7osqfuu 509 17 whenever whenever WRB work_ln56cwsp7ffppl4wxeq7osqfuu 509 18 h(3 h(3 NN work_ln56cwsp7ffppl4wxeq7osqfuu 509 19 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 509 20 < < XX work_ln56cwsp7ffppl4wxeq7osqfuu 509 21 p(3 p(3 NFP work_ln56cwsp7ffppl4wxeq7osqfuu 509 22 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 509 23 − − NNP work_ln56cwsp7ffppl4wxeq7osqfuu 509 24 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 509 25 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 510 1 Let let VB work_ln56cwsp7ffppl4wxeq7osqfuu 510 2 us -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 510 3 assume assume VB work_ln56cwsp7ffppl4wxeq7osqfuu 510 4 by by IN work_ln56cwsp7ffppl4wxeq7osqfuu 510 5 way way NN work_ln56cwsp7ffppl4wxeq7osqfuu 510 6 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 510 7 contradiction contradiction NN work_ln56cwsp7ffppl4wxeq7osqfuu 510 8 that that IN work_ln56cwsp7ffppl4wxeq7osqfuu 510 9 E[(p(3 E[(p(3 NNP work_ln56cwsp7ffppl4wxeq7osqfuu 510 10 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 510 11 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 510 12 0 0 CD work_ln56cwsp7ffppl4wxeq7osqfuu 510 13 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 510 14 0 0 CD work_ln56cwsp7ffppl4wxeq7osqfuu 510 15 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 510 16 ] ] -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 510 17 ≤ ≤ NNP work_ln56cwsp7ffppl4wxeq7osqfuu 510 18 E[(p(3 E[(p(3 NNP work_ln56cwsp7ffppl4wxeq7osqfuu 510 19 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 510 20 − − NNP work_ln56cwsp7ffppl4wxeq7osqfuu 510 21 2,n− 2,n− CD work_ln56cwsp7ffppl4wxeq7osqfuu 510 22 p(3 p(3 NNP work_ln56cwsp7ffppl4wxeq7osqfuu 510 23 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 510 24 + + CC work_ln56cwsp7ffppl4wxeq7osqfuu 510 25 2 2 CD work_ln56cwsp7ffppl4wxeq7osqfuu 510 26 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 510 27 0 0 CD work_ln56cwsp7ffppl4wxeq7osqfuu 510 28 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 510 29 ] ] -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 510 30 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 511 1 Note note VB work_ln56cwsp7ffppl4wxeq7osqfuu 511 2 E[(p(3 e[(p(3 NN work_ln56cwsp7ffppl4wxeq7osqfuu 511 3 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 511 4 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 511 5 0 0 CD work_ln56cwsp7ffppl4wxeq7osqfuu 511 6 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 511 7 0 0 CD work_ln56cwsp7ffppl4wxeq7osqfuu 511 8 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 511 9 ] ] -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 511 10 = = NFP work_ln56cwsp7ffppl4wxeq7osqfuu 511 11 E[(p(3)−2 e[(p(3)−2 XX work_ln56cwsp7ffppl4wxeq7osqfuu 511 12 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 511 13 0 0 CD work_ln56cwsp7ffppl4wxeq7osqfuu 511 14 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 511 15 0 0 CD work_ln56cwsp7ffppl4wxeq7osqfuu 511 16 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 511 17 ] ] -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 511 18 + + NNP work_ln56cwsp7ffppl4wxeq7osqfuu 511 19 ∆(3 ∆(3 NNP work_ln56cwsp7ffppl4wxeq7osqfuu 511 20 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 511 21 p(3)−2 p(3)−2 NN work_ln56cwsp7ffppl4wxeq7osqfuu 511 22 + + SYM work_ln56cwsp7ffppl4wxeq7osqfuu 511 23 ∆ ∆ NN work_ln56cwsp7ffppl4wxeq7osqfuu 511 24 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 511 25 3 3 CD work_ln56cwsp7ffppl4wxeq7osqfuu 511 26 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 511 27 p(3)−1 p(3)−1 NNP work_ln56cwsp7ffppl4wxeq7osqfuu 511 28 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 512 1 Then then RB work_ln56cwsp7ffppl4wxeq7osqfuu 512 2 it -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 512 3 must must MD work_ln56cwsp7ffppl4wxeq7osqfuu 512 4 be be VB work_ln56cwsp7ffppl4wxeq7osqfuu 512 5 that that IN work_ln56cwsp7ffppl4wxeq7osqfuu 512 6 ∆ ∆ NN work_ln56cwsp7ffppl4wxeq7osqfuu 512 7 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 512 8 3 3 CD work_ln56cwsp7ffppl4wxeq7osqfuu 512 9 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 512 10 p(3)−2 p(3)−2 NN work_ln56cwsp7ffppl4wxeq7osqfuu 512 11 + + CD work_ln56cwsp7ffppl4wxeq7osqfuu 512 12 ∆ ∆ NN work_ln56cwsp7ffppl4wxeq7osqfuu 512 13 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 512 14 3 3 CD work_ln56cwsp7ffppl4wxeq7osqfuu 512 15 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 512 16 p(3)−1 p(3)−1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 512 17 ≤ ≤ NN work_ln56cwsp7ffppl4wxeq7osqfuu 512 18 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 512 19 n− n− NNP work_ln56cwsp7ffppl4wxeq7osqfuu 512 20 p p NN work_ln56cwsp7ffppl4wxeq7osqfuu 512 21 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 512 22 3 3 CD work_ln56cwsp7ffppl4wxeq7osqfuu 512 23 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 512 24 + + CC work_ln56cwsp7ffppl4wxeq7osqfuu 512 25 2)∆ 2)∆ CD work_ln56cwsp7ffppl4wxeq7osqfuu 512 26 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 512 27 2 2 CD work_ln56cwsp7ffppl4wxeq7osqfuu 512 28 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 512 29 p(3)−2 p(3)−2 CD work_ln56cwsp7ffppl4wxeq7osqfuu 512 30 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 513 1 The the DT work_ln56cwsp7ffppl4wxeq7osqfuu 513 2 latter latter JJ work_ln56cwsp7ffppl4wxeq7osqfuu 513 3 leads lead VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 513 4 to to IN work_ln56cwsp7ffppl4wxeq7osqfuu 513 5 n n CC work_ln56cwsp7ffppl4wxeq7osqfuu 513 6 ≥ ≥ JJ work_ln56cwsp7ffppl4wxeq7osqfuu 513 7 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 513 8 3p(3)−3)(3p(3)−2 3p(3)−3)(3p(3)−2 NN work_ln56cwsp7ffppl4wxeq7osqfuu 513 9 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 513 10 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 513 11 3p(3)+1 3p(3)+1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 513 12 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 513 13 + + SYM work_ln56cwsp7ffppl4wxeq7osqfuu 513 14 p(3 p(3 NN work_ln56cwsp7ffppl4wxeq7osqfuu 513 15 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 513 16 − − NNP work_ln56cwsp7ffppl4wxeq7osqfuu 513 17 2 2 CD work_ln56cwsp7ffppl4wxeq7osqfuu 513 18 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 514 1 Now now RB work_ln56cwsp7ffppl4wxeq7osqfuu 514 2 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 514 3 since since IN work_ln56cwsp7ffppl4wxeq7osqfuu 514 4 p p NN work_ln56cwsp7ffppl4wxeq7osqfuu 514 5 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 514 6 a a DT work_ln56cwsp7ffppl4wxeq7osqfuu 514 7 plurality plurality NN work_ln56cwsp7ffppl4wxeq7osqfuu 514 8 alternative alternative NN work_ln56cwsp7ffppl4wxeq7osqfuu 514 9 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 514 10 n n IN work_ln56cwsp7ffppl4wxeq7osqfuu 514 11 ≤ ≤ JJ work_ln56cwsp7ffppl4wxeq7osqfuu 514 12 3p(3 3p(3 CD work_ln56cwsp7ffppl4wxeq7osqfuu 514 13 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 514 14 − − NNP work_ln56cwsp7ffppl4wxeq7osqfuu 514 15 2 2 CD work_ln56cwsp7ffppl4wxeq7osqfuu 514 16 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 515 1 Then then RB work_ln56cwsp7ffppl4wxeq7osqfuu 515 2 it -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 515 3 must must MD work_ln56cwsp7ffppl4wxeq7osqfuu 515 4 be be VB work_ln56cwsp7ffppl4wxeq7osqfuu 515 5 that that IN work_ln56cwsp7ffppl4wxeq7osqfuu 515 6 3p(3)−2 3p(3)−2 CD work_ln56cwsp7ffppl4wxeq7osqfuu 515 7 ≥ ≥ NN work_ln56cwsp7ffppl4wxeq7osqfuu 515 8 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 515 9 3p 3p NNP work_ln56cwsp7ffppl4wxeq7osqfuu 515 10 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 515 11 3)−3)(3p(3)−2 3)−3)(3p(3)−2 CD work_ln56cwsp7ffppl4wxeq7osqfuu 515 12 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 515 13 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 515 14 3p(3)+1 3p(3)+1 NNP work_ln56cwsp7ffppl4wxeq7osqfuu 515 15 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 515 16 + + SYM work_ln56cwsp7ffppl4wxeq7osqfuu 515 17 p(3)−2 p(3)−2 NN work_ln56cwsp7ffppl4wxeq7osqfuu 515 18 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 516 1 This this DT work_ln56cwsp7ffppl4wxeq7osqfuu 516 2 can can MD work_ln56cwsp7ffppl4wxeq7osqfuu 516 3 only only RB work_ln56cwsp7ffppl4wxeq7osqfuu 516 4 be be VB work_ln56cwsp7ffppl4wxeq7osqfuu 516 5 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 516 6 case case NN work_ln56cwsp7ffppl4wxeq7osqfuu 516 7 if if IN work_ln56cwsp7ffppl4wxeq7osqfuu 516 8 p(3 p(3 NNP work_ln56cwsp7ffppl4wxeq7osqfuu 516 9 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 516 10 ≤ ≤ NN work_ln56cwsp7ffppl4wxeq7osqfuu 516 11 5 5 CD work_ln56cwsp7ffppl4wxeq7osqfuu 516 12 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 517 1 For for IN work_ln56cwsp7ffppl4wxeq7osqfuu 517 2 all all DT work_ln56cwsp7ffppl4wxeq7osqfuu 517 3 2 2 CD work_ln56cwsp7ffppl4wxeq7osqfuu 517 4 ≤ ≤ NN work_ln56cwsp7ffppl4wxeq7osqfuu 517 5 p(3 p(3 NN work_ln56cwsp7ffppl4wxeq7osqfuu 517 6 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 517 7 ≤ ≤ NNP work_ln56cwsp7ffppl4wxeq7osqfuu 517 8 5 5 CD work_ln56cwsp7ffppl4wxeq7osqfuu 517 9 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 517 10 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 517 11 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 517 12 all all DT work_ln56cwsp7ffppl4wxeq7osqfuu 517 13 p(3 p(3 NN work_ln56cwsp7ffppl4wxeq7osqfuu 517 14 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 517 15 ≤ ≤ NN work_ln56cwsp7ffppl4wxeq7osqfuu 517 16 n n NNP work_ln56cwsp7ffppl4wxeq7osqfuu 517 17 ≤ ≤ NNP work_ln56cwsp7ffppl4wxeq7osqfuu 517 18 3p(3)−2 3p(3)−2 CD work_ln56cwsp7ffppl4wxeq7osqfuu 517 19 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 517 20 direct direct JJ work_ln56cwsp7ffppl4wxeq7osqfuu 517 21 evaluation evaluation NN work_ln56cwsp7ffppl4wxeq7osqfuu 517 22 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 517 23 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 517 24 expression expression NN work_ln56cwsp7ffppl4wxeq7osqfuu 517 25 in in IN work_ln56cwsp7ffppl4wxeq7osqfuu 517 26 point point NN work_ln56cwsp7ffppl4wxeq7osqfuu 517 27 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 517 28 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 517 29 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 517 30 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 517 31 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 517 32 proposition proposition NN work_ln56cwsp7ffppl4wxeq7osqfuu 517 33 shows show VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 517 34 that that IN work_ln56cwsp7ffppl4wxeq7osqfuu 517 35 E[(p(3 E[(p(3 NNP work_ln56cwsp7ffppl4wxeq7osqfuu 517 36 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 517 37 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 517 38 0 0 CD work_ln56cwsp7ffppl4wxeq7osqfuu 517 39 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 517 40 0 0 CD work_ln56cwsp7ffppl4wxeq7osqfuu 517 41 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 517 42 ] ] -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 517 43 > > XX work_ln56cwsp7ffppl4wxeq7osqfuu 517 44 E[(p(3 e[(p(3 NN work_ln56cwsp7ffppl4wxeq7osqfuu 517 45 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 517 46 −2,n−p(3 −2,n−p(3 NN work_ln56cwsp7ffppl4wxeq7osqfuu 517 47 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 517 48 + + CC work_ln56cwsp7ffppl4wxeq7osqfuu 517 49 2 2 CD work_ln56cwsp7ffppl4wxeq7osqfuu 517 50 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 517 51 0 0 CD work_ln56cwsp7ffppl4wxeq7osqfuu 517 52 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 517 53 ] ] -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 517 54 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 517 55 hence hence RB work_ln56cwsp7ffppl4wxeq7osqfuu 517 56 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 517 57 a a DT work_ln56cwsp7ffppl4wxeq7osqfuu 517 58 contradiction contradiction NN work_ln56cwsp7ffppl4wxeq7osqfuu 517 59 arises arise VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 517 60 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 517 61 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 517 62 then then RB work_ln56cwsp7ffppl4wxeq7osqfuu 517 63 it -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 517 64 must must MD work_ln56cwsp7ffppl4wxeq7osqfuu 517 65 be be VB work_ln56cwsp7ffppl4wxeq7osqfuu 517 66 that that IN work_ln56cwsp7ffppl4wxeq7osqfuu 517 67 E[(p(3 E[(p(3 NNP work_ln56cwsp7ffppl4wxeq7osqfuu 517 68 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 517 69 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 517 70 0 0 CD work_ln56cwsp7ffppl4wxeq7osqfuu 517 71 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 517 72 0 0 CD work_ln56cwsp7ffppl4wxeq7osqfuu 517 73 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 517 74 ] ] -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 517 75 > > XX work_ln56cwsp7ffppl4wxeq7osqfuu 517 76 E[(p(3)−2,n−p(3)+2 e[(p(3)−2,n−p(3)+2 XX work_ln56cwsp7ffppl4wxeq7osqfuu 517 77 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 517 78 0 0 CD work_ln56cwsp7ffppl4wxeq7osqfuu 517 79 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 517 80 ] ] -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 517 81 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 517 82 all all DT work_ln56cwsp7ffppl4wxeq7osqfuu 517 83 n n NN work_ln56cwsp7ffppl4wxeq7osqfuu 517 84 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 517 85 all all DT work_ln56cwsp7ffppl4wxeq7osqfuu 517 86 p p NN work_ln56cwsp7ffppl4wxeq7osqfuu 517 87 defined define VBN work_ln56cwsp7ffppl4wxeq7osqfuu 517 88 as as IN work_ln56cwsp7ffppl4wxeq7osqfuu 517 89 in in IN work_ln56cwsp7ffppl4wxeq7osqfuu 517 90 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 517 91 proposition proposition NN work_ln56cwsp7ffppl4wxeq7osqfuu 517 92 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 517 93 as as IN work_ln56cwsp7ffppl4wxeq7osqfuu 517 94 desired desire VBN work_ln56cwsp7ffppl4wxeq7osqfuu 517 95 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 518 1 The the DT work_ln56cwsp7ffppl4wxeq7osqfuu 518 2 latter latter JJ work_ln56cwsp7ffppl4wxeq7osqfuu 518 3 shows show VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 518 4 that that IN work_ln56cwsp7ffppl4wxeq7osqfuu 518 5 it -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 518 6 can can MD work_ln56cwsp7ffppl4wxeq7osqfuu 518 7 only only RB work_ln56cwsp7ffppl4wxeq7osqfuu 518 8 be be VB work_ln56cwsp7ffppl4wxeq7osqfuu 518 9 either either DT work_ln56cwsp7ffppl4wxeq7osqfuu 518 10 h(3 h(3 NN work_ln56cwsp7ffppl4wxeq7osqfuu 518 11 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 518 12 = = NFP work_ln56cwsp7ffppl4wxeq7osqfuu 518 13 p(3 p(3 NN work_ln56cwsp7ffppl4wxeq7osqfuu 518 14 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 518 15 or or CC work_ln56cwsp7ffppl4wxeq7osqfuu 518 16 h(3 h(3 NN work_ln56cwsp7ffppl4wxeq7osqfuu 518 17 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 518 18 = = NFP work_ln56cwsp7ffppl4wxeq7osqfuu 518 19 p(3 p(3 NN work_ln56cwsp7ffppl4wxeq7osqfuu 518 20 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 518 21 − − NNP work_ln56cwsp7ffppl4wxeq7osqfuu 518 22 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 518 23 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 519 1 In in IN work_ln56cwsp7ffppl4wxeq7osqfuu 519 2 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 519 3 first first JJ work_ln56cwsp7ffppl4wxeq7osqfuu 519 4 case case NN work_ln56cwsp7ffppl4wxeq7osqfuu 519 5 it -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 519 6 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 519 7 immediate immediate JJ work_ln56cwsp7ffppl4wxeq7osqfuu 519 8 that that IN work_ln56cwsp7ffppl4wxeq7osqfuu 519 9 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 519 10 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 519 11 h h NN work_ln56cwsp7ffppl4wxeq7osqfuu 519 12 to to TO work_ln56cwsp7ffppl4wxeq7osqfuu 519 13 be be VB work_ln56cwsp7ffppl4wxeq7osqfuu 519 14 an an DT work_ln56cwsp7ffppl4wxeq7osqfuu 519 15 optimal optimal JJ work_ln56cwsp7ffppl4wxeq7osqfuu 519 16 alternative alternative NN work_ln56cwsp7ffppl4wxeq7osqfuu 519 17 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 519 18 then then RB work_ln56cwsp7ffppl4wxeq7osqfuu 519 19 it -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 519 20 can can MD work_ln56cwsp7ffppl4wxeq7osqfuu 519 21 only only RB work_ln56cwsp7ffppl4wxeq7osqfuu 519 22 be be VB work_ln56cwsp7ffppl4wxeq7osqfuu 519 23 that that IN work_ln56cwsp7ffppl4wxeq7osqfuu 519 24 h(2 h(2 . work_ln56cwsp7ffppl4wxeq7osqfuu 519 25 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 519 26 ≥ ≥ UH work_ln56cwsp7ffppl4wxeq7osqfuu 519 27 p(2 p(2 NN work_ln56cwsp7ffppl4wxeq7osqfuu 519 28 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 519 29 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 520 1 For for IN work_ln56cwsp7ffppl4wxeq7osqfuu 520 2 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 520 3 second second JJ work_ln56cwsp7ffppl4wxeq7osqfuu 520 4 case case NN work_ln56cwsp7ffppl4wxeq7osqfuu 520 5 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 520 6 note note VBP work_ln56cwsp7ffppl4wxeq7osqfuu 520 7 that that IN work_ln56cwsp7ffppl4wxeq7osqfuu 520 8 E[Uh(n E[Uh(n NNP work_ln56cwsp7ffppl4wxeq7osqfuu 520 9 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 520 10 | | NNP work_ln56cwsp7ffppl4wxeq7osqfuu 520 11 M M NNP work_ln56cwsp7ffppl4wxeq7osqfuu 520 12 ] ] -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 520 13 = = NFP work_ln56cwsp7ffppl4wxeq7osqfuu 520 14 E[(p E[(p NNP work_ln56cwsp7ffppl4wxeq7osqfuu 520 15 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 520 16 3 3 LS work_ln56cwsp7ffppl4wxeq7osqfuu 520 17 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 520 18 − − NNP work_ln56cwsp7ffppl4wxeq7osqfuu 520 19 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 520 20 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 520 21 h(2),n−p(3 h(2),n−p(3 NNP work_ln56cwsp7ffppl4wxeq7osqfuu 520 22 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 520 23 + + SYM work_ln56cwsp7ffppl4wxeq7osqfuu 520 24 1−h(2 1−h(2 CD work_ln56cwsp7ffppl4wxeq7osqfuu 520 25 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 520 26 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 520 27 ] ] -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 520 28 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 521 1 Now now RB work_ln56cwsp7ffppl4wxeq7osqfuu 521 2 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 521 3 by by IN work_ln56cwsp7ffppl4wxeq7osqfuu 521 4 Lemma Lemma NNP work_ln56cwsp7ffppl4wxeq7osqfuu 521 5 A.1 A.1 NNP work_ln56cwsp7ffppl4wxeq7osqfuu 521 6 E[(p(3)−1 E[(p(3)−1 NNS work_ln56cwsp7ffppl4wxeq7osqfuu 521 7 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 521 8 h(2),n−p(3 h(2),n−p(3 NNP work_ln56cwsp7ffppl4wxeq7osqfuu 521 9 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 521 10 + + SYM work_ln56cwsp7ffppl4wxeq7osqfuu 521 11 1−h(2 1−h(2 CD work_ln56cwsp7ffppl4wxeq7osqfuu 521 12 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 521 13 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 521 14 ] ] -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 521 15 ≤ ≤ NNP work_ln56cwsp7ffppl4wxeq7osqfuu 521 16 E[(p(3)−1 E[(p(3)−1 NNS work_ln56cwsp7ffppl4wxeq7osqfuu 521 17 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 521 18 0 0 CD work_ln56cwsp7ffppl4wxeq7osqfuu 521 19 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 521 20 0)]+h(2)∆(2 0)]+h(2)∆(2 CD work_ln56cwsp7ffppl4wxeq7osqfuu 521 21 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 521 22 p(3)−1 p(3)−1 NNP work_ln56cwsp7ffppl4wxeq7osqfuu 521 23 + + SYM work_ln56cwsp7ffppl4wxeq7osqfuu 521 24 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 521 25 n−p n−p NNP work_ln56cwsp7ffppl4wxeq7osqfuu 521 26 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 521 27 3 3 LS work_ln56cwsp7ffppl4wxeq7osqfuu 521 28 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 521 29 +1−h(2))∆(1 +1−h(2))∆(1 XX work_ln56cwsp7ffppl4wxeq7osqfuu 521 30 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 521 31 p(3)−1 p(3)−1 NNP work_ln56cwsp7ffppl4wxeq7osqfuu 521 32 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 522 1 Now now RB work_ln56cwsp7ffppl4wxeq7osqfuu 522 2 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 522 3 since since IN work_ln56cwsp7ffppl4wxeq7osqfuu 522 4 p p NN work_ln56cwsp7ffppl4wxeq7osqfuu 522 5 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 522 6 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 522 7 plurality plurality NN work_ln56cwsp7ffppl4wxeq7osqfuu 522 8 alternative alternative NN work_ln56cwsp7ffppl4wxeq7osqfuu 522 9 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 522 10 it -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 522 11 must must MD work_ln56cwsp7ffppl4wxeq7osqfuu 522 12 be be VB work_ln56cwsp7ffppl4wxeq7osqfuu 522 13 that that IN work_ln56cwsp7ffppl4wxeq7osqfuu 522 14 n n NNP work_ln56cwsp7ffppl4wxeq7osqfuu 522 15 ≤ ≤ NN work_ln56cwsp7ffppl4wxeq7osqfuu 522 16 3p(3)−1 3p(3)−1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 522 17 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 523 1 Hence hence RB work_ln56cwsp7ffppl4wxeq7osqfuu 523 2 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 523 3 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 523 4 n−p(3 n−p(3 NNP work_ln56cwsp7ffppl4wxeq7osqfuu 523 5 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 523 6 +1−h(2 +1−h(2 ADD work_ln56cwsp7ffppl4wxeq7osqfuu 523 7 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 523 8 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 523 9 ≤ ≤ NNP work_ln56cwsp7ffppl4wxeq7osqfuu 523 10 2p(3)−h(2 2p(3)−h(2 CD work_ln56cwsp7ffppl4wxeq7osqfuu 523 11 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 523 12 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 524 1 For for IN work_ln56cwsp7ffppl4wxeq7osqfuu 524 2 all all DT work_ln56cwsp7ffppl4wxeq7osqfuu 524 3 p(3 p(3 NN work_ln56cwsp7ffppl4wxeq7osqfuu 524 4 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 524 5 ≥ ≥ NN work_ln56cwsp7ffppl4wxeq7osqfuu 524 6 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 524 7 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 524 8 2p(3)−h(2 2p(3)−h(2 CD work_ln56cwsp7ffppl4wxeq7osqfuu 524 9 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 524 10 ≤ ≤ NNP work_ln56cwsp7ffppl4wxeq7osqfuu 524 11 3p(3)−1 3p(3)−1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 524 12 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 525 1 It -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 525 2 can can MD work_ln56cwsp7ffppl4wxeq7osqfuu 525 3 be be VB work_ln56cwsp7ffppl4wxeq7osqfuu 525 4 checked check VBN work_ln56cwsp7ffppl4wxeq7osqfuu 525 5 that that IN work_ln56cwsp7ffppl4wxeq7osqfuu 525 6 ∆ ∆ NN work_ln56cwsp7ffppl4wxeq7osqfuu 525 7 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 525 8 2 2 LS work_ln56cwsp7ffppl4wxeq7osqfuu 525 9 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 525 10 p(3)−1 p(3)−1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 525 11 ∆ ∆ NN work_ln56cwsp7ffppl4wxeq7osqfuu 525 12 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 525 13 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 525 14 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 525 15 p(3)−1 p(3)−1 NNP work_ln56cwsp7ffppl4wxeq7osqfuu 525 16 = = SYM work_ln56cwsp7ffppl4wxeq7osqfuu 525 17 3p(3)−1 3p(3)−1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 525 18 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 526 1 Hence hence RB work_ln56cwsp7ffppl4wxeq7osqfuu 526 2 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 526 3 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 526 4 n− n− NNP work_ln56cwsp7ffppl4wxeq7osqfuu 526 5 p(3 p(3 NNP work_ln56cwsp7ffppl4wxeq7osqfuu 526 6 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 526 7 + + CC work_ln56cwsp7ffppl4wxeq7osqfuu 526 8 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 526 9 − − NNP work_ln56cwsp7ffppl4wxeq7osqfuu 526 10 h(2))∆(1 h(2))∆(1 NN work_ln56cwsp7ffppl4wxeq7osqfuu 526 11 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 526 12 p(3)−1 p(3)−1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 526 13 ≤ ≤ NN work_ln56cwsp7ffppl4wxeq7osqfuu 526 14 ∆ ∆ NN work_ln56cwsp7ffppl4wxeq7osqfuu 526 15 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 526 16 2 2 CD work_ln56cwsp7ffppl4wxeq7osqfuu 526 17 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 526 18 p(3)−1 p(3)−1 NNP work_ln56cwsp7ffppl4wxeq7osqfuu 526 19 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 527 1 Then then RB work_ln56cwsp7ffppl4wxeq7osqfuu 527 2 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 527 3 E[(p E[(p NNP work_ln56cwsp7ffppl4wxeq7osqfuu 527 4 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 527 5 3 3 LS work_ln56cwsp7ffppl4wxeq7osqfuu 527 6 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 527 7 − − NNP work_ln56cwsp7ffppl4wxeq7osqfuu 527 8 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 527 9 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 527 10 h(2),n− h(2),n− NNP work_ln56cwsp7ffppl4wxeq7osqfuu 527 11 p(3 p(3 NN work_ln56cwsp7ffppl4wxeq7osqfuu 527 12 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 527 13 + + CC work_ln56cwsp7ffppl4wxeq7osqfuu 527 14 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 527 15 − − NNP work_ln56cwsp7ffppl4wxeq7osqfuu 527 16 h(2 h(2 . work_ln56cwsp7ffppl4wxeq7osqfuu 527 17 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 527 18 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 527 19 ] ] -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 527 20 ≤ ≤ NNP work_ln56cwsp7ffppl4wxeq7osqfuu 527 21 E[(p(3 E[(p(3 NNP work_ln56cwsp7ffppl4wxeq7osqfuu 527 22 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 527 23 −1 −1 NNP work_ln56cwsp7ffppl4wxeq7osqfuu 527 24 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 527 25 0 0 CD work_ln56cwsp7ffppl4wxeq7osqfuu 527 26 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 527 27 0 0 CD work_ln56cwsp7ffppl4wxeq7osqfuu 527 28 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 527 29 ] ] -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 527 30 + + CC work_ln56cwsp7ffppl4wxeq7osqfuu 527 31 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 527 32 h(2 h(2 NNP work_ln56cwsp7ffppl4wxeq7osqfuu 527 33 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 527 34 + + CD work_ln56cwsp7ffppl4wxeq7osqfuu 527 35 1)∆(2 1)∆(2 NN work_ln56cwsp7ffppl4wxeq7osqfuu 527 36 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 527 37 p(3)−1 p(3)−1 NNP work_ln56cwsp7ffppl4wxeq7osqfuu 527 38 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 528 1 For for IN work_ln56cwsp7ffppl4wxeq7osqfuu 528 2 alternative alternative JJ work_ln56cwsp7ffppl4wxeq7osqfuu 528 3 p p NN work_ln56cwsp7ffppl4wxeq7osqfuu 528 4 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 528 5 E[U E[U NNP work_ln56cwsp7ffppl4wxeq7osqfuu 528 6 p p NN work_ln56cwsp7ffppl4wxeq7osqfuu 528 7 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 528 8 n n NNP work_ln56cwsp7ffppl4wxeq7osqfuu 528 9 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 528 10 | | NNP work_ln56cwsp7ffppl4wxeq7osqfuu 528 11 M M NNP work_ln56cwsp7ffppl4wxeq7osqfuu 528 12 ] ] -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 528 13 ≥ ≥ NNP work_ln56cwsp7ffppl4wxeq7osqfuu 528 14 E[(p(3 e[(p(3 NN work_ln56cwsp7ffppl4wxeq7osqfuu 528 15 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 528 16 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 528 17 0 0 CD work_ln56cwsp7ffppl4wxeq7osqfuu 528 18 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 528 19 0 0 CD work_ln56cwsp7ffppl4wxeq7osqfuu 528 20 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 528 21 ] ] -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 528 22 = = NFP work_ln56cwsp7ffppl4wxeq7osqfuu 528 23 E[(p(3)−1 E[(p(3)−1 NNS work_ln56cwsp7ffppl4wxeq7osqfuu 528 24 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 528 25 0 0 CD work_ln56cwsp7ffppl4wxeq7osqfuu 528 26 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 528 27 0 0 CD work_ln56cwsp7ffppl4wxeq7osqfuu 528 28 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 528 29 ] ] -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 528 30 + + NNP work_ln56cwsp7ffppl4wxeq7osqfuu 528 31 ∆(3 ∆(3 NNP work_ln56cwsp7ffppl4wxeq7osqfuu 528 32 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 528 33 p(3)−1 p(3)−1 NNP work_ln56cwsp7ffppl4wxeq7osqfuu 528 34 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 529 1 Hence hence RB work_ln56cwsp7ffppl4wxeq7osqfuu 529 2 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 529 3 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 529 4 alternative alternative JJ work_ln56cwsp7ffppl4wxeq7osqfuu 529 5 h h NNP work_ln56cwsp7ffppl4wxeq7osqfuu 529 6 to to TO work_ln56cwsp7ffppl4wxeq7osqfuu 529 7 be be VB work_ln56cwsp7ffppl4wxeq7osqfuu 529 8 an an DT work_ln56cwsp7ffppl4wxeq7osqfuu 529 9 αMX αmx NN work_ln56cwsp7ffppl4wxeq7osqfuu 529 10 - - HYPH work_ln56cwsp7ffppl4wxeq7osqfuu 529 11 optimal optimal JJ work_ln56cwsp7ffppl4wxeq7osqfuu 529 12 alternative alternative NN work_ln56cwsp7ffppl4wxeq7osqfuu 529 13 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 529 14 it -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 529 15 must must MD work_ln56cwsp7ffppl4wxeq7osqfuu 529 16 be be VB work_ln56cwsp7ffppl4wxeq7osqfuu 529 17 that that DT work_ln56cwsp7ffppl4wxeq7osqfuu 529 18 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 529 19 h(2 h(2 NNP work_ln56cwsp7ffppl4wxeq7osqfuu 529 20 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 529 21 + + NFP work_ln56cwsp7ffppl4wxeq7osqfuu 529 22 1)∆ 1)∆ NN work_ln56cwsp7ffppl4wxeq7osqfuu 529 23 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 529 24 2 2 CD work_ln56cwsp7ffppl4wxeq7osqfuu 529 25 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 529 26 p(3)−1 p(3)−1 NNP work_ln56cwsp7ffppl4wxeq7osqfuu 529 27 ≥ ≥ CD work_ln56cwsp7ffppl4wxeq7osqfuu 529 28 ∆ ∆ NN work_ln56cwsp7ffppl4wxeq7osqfuu 529 29 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 529 30 3 3 CD work_ln56cwsp7ffppl4wxeq7osqfuu 529 31 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 529 32 p(3)−1 p(3)−1 NNP work_ln56cwsp7ffppl4wxeq7osqfuu 529 33 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 530 1 The the DT work_ln56cwsp7ffppl4wxeq7osqfuu 530 2 latter latter JJ work_ln56cwsp7ffppl4wxeq7osqfuu 530 3 implies imply VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 530 4 that that IN work_ln56cwsp7ffppl4wxeq7osqfuu 530 5 h h NN work_ln56cwsp7ffppl4wxeq7osqfuu 530 6 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 530 7 2 2 CD work_ln56cwsp7ffppl4wxeq7osqfuu 530 8 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 530 9 ≥ ≥ CD work_ln56cwsp7ffppl4wxeq7osqfuu 530 10 3p 3p NNS work_ln56cwsp7ffppl4wxeq7osqfuu 530 11 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 530 12 3 3 CD work_ln56cwsp7ffppl4wxeq7osqfuu 530 13 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 530 14 2 2 CD work_ln56cwsp7ffppl4wxeq7osqfuu 530 15 − − NNP work_ln56cwsp7ffppl4wxeq7osqfuu 530 16 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 530 17 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 530 18 hence hence RB work_ln56cwsp7ffppl4wxeq7osqfuu 530 19 h(2 h(2 . work_ln56cwsp7ffppl4wxeq7osqfuu 530 20 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 530 21 ≥ ≥ NN work_ln56cwsp7ffppl4wxeq7osqfuu 530 22 n−1 n−1 NNP work_ln56cwsp7ffppl4wxeq7osqfuu 530 23 2 2 CD work_ln56cwsp7ffppl4wxeq7osqfuu 530 24 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 530 25 as as IN work_ln56cwsp7ffppl4wxeq7osqfuu 530 26 desired desire VBN work_ln56cwsp7ffppl4wxeq7osqfuu 530 27 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 530 28 � � : work_ln56cwsp7ffppl4wxeq7osqfuu 530 29 Proof Proof NNP work_ln56cwsp7ffppl4wxeq7osqfuu 530 30 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 530 31 Proposition Proposition NNP work_ln56cwsp7ffppl4wxeq7osqfuu 530 32 4.6 4.6 CD work_ln56cwsp7ffppl4wxeq7osqfuu 530 33 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 531 1 We -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 531 2 start start VBP work_ln56cwsp7ffppl4wxeq7osqfuu 531 3 by by IN work_ln56cwsp7ffppl4wxeq7osqfuu 531 4 noticing notice VBG work_ln56cwsp7ffppl4wxeq7osqfuu 531 5 that that IN work_ln56cwsp7ffppl4wxeq7osqfuu 531 6 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 531 7 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 531 8 every every DT work_ln56cwsp7ffppl4wxeq7osqfuu 531 9 l l NN work_ln56cwsp7ffppl4wxeq7osqfuu 531 10 ∈ ∈ NNP work_ln56cwsp7ffppl4wxeq7osqfuu 531 11 P(M P(M NNP work_ln56cwsp7ffppl4wxeq7osqfuu 531 12 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 531 13 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 531 14 index index NN work_ln56cwsp7ffppl4wxeq7osqfuu 531 15 γlMX γlMX NNP work_ln56cwsp7ffppl4wxeq7osqfuu 531 16 = = SYM work_ln56cwsp7ffppl4wxeq7osqfuu 531 17 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 531 18 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 532 1 This this DT work_ln56cwsp7ffppl4wxeq7osqfuu 532 2 follows follow VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 532 3 trivially trivially RB work_ln56cwsp7ffppl4wxeq7osqfuu 532 4 from from IN work_ln56cwsp7ffppl4wxeq7osqfuu 532 5 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 532 6 fact fact NN work_ln56cwsp7ffppl4wxeq7osqfuu 532 7 that that IN work_ln56cwsp7ffppl4wxeq7osqfuu 532 8 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 532 9 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 532 10 every every DT work_ln56cwsp7ffppl4wxeq7osqfuu 532 11 l l NN work_ln56cwsp7ffppl4wxeq7osqfuu 532 12 ∈ ∈ NNP work_ln56cwsp7ffppl4wxeq7osqfuu 532 13 P(M P(M NNP work_ln56cwsp7ffppl4wxeq7osqfuu 532 14 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 532 15 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 532 16 there there EX work_ln56cwsp7ffppl4wxeq7osqfuu 532 17 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 532 18 an an DT work_ln56cwsp7ffppl4wxeq7osqfuu 532 19 h h NN work_ln56cwsp7ffppl4wxeq7osqfuu 532 20 ∈ ∈ NN work_ln56cwsp7ffppl4wxeq7osqfuu 532 21 K k NN work_ln56cwsp7ffppl4wxeq7osqfuu 532 22 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 532 23 possibly possibly RB work_ln56cwsp7ffppl4wxeq7osqfuu 532 24 a a DT work_ln56cwsp7ffppl4wxeq7osqfuu 532 25 different different JJ work_ln56cwsp7ffppl4wxeq7osqfuu 532 26 h h NN work_ln56cwsp7ffppl4wxeq7osqfuu 532 27 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 532 28 every every DT work_ln56cwsp7ffppl4wxeq7osqfuu 532 29 l l NN work_ln56cwsp7ffppl4wxeq7osqfuu 532 30 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 532 31 such such JJ work_ln56cwsp7ffppl4wxeq7osqfuu 532 32 that that IN work_ln56cwsp7ffppl4wxeq7osqfuu 532 33 Ml Ml NNP work_ln56cwsp7ffppl4wxeq7osqfuu 532 34 > > NNP work_ln56cwsp7ffppl4wxeq7osqfuu 532 35 Mh Mh NNP work_ln56cwsp7ffppl4wxeq7osqfuu 532 36 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 532 37 hence hence RB work_ln56cwsp7ffppl4wxeq7osqfuu 532 38 Ul(n Ul(n NNP work_ln56cwsp7ffppl4wxeq7osqfuu 532 39 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 532 40 > > XX work_ln56cwsp7ffppl4wxeq7osqfuu 532 41 U u NN work_ln56cwsp7ffppl4wxeq7osqfuu 532 42 h h NN work_ln56cwsp7ffppl4wxeq7osqfuu 532 43 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 532 44 n n NN work_ln56cwsp7ffppl4wxeq7osqfuu 532 45 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 532 46 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 533 1 We -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 533 2 now now RB work_ln56cwsp7ffppl4wxeq7osqfuu 533 3 show show VBP work_ln56cwsp7ffppl4wxeq7osqfuu 533 4 that that IN work_ln56cwsp7ffppl4wxeq7osqfuu 533 5 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 533 6 every every DT work_ln56cwsp7ffppl4wxeq7osqfuu 533 7 l l NN work_ln56cwsp7ffppl4wxeq7osqfuu 533 8 ∈ ∈ NNP work_ln56cwsp7ffppl4wxeq7osqfuu 533 9 K K NNP work_ln56cwsp7ffppl4wxeq7osqfuu 533 10 \P(M \p(m NN work_ln56cwsp7ffppl4wxeq7osqfuu 533 11 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 533 12 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 533 13 index index NN work_ln56cwsp7ffppl4wxeq7osqfuu 533 14 γlMX γlMX NNP work_ln56cwsp7ffppl4wxeq7osqfuu 533 15 < < XX work_ln56cwsp7ffppl4wxeq7osqfuu 533 16 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 533 17 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 534 1 Suppose suppose VB work_ln56cwsp7ffppl4wxeq7osqfuu 534 2 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 534 3 w.l.o.g w.l.o.g NNP work_ln56cwsp7ffppl4wxeq7osqfuu 534 4 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 535 1 that that IN work_ln56cwsp7ffppl4wxeq7osqfuu 535 2 l l NN work_ln56cwsp7ffppl4wxeq7osqfuu 535 3 = = SYM work_ln56cwsp7ffppl4wxeq7osqfuu 535 4 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 535 5 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 536 1 Since since IN work_ln56cwsp7ffppl4wxeq7osqfuu 536 2 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 536 3 6∈ 6∈ CD work_ln56cwsp7ffppl4wxeq7osqfuu 536 4 P(M P(M NNP work_ln56cwsp7ffppl4wxeq7osqfuu 536 5 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 536 6 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 536 7 every every DT work_ln56cwsp7ffppl4wxeq7osqfuu 536 8 h h NN work_ln56cwsp7ffppl4wxeq7osqfuu 536 9 > > NN work_ln56cwsp7ffppl4wxeq7osqfuu 536 10 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 536 11 there there EX work_ln56cwsp7ffppl4wxeq7osqfuu 536 12 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 536 13 an an DT work_ln56cwsp7ffppl4wxeq7osqfuu 536 14 agent agent NN work_ln56cwsp7ffppl4wxeq7osqfuu 536 15 ih ih NN work_ln56cwsp7ffppl4wxeq7osqfuu 536 16 such such JJ work_ln56cwsp7ffppl4wxeq7osqfuu 536 17 that that IN work_ln56cwsp7ffppl4wxeq7osqfuu 536 18 m1ih m1ih NNP work_ln56cwsp7ffppl4wxeq7osqfuu 536 19 < < XX work_ln56cwsp7ffppl4wxeq7osqfuu 536 20 m m NNP work_ln56cwsp7ffppl4wxeq7osqfuu 536 21 h h NNP work_ln56cwsp7ffppl4wxeq7osqfuu 536 22 ih ih NN work_ln56cwsp7ffppl4wxeq7osqfuu 536 23 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 537 1 9Note 9note VB work_ln56cwsp7ffppl4wxeq7osqfuu 537 2 that that DT work_ln56cwsp7ffppl4wxeq7osqfuu 537 3 vector vector NN work_ln56cwsp7ffppl4wxeq7osqfuu 537 4 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 537 5 p(3 p(3 NN work_ln56cwsp7ffppl4wxeq7osqfuu 537 6 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 537 7 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 537 8 0 0 CD work_ln56cwsp7ffppl4wxeq7osqfuu 537 9 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 537 10 0 0 CD work_ln56cwsp7ffppl4wxeq7osqfuu 537 11 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 537 12 may may MD work_ln56cwsp7ffppl4wxeq7osqfuu 537 13 not not RB work_ln56cwsp7ffppl4wxeq7osqfuu 537 14 be be VB work_ln56cwsp7ffppl4wxeq7osqfuu 537 15 feasible feasible JJ work_ln56cwsp7ffppl4wxeq7osqfuu 537 16 in in IN work_ln56cwsp7ffppl4wxeq7osqfuu 537 17 M. M. NNP work_ln56cwsp7ffppl4wxeq7osqfuu 537 18 22 22 CD work_ln56cwsp7ffppl4wxeq7osqfuu 537 19 Denote Denote NNP work_ln56cwsp7ffppl4wxeq7osqfuu 537 20 all all PDT work_ln56cwsp7ffppl4wxeq7osqfuu 537 21 these these DT work_ln56cwsp7ffppl4wxeq7osqfuu 537 22 agents agent NNS work_ln56cwsp7ffppl4wxeq7osqfuu 537 23 by by IN work_ln56cwsp7ffppl4wxeq7osqfuu 537 24 I i NN work_ln56cwsp7ffppl4wxeq7osqfuu 537 25 = = SYM work_ln56cwsp7ffppl4wxeq7osqfuu 537 26 ∪h∈K\{1}{ih ∪h∈K\{1}{ih NNS work_ln56cwsp7ffppl4wxeq7osqfuu 537 27 } } -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 537 28 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 538 1 P(U1(n p(u1(n CD work_ln56cwsp7ffppl4wxeq7osqfuu 538 2 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 538 3 < < XX work_ln56cwsp7ffppl4wxeq7osqfuu 538 4 U u NN work_ln56cwsp7ffppl4wxeq7osqfuu 538 5 h h NN work_ln56cwsp7ffppl4wxeq7osqfuu 538 6 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 538 7 n n NN work_ln56cwsp7ffppl4wxeq7osqfuu 538 8 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 538 9 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 538 10 all all DT work_ln56cwsp7ffppl4wxeq7osqfuu 538 11 h h NN work_ln56cwsp7ffppl4wxeq7osqfuu 538 12 > > NN work_ln56cwsp7ffppl4wxeq7osqfuu 538 13 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 538 14 | | NNP work_ln56cwsp7ffppl4wxeq7osqfuu 538 15 M M NNP work_ln56cwsp7ffppl4wxeq7osqfuu 538 16 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 538 17 ≥ ≥ CD work_ln56cwsp7ffppl4wxeq7osqfuu 538 18 P(U1(n p(u1(n NN work_ln56cwsp7ffppl4wxeq7osqfuu 538 19 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 538 20 = = NFP work_ln56cwsp7ffppl4wxeq7osqfuu 538 21 U u NN work_ln56cwsp7ffppl4wxeq7osqfuu 538 22 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 538 23 j j NN work_ln56cwsp7ffppl4wxeq7osqfuu 538 24 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 538 25 any any DT work_ln56cwsp7ffppl4wxeq7osqfuu 538 26 j j NN work_ln56cwsp7ffppl4wxeq7osqfuu 538 27 ∈ ∈ NNP work_ln56cwsp7ffppl4wxeq7osqfuu 538 28 I -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 538 29 | | NNP work_ln56cwsp7ffppl4wxeq7osqfuu 538 30 M m NN work_ln56cwsp7ffppl4wxeq7osqfuu 538 31 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 538 32 · · NFP work_ln56cwsp7ffppl4wxeq7osqfuu 538 33 P(U2(n P(U2(n NNP work_ln56cwsp7ffppl4wxeq7osqfuu 538 34 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 538 35 = = NFP work_ln56cwsp7ffppl4wxeq7osqfuu 538 36 U u NN work_ln56cwsp7ffppl4wxeq7osqfuu 538 37 2 2 CD work_ln56cwsp7ffppl4wxeq7osqfuu 538 38 i2 i2 NN work_ln56cwsp7ffppl4wxeq7osqfuu 538 39 | | NNP work_ln56cwsp7ffppl4wxeq7osqfuu 538 40 M m NN work_ln56cwsp7ffppl4wxeq7osqfuu 538 41 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 538 42 · · NFP work_ln56cwsp7ffppl4wxeq7osqfuu 538 43 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 539 1 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 540 1 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 541 1 · · NFP work_ln56cwsp7ffppl4wxeq7osqfuu 541 2 P(Uk(n P(Uk(n NNP work_ln56cwsp7ffppl4wxeq7osqfuu 541 3 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 541 4 = = NFP work_ln56cwsp7ffppl4wxeq7osqfuu 541 5 U u NN work_ln56cwsp7ffppl4wxeq7osqfuu 541 6 k k NN work_ln56cwsp7ffppl4wxeq7osqfuu 541 7 ik ik NN work_ln56cwsp7ffppl4wxeq7osqfuu 541 8 | | NNP work_ln56cwsp7ffppl4wxeq7osqfuu 541 9 M M NNP work_ln56cwsp7ffppl4wxeq7osqfuu 541 10 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 541 11 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 542 1 Clearly clearly RB work_ln56cwsp7ffppl4wxeq7osqfuu 542 2 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 542 3 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 542 4 latter latter NN work_ln56cwsp7ffppl4wxeq7osqfuu 542 5 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 542 6 strictly strictly RB work_ln56cwsp7ffppl4wxeq7osqfuu 542 7 above above IN work_ln56cwsp7ffppl4wxeq7osqfuu 542 8 0 0 CD work_ln56cwsp7ffppl4wxeq7osqfuu 542 9 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 542 10 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 542 11 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 542 12 result result NN work_ln56cwsp7ffppl4wxeq7osqfuu 542 13 follows follow VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 542 14 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 542 15 � � : work_ln56cwsp7ffppl4wxeq7osqfuu 542 16 Proof Proof NNP work_ln56cwsp7ffppl4wxeq7osqfuu 542 17 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 542 18 Theorem Theorem NNP work_ln56cwsp7ffppl4wxeq7osqfuu 542 19 4.5 4.5 CD work_ln56cwsp7ffppl4wxeq7osqfuu 542 20 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 543 1 Take take VB work_ln56cwsp7ffppl4wxeq7osqfuu 543 2 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 543 3 structure structure NN work_ln56cwsp7ffppl4wxeq7osqfuu 543 4 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 543 5 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 543 6 proof proof NN work_ln56cwsp7ffppl4wxeq7osqfuu 543 7 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 543 8 Theorem Theorem NNP work_ln56cwsp7ffppl4wxeq7osqfuu 543 9 3.5 3.5 CD work_ln56cwsp7ffppl4wxeq7osqfuu 543 10 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 544 1 Here here RB work_ln56cwsp7ffppl4wxeq7osqfuu 544 2 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 544 3 too too RB work_ln56cwsp7ffppl4wxeq7osqfuu 544 4 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 544 5 we -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 544 6 provide provide VBP work_ln56cwsp7ffppl4wxeq7osqfuu 544 7 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 544 8 proof proof NN work_ln56cwsp7ffppl4wxeq7osqfuu 544 9 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 544 10 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 544 11 uniform uniform JJ work_ln56cwsp7ffppl4wxeq7osqfuu 544 12 distribution distribution NN work_ln56cwsp7ffppl4wxeq7osqfuu 544 13 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 545 1 The the DT work_ln56cwsp7ffppl4wxeq7osqfuu 545 2 values value NNS work_ln56cwsp7ffppl4wxeq7osqfuu 545 3 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 545 4 γMX(M γMX(M NNPS work_ln56cwsp7ffppl4wxeq7osqfuu 545 5 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 545 6 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 545 7 any any DT work_ln56cwsp7ffppl4wxeq7osqfuu 545 8 other other JJ work_ln56cwsp7ffppl4wxeq7osqfuu 545 9 parabolic parabolic JJ work_ln56cwsp7ffppl4wxeq7osqfuu 545 10 function function NN work_ln56cwsp7ffppl4wxeq7osqfuu 545 11 are be VBP work_ln56cwsp7ffppl4wxeq7osqfuu 545 12 exactly exactly RB work_ln56cwsp7ffppl4wxeq7osqfuu 545 13 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 545 14 ones one NNS work_ln56cwsp7ffppl4wxeq7osqfuu 545 15 provided provide VBN work_ln56cwsp7ffppl4wxeq7osqfuu 545 16 below below RB work_ln56cwsp7ffppl4wxeq7osqfuu 545 17 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 546 1 Then then RB work_ln56cwsp7ffppl4wxeq7osqfuu 546 2 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 546 3 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 546 4 values value NNS work_ln56cwsp7ffppl4wxeq7osqfuu 546 5 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 546 6 γMX(M γMX(M NNP work_ln56cwsp7ffppl4wxeq7osqfuu 546 7 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 546 8 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 546 9 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 546 10 different different JJ work_ln56cwsp7ffppl4wxeq7osqfuu 546 11 types type NNS work_ln56cwsp7ffppl4wxeq7osqfuu 546 12 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 546 13 societies society NNS work_ln56cwsp7ffppl4wxeq7osqfuu 546 14 are be VBP work_ln56cwsp7ffppl4wxeq7osqfuu 546 15 : : : work_ln56cwsp7ffppl4wxeq7osqfuu 546 16 Type type NN work_ln56cwsp7ffppl4wxeq7osqfuu 546 17 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 546 18 : : : work_ln56cwsp7ffppl4wxeq7osqfuu 546 19 It -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 546 20 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 546 21 straightforward straightforward JJ work_ln56cwsp7ffppl4wxeq7osqfuu 546 22 that that IN work_ln56cwsp7ffppl4wxeq7osqfuu 546 23 γMX(M γMX(M NNP work_ln56cwsp7ffppl4wxeq7osqfuu 546 24 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 546 25 = = NFP work_ln56cwsp7ffppl4wxeq7osqfuu 546 26 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 546 27 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 546 28 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 546 29 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 546 30 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 546 31 0 0 CD work_ln56cwsp7ffppl4wxeq7osqfuu 546 32 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 546 33 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 547 1 Type type NN work_ln56cwsp7ffppl4wxeq7osqfuu 547 2 2 2 CD work_ln56cwsp7ffppl4wxeq7osqfuu 547 3 : : : work_ln56cwsp7ffppl4wxeq7osqfuu 547 4 It -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 547 5 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 547 6 straightforward straightforward JJ work_ln56cwsp7ffppl4wxeq7osqfuu 547 7 that that IN work_ln56cwsp7ffppl4wxeq7osqfuu 547 8 γMX(M γMX(M NNP work_ln56cwsp7ffppl4wxeq7osqfuu 547 9 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 547 10 = = NFP work_ln56cwsp7ffppl4wxeq7osqfuu 547 11 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 547 12 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 547 13 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 547 14 1/2 1/2 CD work_ln56cwsp7ffppl4wxeq7osqfuu 547 15 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 547 16 1/2 1/2 CD work_ln56cwsp7ffppl4wxeq7osqfuu 547 17 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 547 18 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 548 1 Type type NN work_ln56cwsp7ffppl4wxeq7osqfuu 548 2 3 3 CD work_ln56cwsp7ffppl4wxeq7osqfuu 548 3 : : : work_ln56cwsp7ffppl4wxeq7osqfuu 548 4 It -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 548 5 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 548 6 straightforward straightforward JJ work_ln56cwsp7ffppl4wxeq7osqfuu 548 7 that that IN work_ln56cwsp7ffppl4wxeq7osqfuu 548 8 γMX(M γMX(M NNP work_ln56cwsp7ffppl4wxeq7osqfuu 548 9 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 548 10 = = NFP work_ln56cwsp7ffppl4wxeq7osqfuu 548 11 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 548 12 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 548 13 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 548 14 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 548 15 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 548 16 0 0 CD work_ln56cwsp7ffppl4wxeq7osqfuu 548 17 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 548 18 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 549 1 Type type NN work_ln56cwsp7ffppl4wxeq7osqfuu 549 2 4 4 CD work_ln56cwsp7ffppl4wxeq7osqfuu 549 3 : : : work_ln56cwsp7ffppl4wxeq7osqfuu 549 4 It -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 549 5 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 549 6 easy easy JJ work_ln56cwsp7ffppl4wxeq7osqfuu 549 7 to to TO work_ln56cwsp7ffppl4wxeq7osqfuu 549 8 appreciate appreciate VB work_ln56cwsp7ffppl4wxeq7osqfuu 549 9 that that DT work_ln56cwsp7ffppl4wxeq7osqfuu 549 10 alternative alternative NN work_ln56cwsp7ffppl4wxeq7osqfuu 549 11 2 2 CD work_ln56cwsp7ffppl4wxeq7osqfuu 549 12 can can MD work_ln56cwsp7ffppl4wxeq7osqfuu 549 13 never never RB work_ln56cwsp7ffppl4wxeq7osqfuu 549 14 be be VB work_ln56cwsp7ffppl4wxeq7osqfuu 549 15 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 549 16 maximax maximax NNP work_ln56cwsp7ffppl4wxeq7osqfuu 549 17 alternative alternative NN work_ln56cwsp7ffppl4wxeq7osqfuu 549 18 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 549 19 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 549 20 hence hence RB work_ln56cwsp7ffppl4wxeq7osqfuu 549 21 γMX(M γmx(m JJ work_ln56cwsp7ffppl4wxeq7osqfuu 549 22 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 549 23 = = NFP work_ln56cwsp7ffppl4wxeq7osqfuu 549 24 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 549 25 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 549 26 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 549 27 0 0 CD work_ln56cwsp7ffppl4wxeq7osqfuu 549 28 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 549 29 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 549 30 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 549 31 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 550 1 Type type NN work_ln56cwsp7ffppl4wxeq7osqfuu 550 2 5 5 CD work_ln56cwsp7ffppl4wxeq7osqfuu 550 3 : : : work_ln56cwsp7ffppl4wxeq7osqfuu 550 4 It -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 550 5 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 550 6 straightforward straightforward JJ work_ln56cwsp7ffppl4wxeq7osqfuu 550 7 that that IN work_ln56cwsp7ffppl4wxeq7osqfuu 550 8 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 550 9 = = SYM work_ln56cwsp7ffppl4wxeq7osqfuu 550 10 γ1MX(M γ1mx(m NN work_ln56cwsp7ffppl4wxeq7osqfuu 550 11 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 550 12 > > XX work_ln56cwsp7ffppl4wxeq7osqfuu 550 13 γ γ DT work_ln56cwsp7ffppl4wxeq7osqfuu 550 14 3 3 CD work_ln56cwsp7ffppl4wxeq7osqfuu 550 15 MX(M mx(m NN work_ln56cwsp7ffppl4wxeq7osqfuu 550 16 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 550 17 > > XX work_ln56cwsp7ffppl4wxeq7osqfuu 550 18 γ γ DT work_ln56cwsp7ffppl4wxeq7osqfuu 550 19 2 2 CD work_ln56cwsp7ffppl4wxeq7osqfuu 550 20 MX(M mx(m NN work_ln56cwsp7ffppl4wxeq7osqfuu 550 21 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 550 22 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 551 1 Finally finally RB work_ln56cwsp7ffppl4wxeq7osqfuu 551 2 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 551 3 taking take VBG work_ln56cwsp7ffppl4wxeq7osqfuu 551 4 into into IN work_ln56cwsp7ffppl4wxeq7osqfuu 551 5 consideration consideration NN work_ln56cwsp7ffppl4wxeq7osqfuu 551 6 all all DT work_ln56cwsp7ffppl4wxeq7osqfuu 551 7 five five CD work_ln56cwsp7ffppl4wxeq7osqfuu 551 8 cases case NNS work_ln56cwsp7ffppl4wxeq7osqfuu 551 9 together together RB work_ln56cwsp7ffppl4wxeq7osqfuu 551 10 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 551 11 explosion explosion NN work_ln56cwsp7ffppl4wxeq7osqfuu 551 12 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 551 13 an an DT work_ln56cwsp7ffppl4wxeq7osqfuu 551 14 optimal optimal JJ work_ln56cwsp7ffppl4wxeq7osqfuu 551 15 decision decision NN work_ln56cwsp7ffppl4wxeq7osqfuu 551 16 rule rule NN work_ln56cwsp7ffppl4wxeq7osqfuu 551 17 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 552 1 The the DT work_ln56cwsp7ffppl4wxeq7osqfuu 552 2 second second JJ work_ln56cwsp7ffppl4wxeq7osqfuu 552 3 part part NN work_ln56cwsp7ffppl4wxeq7osqfuu 552 4 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 552 5 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 552 6 Theorem theorem NN work_ln56cwsp7ffppl4wxeq7osqfuu 552 7 follows follow VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 552 8 trivially trivially RB work_ln56cwsp7ffppl4wxeq7osqfuu 552 9 from from IN work_ln56cwsp7ffppl4wxeq7osqfuu 552 10 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 552 11 above above JJ work_ln56cwsp7ffppl4wxeq7osqfuu 552 12 anal- anal- JJ work_ln56cwsp7ffppl4wxeq7osqfuu 552 13 ysis ysis NN work_ln56cwsp7ffppl4wxeq7osqfuu 552 14 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 553 1 � � JJ work_ln56cwsp7ffppl4wxeq7osqfuu 553 2 Proof Proof NNP work_ln56cwsp7ffppl4wxeq7osqfuu 553 3 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 553 4 Theorem Theorem NNP work_ln56cwsp7ffppl4wxeq7osqfuu 553 5 5.1 5.1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 553 6 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 554 1 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 554 2 1 1 LS work_ln56cwsp7ffppl4wxeq7osqfuu 554 3 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 554 4 Recall recall VB work_ln56cwsp7ffppl4wxeq7osqfuu 554 5 that that IN work_ln56cwsp7ffppl4wxeq7osqfuu 554 6 we -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 554 7 denote denote VBP work_ln56cwsp7ffppl4wxeq7osqfuu 554 8 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 554 9 distribution distribution NN work_ln56cwsp7ffppl4wxeq7osqfuu 554 10 function function NN work_ln56cwsp7ffppl4wxeq7osqfuu 554 11 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 554 12 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 554 13 l l NN work_ln56cwsp7ffppl4wxeq7osqfuu 554 14 - - HYPH work_ln56cwsp7ffppl4wxeq7osqfuu 554 15 th th NNP work_ln56cwsp7ffppl4wxeq7osqfuu 554 16 order order NN work_ln56cwsp7ffppl4wxeq7osqfuu 554 17 statistic statistic NN work_ln56cwsp7ffppl4wxeq7osqfuu 554 18 by by IN work_ln56cwsp7ffppl4wxeq7osqfuu 554 19 F F NNP work_ln56cwsp7ffppl4wxeq7osqfuu 554 20 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 554 21 l)(t l)(t NNP work_ln56cwsp7ffppl4wxeq7osqfuu 554 22 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 554 23 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 555 1 First first RB work_ln56cwsp7ffppl4wxeq7osqfuu 555 2 note note VB work_ln56cwsp7ffppl4wxeq7osqfuu 555 3 that that IN work_ln56cwsp7ffppl4wxeq7osqfuu 555 4 P(Ul(1 p(ul(1 NN work_ln56cwsp7ffppl4wxeq7osqfuu 555 5 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 555 6 ≤ ≤ NN work_ln56cwsp7ffppl4wxeq7osqfuu 555 7 t|M t|m NN work_ln56cwsp7ffppl4wxeq7osqfuu 555 8 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 555 9 = = NFP work_ln56cwsp7ffppl4wxeq7osqfuu 555 10 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 555 11 − − NNP work_ln56cwsp7ffppl4wxeq7osqfuu 555 12 P(U P(U NNP work_ln56cwsp7ffppl4wxeq7osqfuu 555 13 l l NN work_ln56cwsp7ffppl4wxeq7osqfuu 555 14 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 555 15 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 555 16 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 555 17 > > XX work_ln56cwsp7ffppl4wxeq7osqfuu 555 18 t|M t|m NN work_ln56cwsp7ffppl4wxeq7osqfuu 555 19 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 555 20 = = NFP work_ln56cwsp7ffppl4wxeq7osqfuu 555 21 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 555 22 − − NNP work_ln56cwsp7ffppl4wxeq7osqfuu 555 23 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 555 24 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 555 25 −F −F NNP work_ln56cwsp7ffppl4wxeq7osqfuu 555 26 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 555 27 k)(t))l(k k)(t))l(k NNP work_ln56cwsp7ffppl4wxeq7osqfuu 555 28 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 555 29 · · NFP work_ln56cwsp7ffppl4wxeq7osqfuu 555 30 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 556 1 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 557 1 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 558 1 · · NFP work_ln56cwsp7ffppl4wxeq7osqfuu 558 2 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 558 3 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 558 4 −F −F NNP work_ln56cwsp7ffppl4wxeq7osqfuu 558 5 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 558 6 1)(t))l(1 1)(t))l(1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 558 7 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 558 8 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 559 1 Given give VBN work_ln56cwsp7ffppl4wxeq7osqfuu 559 2 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 559 3 symmetry symmetry NN work_ln56cwsp7ffppl4wxeq7osqfuu 559 4 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 559 5 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 559 6 culture culture NN work_ln56cwsp7ffppl4wxeq7osqfuu 559 7 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 559 8 it -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 559 9 follows follow VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 559 10 that that IN work_ln56cwsp7ffppl4wxeq7osqfuu 559 11 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 559 12 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 559 13 every every DT work_ln56cwsp7ffppl4wxeq7osqfuu 559 14 l l NN work_ln56cwsp7ffppl4wxeq7osqfuu 559 15 ∈ ∈ NNP work_ln56cwsp7ffppl4wxeq7osqfuu 559 16 K K NNP work_ln56cwsp7ffppl4wxeq7osqfuu 559 17 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 559 18 F F NNP work_ln56cwsp7ffppl4wxeq7osqfuu 559 19 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 559 20 l)(t l)(t NNP work_ln56cwsp7ffppl4wxeq7osqfuu 559 21 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 559 22 = = SYM work_ln56cwsp7ffppl4wxeq7osqfuu 559 23 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 559 24 − − NNP work_ln56cwsp7ffppl4wxeq7osqfuu 559 25 F F NNP work_ln56cwsp7ffppl4wxeq7osqfuu 559 26 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 559 27 k−l+1)(1 k−l+1)(1 NNP work_ln56cwsp7ffppl4wxeq7osqfuu 559 28 − − NNP work_ln56cwsp7ffppl4wxeq7osqfuu 559 29 t t NNP work_ln56cwsp7ffppl4wxeq7osqfuu 559 30 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 559 31 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 560 1 Therefore therefore RB work_ln56cwsp7ffppl4wxeq7osqfuu 560 2 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 560 3 P(Ul(1 p(ul(1 NN work_ln56cwsp7ffppl4wxeq7osqfuu 560 4 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 560 5 ≤ ≤ NN work_ln56cwsp7ffppl4wxeq7osqfuu 560 6 t|M t|m NN work_ln56cwsp7ffppl4wxeq7osqfuu 560 7 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 560 8 = = NFP work_ln56cwsp7ffppl4wxeq7osqfuu 560 9 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 560 10 −F −f NN work_ln56cwsp7ffppl4wxeq7osqfuu 560 11 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 560 12 1)(1 1)(1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 560 13 − − NNP work_ln56cwsp7ffppl4wxeq7osqfuu 560 14 t)l(k t)l(k NNP work_ln56cwsp7ffppl4wxeq7osqfuu 560 15 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 560 16 · · NFP work_ln56cwsp7ffppl4wxeq7osqfuu 560 17 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 561 1 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 562 1 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 563 1 · · NFP work_ln56cwsp7ffppl4wxeq7osqfuu 563 2 F F NNP work_ln56cwsp7ffppl4wxeq7osqfuu 563 3 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 563 4 k)(1 k)(1 NNP work_ln56cwsp7ffppl4wxeq7osqfuu 563 5 − − NNP work_ln56cwsp7ffppl4wxeq7osqfuu 563 6 t)l(1 t)l(1 , work_ln56cwsp7ffppl4wxeq7osqfuu 563 7 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 563 8 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 564 1 The the DT work_ln56cwsp7ffppl4wxeq7osqfuu 564 2 latter latter JJ work_ln56cwsp7ffppl4wxeq7osqfuu 564 3 expression expression NN work_ln56cwsp7ffppl4wxeq7osqfuu 564 4 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 564 5 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 564 6 −P(Ul(n −P(Ul(n NNP work_ln56cwsp7ffppl4wxeq7osqfuu 564 7 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 564 8 ≤ ≤ NN work_ln56cwsp7ffppl4wxeq7osqfuu 564 9 t|(k t|(k NNS work_ln56cwsp7ffppl4wxeq7osqfuu 564 10 + + SYM work_ln56cwsp7ffppl4wxeq7osqfuu 564 11 1)1 1)1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 564 12 − − NNP work_ln56cwsp7ffppl4wxeq7osqfuu 564 13 M M NNP work_ln56cwsp7ffppl4wxeq7osqfuu 564 14 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 564 15 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 565 1 It -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 565 2 follows follow VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 565 3 that that IN work_ln56cwsp7ffppl4wxeq7osqfuu 565 4 E[Ul(1 e[ul(1 NN work_ln56cwsp7ffppl4wxeq7osqfuu 565 5 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 565 6 | | NNP work_ln56cwsp7ffppl4wxeq7osqfuu 565 7 M M NNP work_ln56cwsp7ffppl4wxeq7osqfuu 565 8 ] ] -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 565 9 = = SYM work_ln56cwsp7ffppl4wxeq7osqfuu 565 10 E[U E[U NNP work_ln56cwsp7ffppl4wxeq7osqfuu 565 11 l l NN work_ln56cwsp7ffppl4wxeq7osqfuu 565 12 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 565 13 n n NNP work_ln56cwsp7ffppl4wxeq7osqfuu 565 14 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 565 15 | | NNP work_ln56cwsp7ffppl4wxeq7osqfuu 565 16 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 565 17 k k NN work_ln56cwsp7ffppl4wxeq7osqfuu 565 18 + + CC work_ln56cwsp7ffppl4wxeq7osqfuu 565 19 1)1 1)1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 565 20 − − NNP work_ln56cwsp7ffppl4wxeq7osqfuu 565 21 M M NNP work_ln56cwsp7ffppl4wxeq7osqfuu 565 22 ] ] -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 565 23 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 565 24 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 565 25 hence hence RB work_ln56cwsp7ffppl4wxeq7osqfuu 565 26 αlMN αlMN NNP work_ln56cwsp7ffppl4wxeq7osqfuu 565 27 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 565 28 M m NN work_ln56cwsp7ffppl4wxeq7osqfuu 565 29 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 565 30 = = NFP work_ln56cwsp7ffppl4wxeq7osqfuu 565 31 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 565 32 −α −α CD work_ln56cwsp7ffppl4wxeq7osqfuu 565 33 l l NN work_ln56cwsp7ffppl4wxeq7osqfuu 565 34 MX((k MX((k NNP work_ln56cwsp7ffppl4wxeq7osqfuu 565 35 + + CC work_ln56cwsp7ffppl4wxeq7osqfuu 565 36 1)1 1)1 NNP work_ln56cwsp7ffppl4wxeq7osqfuu 565 37 −M −M NNP work_ln56cwsp7ffppl4wxeq7osqfuu 565 38 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 565 39 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 566 1 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 566 2 2 2 LS work_ln56cwsp7ffppl4wxeq7osqfuu 566 3 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 566 4 Given give VBN work_ln56cwsp7ffppl4wxeq7osqfuu 566 5 M M NNP work_ln56cwsp7ffppl4wxeq7osqfuu 566 6 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 566 7 βlMN βlMN NNP work_ln56cwsp7ffppl4wxeq7osqfuu 566 8 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 566 9 M M NNP work_ln56cwsp7ffppl4wxeq7osqfuu 566 10 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 566 11 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 566 12 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 566 13 probability probability NN work_ln56cwsp7ffppl4wxeq7osqfuu 566 14 that that IN work_ln56cwsp7ffppl4wxeq7osqfuu 566 15 alternative alternative JJ work_ln56cwsp7ffppl4wxeq7osqfuu 566 16 l l NNP work_ln56cwsp7ffppl4wxeq7osqfuu 566 17 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 566 18 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 566 19 best good JJS work_ln56cwsp7ffppl4wxeq7osqfuu 566 20 maximin maximin NN work_ln56cwsp7ffppl4wxeq7osqfuu 566 21 alternative alternative NN work_ln56cwsp7ffppl4wxeq7osqfuu 566 22 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 567 1 That that RB work_ln56cwsp7ffppl4wxeq7osqfuu 567 2 is is RB work_ln56cwsp7ffppl4wxeq7osqfuu 567 3 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 567 4 βlMN βlMN NNP work_ln56cwsp7ffppl4wxeq7osqfuu 567 5 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 567 6 M M NNP work_ln56cwsp7ffppl4wxeq7osqfuu 567 7 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 567 8 = = NFP work_ln56cwsp7ffppl4wxeq7osqfuu 567 9 P(U P(U NNP work_ln56cwsp7ffppl4wxeq7osqfuu 567 10 l l NN work_ln56cwsp7ffppl4wxeq7osqfuu 567 11 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 567 12 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 567 13 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 567 14 > > XX work_ln56cwsp7ffppl4wxeq7osqfuu 567 15 U u NN work_ln56cwsp7ffppl4wxeq7osqfuu 567 16 h h NN work_ln56cwsp7ffppl4wxeq7osqfuu 567 17 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 567 18 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 567 19 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 567 20 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 567 21 all all DT work_ln56cwsp7ffppl4wxeq7osqfuu 567 22 h h NN work_ln56cwsp7ffppl4wxeq7osqfuu 567 23 ∈ ∈ NNP work_ln56cwsp7ffppl4wxeq7osqfuu 567 24 K k NN work_ln56cwsp7ffppl4wxeq7osqfuu 567 25 \ \ NN work_ln56cwsp7ffppl4wxeq7osqfuu 567 26 { { -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 567 27 l l NN work_ln56cwsp7ffppl4wxeq7osqfuu 567 28 } } -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 567 29 | | NNP work_ln56cwsp7ffppl4wxeq7osqfuu 567 30 M M NNP work_ln56cwsp7ffppl4wxeq7osqfuu 567 31 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 567 32 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 568 1 Equiv- Equiv- NNP work_ln56cwsp7ffppl4wxeq7osqfuu 568 2 alently alently RB work_ln56cwsp7ffppl4wxeq7osqfuu 568 3 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 568 4 βlMN βlMN NNP work_ln56cwsp7ffppl4wxeq7osqfuu 568 5 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 568 6 M M NNP work_ln56cwsp7ffppl4wxeq7osqfuu 568 7 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 568 8 = = NFP work_ln56cwsp7ffppl4wxeq7osqfuu 568 9 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 568 10 − − NNP work_ln56cwsp7ffppl4wxeq7osqfuu 568 11 P(There p(there PRP work_ln56cwsp7ffppl4wxeq7osqfuu 568 12 exists exist VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 568 13 h h NNP work_ln56cwsp7ffppl4wxeq7osqfuu 568 14 ∈ ∈ NNP work_ln56cwsp7ffppl4wxeq7osqfuu 568 15 K k NN work_ln56cwsp7ffppl4wxeq7osqfuu 568 16 \ \ NN work_ln56cwsp7ffppl4wxeq7osqfuu 568 17 { { -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 568 18 l l NN work_ln56cwsp7ffppl4wxeq7osqfuu 568 19 } } -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 568 20 such such JJ work_ln56cwsp7ffppl4wxeq7osqfuu 568 21 that that IN work_ln56cwsp7ffppl4wxeq7osqfuu 568 22 U U NNP work_ln56cwsp7ffppl4wxeq7osqfuu 568 23 l l NN work_ln56cwsp7ffppl4wxeq7osqfuu 568 24 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 568 25 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 568 26 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 568 27 < < XX work_ln56cwsp7ffppl4wxeq7osqfuu 568 28 U u NN work_ln56cwsp7ffppl4wxeq7osqfuu 568 29 h h NN work_ln56cwsp7ffppl4wxeq7osqfuu 568 30 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 568 31 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 568 32 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 568 33 | | NNP work_ln56cwsp7ffppl4wxeq7osqfuu 568 34 M M NNP work_ln56cwsp7ffppl4wxeq7osqfuu 568 35 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 568 36 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 569 1 For for IN work_ln56cwsp7ffppl4wxeq7osqfuu 569 2 every every DT work_ln56cwsp7ffppl4wxeq7osqfuu 569 3 symmetric symmetric JJ work_ln56cwsp7ffppl4wxeq7osqfuu 569 4 culture culture NN work_ln56cwsp7ffppl4wxeq7osqfuu 569 5 we -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 569 6 then then RB work_ln56cwsp7ffppl4wxeq7osqfuu 569 7 have have VBP work_ln56cwsp7ffppl4wxeq7osqfuu 569 8 that that DT work_ln56cwsp7ffppl4wxeq7osqfuu 569 9 βlMN βlMN NNP work_ln56cwsp7ffppl4wxeq7osqfuu 569 10 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 569 11 M M NNP work_ln56cwsp7ffppl4wxeq7osqfuu 569 12 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 569 13 = = NFP work_ln56cwsp7ffppl4wxeq7osqfuu 569 14 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 569 15 − − NNP work_ln56cwsp7ffppl4wxeq7osqfuu 569 16 P(There p(there PRP work_ln56cwsp7ffppl4wxeq7osqfuu 569 17 exists exist VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 569 18 h h NN work_ln56cwsp7ffppl4wxeq7osqfuu 569 19 ∈ ∈ NNP work_ln56cwsp7ffppl4wxeq7osqfuu 569 20 K K NNP work_ln56cwsp7ffppl4wxeq7osqfuu 569 21 \{l \{l NNP work_ln56cwsp7ffppl4wxeq7osqfuu 569 22 } } -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 569 23 such such JJ work_ln56cwsp7ffppl4wxeq7osqfuu 569 24 that that IN work_ln56cwsp7ffppl4wxeq7osqfuu 569 25 Ul(n Ul(n NNP work_ln56cwsp7ffppl4wxeq7osqfuu 569 26 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 569 27 > > XX work_ln56cwsp7ffppl4wxeq7osqfuu 569 28 U u NN work_ln56cwsp7ffppl4wxeq7osqfuu 569 29 h h NN work_ln56cwsp7ffppl4wxeq7osqfuu 569 30 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 569 31 n n NNP work_ln56cwsp7ffppl4wxeq7osqfuu 569 32 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 569 33 | | NNP work_ln56cwsp7ffppl4wxeq7osqfuu 569 34 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 569 35 k k NN work_ln56cwsp7ffppl4wxeq7osqfuu 569 36 + + CC work_ln56cwsp7ffppl4wxeq7osqfuu 569 37 1)1 1)1 NNP work_ln56cwsp7ffppl4wxeq7osqfuu 569 38 −M −M NNP work_ln56cwsp7ffppl4wxeq7osqfuu 569 39 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 569 40 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 570 1 The the DT work_ln56cwsp7ffppl4wxeq7osqfuu 570 2 latter latter JJ work_ln56cwsp7ffppl4wxeq7osqfuu 570 3 expression expression NN work_ln56cwsp7ffppl4wxeq7osqfuu 570 4 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 570 5 equivalent equivalent JJ work_ln56cwsp7ffppl4wxeq7osqfuu 570 6 to to IN work_ln56cwsp7ffppl4wxeq7osqfuu 570 7 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 570 8 −γlMX((k −γlmx((k NN work_ln56cwsp7ffppl4wxeq7osqfuu 570 9 + + CC work_ln56cwsp7ffppl4wxeq7osqfuu 570 10 1)1 1)1 NNP work_ln56cwsp7ffppl4wxeq7osqfuu 570 11 −M −M NNP work_ln56cwsp7ffppl4wxeq7osqfuu 570 12 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 570 13 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 571 1 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 571 2 3 3 LS work_ln56cwsp7ffppl4wxeq7osqfuu 571 3 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 571 4 Given give VBN work_ln56cwsp7ffppl4wxeq7osqfuu 571 5 M M NNP work_ln56cwsp7ffppl4wxeq7osqfuu 571 6 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 571 7 γlMN γlMN NNP work_ln56cwsp7ffppl4wxeq7osqfuu 571 8 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 571 9 M M NNP work_ln56cwsp7ffppl4wxeq7osqfuu 571 10 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 571 11 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 571 12 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 571 13 probability probability NN work_ln56cwsp7ffppl4wxeq7osqfuu 571 14 that that IN work_ln56cwsp7ffppl4wxeq7osqfuu 571 15 alternative alternative JJ work_ln56cwsp7ffppl4wxeq7osqfuu 571 16 l l NNP work_ln56cwsp7ffppl4wxeq7osqfuu 571 17 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 571 18 not not RB work_ln56cwsp7ffppl4wxeq7osqfuu 571 19 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 571 20 worst bad JJS work_ln56cwsp7ffppl4wxeq7osqfuu 571 21 max- max- NNP work_ln56cwsp7ffppl4wxeq7osqfuu 571 22 imin imin NNP work_ln56cwsp7ffppl4wxeq7osqfuu 571 23 alternative alternative NN work_ln56cwsp7ffppl4wxeq7osqfuu 571 24 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 572 1 That that RB work_ln56cwsp7ffppl4wxeq7osqfuu 572 2 is is RB work_ln56cwsp7ffppl4wxeq7osqfuu 572 3 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 572 4 γlMN γlMN NNP work_ln56cwsp7ffppl4wxeq7osqfuu 572 5 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 572 6 M M NNP work_ln56cwsp7ffppl4wxeq7osqfuu 572 7 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 572 8 = = NFP work_ln56cwsp7ffppl4wxeq7osqfuu 572 9 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 572 10 − − NNP work_ln56cwsp7ffppl4wxeq7osqfuu 572 11 P(U P(U NNP work_ln56cwsp7ffppl4wxeq7osqfuu 572 12 l l NN work_ln56cwsp7ffppl4wxeq7osqfuu 572 13 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 572 14 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 572 15 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 572 16 < < XX work_ln56cwsp7ffppl4wxeq7osqfuu 572 17 U u NN work_ln56cwsp7ffppl4wxeq7osqfuu 572 18 h h NN work_ln56cwsp7ffppl4wxeq7osqfuu 572 19 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 572 20 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 572 21 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 572 22 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 572 23 all all DT work_ln56cwsp7ffppl4wxeq7osqfuu 572 24 h h NN work_ln56cwsp7ffppl4wxeq7osqfuu 572 25 ∈ ∈ NNP work_ln56cwsp7ffppl4wxeq7osqfuu 572 26 K k NN work_ln56cwsp7ffppl4wxeq7osqfuu 572 27 \ \ NN work_ln56cwsp7ffppl4wxeq7osqfuu 572 28 { { -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 572 29 l l NN work_ln56cwsp7ffppl4wxeq7osqfuu 572 30 } } -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 572 31 | | NNP work_ln56cwsp7ffppl4wxeq7osqfuu 572 32 M M NNP work_ln56cwsp7ffppl4wxeq7osqfuu 572 33 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 572 34 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 573 1 Equivalently equivalently RB work_ln56cwsp7ffppl4wxeq7osqfuu 573 2 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 573 3 γlMN γlMN NNP work_ln56cwsp7ffppl4wxeq7osqfuu 573 4 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 573 5 M M NNP work_ln56cwsp7ffppl4wxeq7osqfuu 573 6 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 573 7 = = NFP work_ln56cwsp7ffppl4wxeq7osqfuu 573 8 P(There p(there NN work_ln56cwsp7ffppl4wxeq7osqfuu 573 9 exists exist VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 573 10 h h NNP work_ln56cwsp7ffppl4wxeq7osqfuu 573 11 ∈ ∈ NNP work_ln56cwsp7ffppl4wxeq7osqfuu 573 12 K k NN work_ln56cwsp7ffppl4wxeq7osqfuu 573 13 \ \ NN work_ln56cwsp7ffppl4wxeq7osqfuu 573 14 { { -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 573 15 l l NN work_ln56cwsp7ffppl4wxeq7osqfuu 573 16 } } -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 573 17 such such JJ work_ln56cwsp7ffppl4wxeq7osqfuu 573 18 that that IN work_ln56cwsp7ffppl4wxeq7osqfuu 573 19 U U NNP work_ln56cwsp7ffppl4wxeq7osqfuu 573 20 l l NN work_ln56cwsp7ffppl4wxeq7osqfuu 573 21 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 573 22 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 573 23 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 573 24 > > XX work_ln56cwsp7ffppl4wxeq7osqfuu 573 25 U u NN work_ln56cwsp7ffppl4wxeq7osqfuu 573 26 h h NN work_ln56cwsp7ffppl4wxeq7osqfuu 573 27 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 573 28 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 573 29 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 573 30 | | NNP work_ln56cwsp7ffppl4wxeq7osqfuu 573 31 M M NNP work_ln56cwsp7ffppl4wxeq7osqfuu 573 32 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 573 33 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 574 1 For for IN work_ln56cwsp7ffppl4wxeq7osqfuu 574 2 every every DT work_ln56cwsp7ffppl4wxeq7osqfuu 574 3 symmetric symmetric JJ work_ln56cwsp7ffppl4wxeq7osqfuu 574 4 culture culture NN work_ln56cwsp7ffppl4wxeq7osqfuu 574 5 we -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 574 6 then then RB work_ln56cwsp7ffppl4wxeq7osqfuu 574 7 have have VBP work_ln56cwsp7ffppl4wxeq7osqfuu 574 8 that that DT work_ln56cwsp7ffppl4wxeq7osqfuu 574 9 γlMN γlMN NNP work_ln56cwsp7ffppl4wxeq7osqfuu 574 10 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 574 11 M m NN work_ln56cwsp7ffppl4wxeq7osqfuu 574 12 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 574 13 = = NFP work_ln56cwsp7ffppl4wxeq7osqfuu 574 14 P(There p(there NN work_ln56cwsp7ffppl4wxeq7osqfuu 574 15 exists exist VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 574 16 h h NNP work_ln56cwsp7ffppl4wxeq7osqfuu 574 17 ∈ ∈ NNP work_ln56cwsp7ffppl4wxeq7osqfuu 574 18 K k NN work_ln56cwsp7ffppl4wxeq7osqfuu 574 19 \ \ NN work_ln56cwsp7ffppl4wxeq7osqfuu 574 20 { { -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 574 21 l l NN work_ln56cwsp7ffppl4wxeq7osqfuu 574 22 } } -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 574 23 such such JJ work_ln56cwsp7ffppl4wxeq7osqfuu 574 24 that that IN work_ln56cwsp7ffppl4wxeq7osqfuu 574 25 Ul(n Ul(n NNP work_ln56cwsp7ffppl4wxeq7osqfuu 574 26 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 574 27 < < XX work_ln56cwsp7ffppl4wxeq7osqfuu 574 28 U u NN work_ln56cwsp7ffppl4wxeq7osqfuu 574 29 h h NN work_ln56cwsp7ffppl4wxeq7osqfuu 574 30 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 574 31 n n NN work_ln56cwsp7ffppl4wxeq7osqfuu 574 32 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 574 33 | | NNP work_ln56cwsp7ffppl4wxeq7osqfuu 574 34 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 574 35 k k NN work_ln56cwsp7ffppl4wxeq7osqfuu 574 36 + + CC work_ln56cwsp7ffppl4wxeq7osqfuu 574 37 1)1 1)1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 574 38 − − NNP work_ln56cwsp7ffppl4wxeq7osqfuu 574 39 M M NNP work_ln56cwsp7ffppl4wxeq7osqfuu 574 40 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 574 41 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 575 1 The the DT work_ln56cwsp7ffppl4wxeq7osqfuu 575 2 latter latter JJ work_ln56cwsp7ffppl4wxeq7osqfuu 575 3 expression expression NN work_ln56cwsp7ffppl4wxeq7osqfuu 575 4 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 575 5 equiva- equiva- NNP work_ln56cwsp7ffppl4wxeq7osqfuu 575 6 lent lend VBN work_ln56cwsp7ffppl4wxeq7osqfuu 575 7 to to IN work_ln56cwsp7ffppl4wxeq7osqfuu 575 8 1−P(Ul(n 1−P(Ul(n NNP work_ln56cwsp7ffppl4wxeq7osqfuu 575 9 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 575 10 > > XX work_ln56cwsp7ffppl4wxeq7osqfuu 575 11 U u NN work_ln56cwsp7ffppl4wxeq7osqfuu 575 12 h h NN work_ln56cwsp7ffppl4wxeq7osqfuu 575 13 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 575 14 n n NN work_ln56cwsp7ffppl4wxeq7osqfuu 575 15 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 575 16 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 575 17 all all DT work_ln56cwsp7ffppl4wxeq7osqfuu 575 18 h h NN work_ln56cwsp7ffppl4wxeq7osqfuu 575 19 ∈ ∈ JJ work_ln56cwsp7ffppl4wxeq7osqfuu 575 20 K\{l k\{l NN work_ln56cwsp7ffppl4wxeq7osqfuu 575 21 } } -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 575 22 | | NNP work_ln56cwsp7ffppl4wxeq7osqfuu 575 23 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 575 24 k+1)1−M k+1)1−M NNP work_ln56cwsp7ffppl4wxeq7osqfuu 575 25 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 575 26 = = NFP work_ln56cwsp7ffppl4wxeq7osqfuu 575 27 1−β 1−β CD work_ln56cwsp7ffppl4wxeq7osqfuu 575 28 l l NNP work_ln56cwsp7ffppl4wxeq7osqfuu 575 29 MX((k+1)1−M mx((k+1)1−m NN work_ln56cwsp7ffppl4wxeq7osqfuu 575 30 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 575 31 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 575 32 � � NNP work_ln56cwsp7ffppl4wxeq7osqfuu 575 33 23 23 CD work_ln56cwsp7ffppl4wxeq7osqfuu 575 34 Appendix Appendix NNP work_ln56cwsp7ffppl4wxeq7osqfuu 575 35 B. B. NNP work_ln56cwsp7ffppl4wxeq7osqfuu 575 36 Computational Computational NNP work_ln56cwsp7ffppl4wxeq7osqfuu 575 37 Analysis10 Analysis10 NNP work_ln56cwsp7ffppl4wxeq7osqfuu 575 38 In in IN work_ln56cwsp7ffppl4wxeq7osqfuu 575 39 this this DT work_ln56cwsp7ffppl4wxeq7osqfuu 575 40 section section NN work_ln56cwsp7ffppl4wxeq7osqfuu 575 41 we -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 575 42 provide provide VBP work_ln56cwsp7ffppl4wxeq7osqfuu 575 43 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 575 44 technical technical JJ work_ln56cwsp7ffppl4wxeq7osqfuu 575 45 details detail NNS work_ln56cwsp7ffppl4wxeq7osqfuu 575 46 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 575 47 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 575 48 computational computational JJ work_ln56cwsp7ffppl4wxeq7osqfuu 575 49 analysis analysis NN work_ln56cwsp7ffppl4wxeq7osqfuu 575 50 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 575 51 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 575 52 report report VB work_ln56cwsp7ffppl4wxeq7osqfuu 575 53 some some DT work_ln56cwsp7ffppl4wxeq7osqfuu 575 54 further further JJ work_ln56cwsp7ffppl4wxeq7osqfuu 575 55 results result NNS work_ln56cwsp7ffppl4wxeq7osqfuu 575 56 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 576 1 We -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 576 2 study study VBP work_ln56cwsp7ffppl4wxeq7osqfuu 576 3 societies society NNS work_ln56cwsp7ffppl4wxeq7osqfuu 576 4 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 576 5 size size NN work_ln56cwsp7ffppl4wxeq7osqfuu 576 6 n×k n×k NNP work_ln56cwsp7ffppl4wxeq7osqfuu 576 7 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 576 8 with with IN work_ln56cwsp7ffppl4wxeq7osqfuu 576 9 n×k n×k NNP work_ln56cwsp7ffppl4wxeq7osqfuu 576 10 ∈{2 ∈{2 NNP work_ln56cwsp7ffppl4wxeq7osqfuu 576 11 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 576 12 3 3 CD work_ln56cwsp7ffppl4wxeq7osqfuu 576 13 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 576 14 5 5 CD work_ln56cwsp7ffppl4wxeq7osqfuu 576 15 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 576 16 10 10 CD work_ln56cwsp7ffppl4wxeq7osqfuu 576 17 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 576 18 100}×{3 100}×{3 CD work_ln56cwsp7ffppl4wxeq7osqfuu 576 19 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 576 20 4 4 CD work_ln56cwsp7ffppl4wxeq7osqfuu 576 21 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 576 22 5 5 CD work_ln56cwsp7ffppl4wxeq7osqfuu 576 23 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 576 24 7 7 CD work_ln56cwsp7ffppl4wxeq7osqfuu 576 25 } } -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 576 26 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 576 27 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 576 28 three three CD work_ln56cwsp7ffppl4wxeq7osqfuu 576 29 different different JJ work_ln56cwsp7ffppl4wxeq7osqfuu 576 30 cultures culture NNS work_ln56cwsp7ffppl4wxeq7osqfuu 576 31 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 577 1 First first RB work_ln56cwsp7ffppl4wxeq7osqfuu 577 2 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 577 3 we -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 577 4 consider consider VBP work_ln56cwsp7ffppl4wxeq7osqfuu 577 5 societies society NNS work_ln56cwsp7ffppl4wxeq7osqfuu 577 6 where where WRB work_ln56cwsp7ffppl4wxeq7osqfuu 577 7 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 577 8 utility utility NN work_ln56cwsp7ffppl4wxeq7osqfuu 577 9 values value NNS work_ln56cwsp7ffppl4wxeq7osqfuu 577 10 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 577 11 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 577 12 individu- individu- NN work_ln56cwsp7ffppl4wxeq7osqfuu 577 13 als als NN work_ln56cwsp7ffppl4wxeq7osqfuu 577 14 are be VBP work_ln56cwsp7ffppl4wxeq7osqfuu 577 15 drawn draw VBN work_ln56cwsp7ffppl4wxeq7osqfuu 577 16 independently independently RB work_ln56cwsp7ffppl4wxeq7osqfuu 577 17 from from IN work_ln56cwsp7ffppl4wxeq7osqfuu 577 18 a a DT work_ln56cwsp7ffppl4wxeq7osqfuu 577 19 uniform uniform JJ work_ln56cwsp7ffppl4wxeq7osqfuu 577 20 distribution distribution NN work_ln56cwsp7ffppl4wxeq7osqfuu 577 21 on on IN work_ln56cwsp7ffppl4wxeq7osqfuu 577 22 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 577 23 interval interval NN work_ln56cwsp7ffppl4wxeq7osqfuu 577 24 [ [ -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 577 25 0 0 CD work_ln56cwsp7ffppl4wxeq7osqfuu 577 26 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 577 27 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 577 28 ] ] -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 577 29 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 578 1 Second second JJ work_ln56cwsp7ffppl4wxeq7osqfuu 578 2 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 578 3 we -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 578 4 consider consider VBP work_ln56cwsp7ffppl4wxeq7osqfuu 578 5 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 578 6 standard standard JJ work_ln56cwsp7ffppl4wxeq7osqfuu 578 7 normal normal JJ work_ln56cwsp7ffppl4wxeq7osqfuu 578 8 distribution distribution NN work_ln56cwsp7ffppl4wxeq7osqfuu 578 9 in in IN work_ln56cwsp7ffppl4wxeq7osqfuu 578 10 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 578 11 interval interval NN work_ln56cwsp7ffppl4wxeq7osqfuu 578 12 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 578 13 −∞,∞ −∞,∞ NNP work_ln56cwsp7ffppl4wxeq7osqfuu 578 14 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 578 15 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 579 1 Finally finally RB work_ln56cwsp7ffppl4wxeq7osqfuu 579 2 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 579 3 to to TO work_ln56cwsp7ffppl4wxeq7osqfuu 579 4 study study VB work_ln56cwsp7ffppl4wxeq7osqfuu 579 5 societies society NNS work_ln56cwsp7ffppl4wxeq7osqfuu 579 6 with with IN work_ln56cwsp7ffppl4wxeq7osqfuu 579 7 cultures culture NNS work_ln56cwsp7ffppl4wxeq7osqfuu 579 8 having have VBG work_ln56cwsp7ffppl4wxeq7osqfuu 579 9 asymmetric asymmetric JJ work_ln56cwsp7ffppl4wxeq7osqfuu 579 10 density density NN work_ln56cwsp7ffppl4wxeq7osqfuu 579 11 functions function NNS work_ln56cwsp7ffppl4wxeq7osqfuu 579 12 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 579 13 we -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 579 14 study study VBP work_ln56cwsp7ffppl4wxeq7osqfuu 579 15 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 579 16 case case NN work_ln56cwsp7ffppl4wxeq7osqfuu 579 17 where where WRB work_ln56cwsp7ffppl4wxeq7osqfuu 579 18 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 579 19 utility utility NN work_ln56cwsp7ffppl4wxeq7osqfuu 579 20 values value NNS work_ln56cwsp7ffppl4wxeq7osqfuu 579 21 are be VBP work_ln56cwsp7ffppl4wxeq7osqfuu 579 22 drawn draw VBN work_ln56cwsp7ffppl4wxeq7osqfuu 579 23 independently independently RB work_ln56cwsp7ffppl4wxeq7osqfuu 579 24 from from IN work_ln56cwsp7ffppl4wxeq7osqfuu 579 25 an an DT work_ln56cwsp7ffppl4wxeq7osqfuu 579 26 exponential exponential JJ work_ln56cwsp7ffppl4wxeq7osqfuu 579 27 distribution distribution NN work_ln56cwsp7ffppl4wxeq7osqfuu 579 28 with with IN work_ln56cwsp7ffppl4wxeq7osqfuu 579 29 λ λ NN work_ln56cwsp7ffppl4wxeq7osqfuu 579 30 = = SYM work_ln56cwsp7ffppl4wxeq7osqfuu 579 31 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 579 32 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 580 1 For for IN work_ln56cwsp7ffppl4wxeq7osqfuu 580 2 every every DT work_ln56cwsp7ffppl4wxeq7osqfuu 580 3 single single JJ work_ln56cwsp7ffppl4wxeq7osqfuu 580 4 size size NN work_ln56cwsp7ffppl4wxeq7osqfuu 580 5 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 580 6 society society NN work_ln56cwsp7ffppl4wxeq7osqfuu 580 7 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 580 8 culture culture NN work_ln56cwsp7ffppl4wxeq7osqfuu 580 9 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 580 10 we -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 580 11 independently independently RB work_ln56cwsp7ffppl4wxeq7osqfuu 580 12 draw draw VBP work_ln56cwsp7ffppl4wxeq7osqfuu 580 13 3 3 CD work_ln56cwsp7ffppl4wxeq7osqfuu 580 14 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 580 15 841 841 CD work_ln56cwsp7ffppl4wxeq7osqfuu 580 16 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 580 17 600 600 CD work_ln56cwsp7ffppl4wxeq7osqfuu 580 18 car- car- NN work_ln56cwsp7ffppl4wxeq7osqfuu 580 19 dinal dinal JJ work_ln56cwsp7ffppl4wxeq7osqfuu 580 20 societies society NNS work_ln56cwsp7ffppl4wxeq7osqfuu 580 21 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 581 1 Then then RB work_ln56cwsp7ffppl4wxeq7osqfuu 581 2 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 581 3 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 581 4 every every DT work_ln56cwsp7ffppl4wxeq7osqfuu 581 5 combination combination NN work_ln56cwsp7ffppl4wxeq7osqfuu 581 6 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 581 7 size size NN work_ln56cwsp7ffppl4wxeq7osqfuu 581 8 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 581 9 society society NN work_ln56cwsp7ffppl4wxeq7osqfuu 581 10 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 581 11 culture culture NN work_ln56cwsp7ffppl4wxeq7osqfuu 581 12 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 581 13 we -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 581 14 check check VBP work_ln56cwsp7ffppl4wxeq7osqfuu 581 15 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 581 16 performance performance NN work_ln56cwsp7ffppl4wxeq7osqfuu 581 17 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 581 18 a a DT work_ln56cwsp7ffppl4wxeq7osqfuu 581 19 set set NN work_ln56cwsp7ffppl4wxeq7osqfuu 581 20 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 581 21 scoring score VBG work_ln56cwsp7ffppl4wxeq7osqfuu 581 22 rules rule NNS work_ln56cwsp7ffppl4wxeq7osqfuu 581 23 across across IN work_ln56cwsp7ffppl4wxeq7osqfuu 581 24 all all PDT work_ln56cwsp7ffppl4wxeq7osqfuu 581 25 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 581 26 3 3 CD work_ln56cwsp7ffppl4wxeq7osqfuu 581 27 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 581 28 841 841 CD work_ln56cwsp7ffppl4wxeq7osqfuu 581 29 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 581 30 600 600 CD work_ln56cwsp7ffppl4wxeq7osqfuu 581 31 simulated simulate VBN work_ln56cwsp7ffppl4wxeq7osqfuu 581 32 cardinal cardinal JJ work_ln56cwsp7ffppl4wxeq7osqfuu 581 33 societies society NNS work_ln56cwsp7ffppl4wxeq7osqfuu 581 34 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 582 1 The the DT work_ln56cwsp7ffppl4wxeq7osqfuu 582 2 set set NN work_ln56cwsp7ffppl4wxeq7osqfuu 582 3 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 582 4 scoring score VBG work_ln56cwsp7ffppl4wxeq7osqfuu 582 5 rules rule NNS work_ln56cwsp7ffppl4wxeq7osqfuu 582 6 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 582 7 defined define VBN work_ln56cwsp7ffppl4wxeq7osqfuu 582 8 as as IN work_ln56cwsp7ffppl4wxeq7osqfuu 582 9 follows follow VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 582 10 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 583 1 We -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 583 2 randomly randomly RB work_ln56cwsp7ffppl4wxeq7osqfuu 583 3 generate generate VBP work_ln56cwsp7ffppl4wxeq7osqfuu 583 4 47 47 CD work_ln56cwsp7ffppl4wxeq7osqfuu 583 5 scoring score VBG work_ln56cwsp7ffppl4wxeq7osqfuu 583 6 rules rule NNS work_ln56cwsp7ffppl4wxeq7osqfuu 583 7 by by IN work_ln56cwsp7ffppl4wxeq7osqfuu 583 8 independently independently RB work_ln56cwsp7ffppl4wxeq7osqfuu 583 9 drawing draw VBG work_ln56cwsp7ffppl4wxeq7osqfuu 583 10 values value NNS work_ln56cwsp7ffppl4wxeq7osqfuu 583 11 from from IN work_ln56cwsp7ffppl4wxeq7osqfuu 583 12 a a DT work_ln56cwsp7ffppl4wxeq7osqfuu 583 13 uniform uniform JJ work_ln56cwsp7ffppl4wxeq7osqfuu 583 14 distribution distribution NN work_ln56cwsp7ffppl4wxeq7osqfuu 583 15 on on IN work_ln56cwsp7ffppl4wxeq7osqfuu 583 16 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 583 17 in- in- JJ work_ln56cwsp7ffppl4wxeq7osqfuu 583 18 terval terval NN work_ln56cwsp7ffppl4wxeq7osqfuu 583 19 [ [ -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 583 20 0 0 CD work_ln56cwsp7ffppl4wxeq7osqfuu 583 21 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 583 22 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 583 23 ] ] -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 583 24 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 584 1 Apart apart RB work_ln56cwsp7ffppl4wxeq7osqfuu 584 2 from from IN work_ln56cwsp7ffppl4wxeq7osqfuu 584 3 this this DT work_ln56cwsp7ffppl4wxeq7osqfuu 584 4 47 47 CD work_ln56cwsp7ffppl4wxeq7osqfuu 584 5 randomly randomly RB work_ln56cwsp7ffppl4wxeq7osqfuu 584 6 - - HYPH work_ln56cwsp7ffppl4wxeq7osqfuu 584 7 generated generate VBN work_ln56cwsp7ffppl4wxeq7osqfuu 584 8 scoring score VBG work_ln56cwsp7ffppl4wxeq7osqfuu 584 9 rules rule NNS work_ln56cwsp7ffppl4wxeq7osqfuu 584 10 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 584 11 our -PRON- PRP$ work_ln56cwsp7ffppl4wxeq7osqfuu 584 12 analysis analysis NN work_ln56cwsp7ffppl4wxeq7osqfuu 584 13 always always RB work_ln56cwsp7ffppl4wxeq7osqfuu 584 14 includes include VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 584 15 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 584 16 three three CD work_ln56cwsp7ffppl4wxeq7osqfuu 584 17 most most RBS work_ln56cwsp7ffppl4wxeq7osqfuu 584 18 prominent prominent JJ work_ln56cwsp7ffppl4wxeq7osqfuu 584 19 ones one NNS work_ln56cwsp7ffppl4wxeq7osqfuu 584 20 : : : work_ln56cwsp7ffppl4wxeq7osqfuu 584 21 plurality plurality NN work_ln56cwsp7ffppl4wxeq7osqfuu 584 22 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 584 23 Borda Borda NNP work_ln56cwsp7ffppl4wxeq7osqfuu 584 24 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 584 25 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 584 26 negative negative JJ work_ln56cwsp7ffppl4wxeq7osqfuu 584 27 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 585 1 Finally finally RB work_ln56cwsp7ffppl4wxeq7osqfuu 585 2 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 585 3 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 585 4 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 585 5 case case NN work_ln56cwsp7ffppl4wxeq7osqfuu 585 6 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 585 7 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 585 8 analysis analysis NN work_ln56cwsp7ffppl4wxeq7osqfuu 585 9 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 585 10 utilitarianism utilitarianism NN work_ln56cwsp7ffppl4wxeq7osqfuu 585 11 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 585 12 we -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 585 13 also also RB work_ln56cwsp7ffppl4wxeq7osqfuu 585 14 include include VBP work_ln56cwsp7ffppl4wxeq7osqfuu 585 15 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 585 16 optimal optimal JJ work_ln56cwsp7ffppl4wxeq7osqfuu 585 17 scoring score VBG work_ln56cwsp7ffppl4wxeq7osqfuu 585 18 rules rule NNS work_ln56cwsp7ffppl4wxeq7osqfuu 585 19 as as IN work_ln56cwsp7ffppl4wxeq7osqfuu 585 20 predicted predict VBN work_ln56cwsp7ffppl4wxeq7osqfuu 585 21 in in IN work_ln56cwsp7ffppl4wxeq7osqfuu 585 22 Theorem Theorem NNP work_ln56cwsp7ffppl4wxeq7osqfuu 585 23 3.1 3.1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 585 24 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 586 1 Since since IN work_ln56cwsp7ffppl4wxeq7osqfuu 586 2 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 586 3 β β NNP work_ln56cwsp7ffppl4wxeq7osqfuu 586 4 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 586 5 γ γ NNP work_ln56cwsp7ffppl4wxeq7osqfuu 586 6 indices indices NNP work_ln56cwsp7ffppl4wxeq7osqfuu 586 7 measure measure VBP work_ln56cwsp7ffppl4wxeq7osqfuu 586 8 probabilities probability NNS work_ln56cwsp7ffppl4wxeq7osqfuu 586 9 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 586 10 success success NN work_ln56cwsp7ffppl4wxeq7osqfuu 586 11 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 586 12 we -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 586 13 use use VBP work_ln56cwsp7ffppl4wxeq7osqfuu 586 14 interval interval JJ work_ln56cwsp7ffppl4wxeq7osqfuu 586 15 estimation estimation NN work_ln56cwsp7ffppl4wxeq7osqfuu 586 16 methods method NNS work_ln56cwsp7ffppl4wxeq7osqfuu 586 17 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 586 18 binomial binomial JJ work_ln56cwsp7ffppl4wxeq7osqfuu 586 19 distributions distribution NNS work_ln56cwsp7ffppl4wxeq7osqfuu 586 20 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 587 1 Our -PRON- PRP$ work_ln56cwsp7ffppl4wxeq7osqfuu 587 2 sample sample NN work_ln56cwsp7ffppl4wxeq7osqfuu 587 3 size size NN work_ln56cwsp7ffppl4wxeq7osqfuu 587 4 provides provide VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 587 5 a a DT work_ln56cwsp7ffppl4wxeq7osqfuu 587 6 confidence confidence NN work_ln56cwsp7ffppl4wxeq7osqfuu 587 7 interval interval NN work_ln56cwsp7ffppl4wxeq7osqfuu 587 8 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 587 9 length length NN work_ln56cwsp7ffppl4wxeq7osqfuu 587 10 .001 .001 CD work_ln56cwsp7ffppl4wxeq7osqfuu 587 11 around around IN work_ln56cwsp7ffppl4wxeq7osqfuu 587 12 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 587 13 value value NN work_ln56cwsp7ffppl4wxeq7osqfuu 587 14 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 587 15 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 587 16 corresponding corresponding NN work_ln56cwsp7ffppl4wxeq7osqfuu 587 17 index,11 index,11 RB work_ln56cwsp7ffppl4wxeq7osqfuu 587 18 assuming assume VBG work_ln56cwsp7ffppl4wxeq7osqfuu 587 19 that that IN work_ln56cwsp7ffppl4wxeq7osqfuu 587 20 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 587 21 variance variance NN work_ln56cwsp7ffppl4wxeq7osqfuu 587 22 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 587 23 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 587 24 value value NN work_ln56cwsp7ffppl4wxeq7osqfuu 587 25 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 587 26 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 587 27 index index NN work_ln56cwsp7ffppl4wxeq7osqfuu 587 28 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 587 29 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 587 30 highest high JJS work_ln56cwsp7ffppl4wxeq7osqfuu 587 31 possible possible JJ work_ln56cwsp7ffppl4wxeq7osqfuu 587 32 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 587 33 a a DT work_ln56cwsp7ffppl4wxeq7osqfuu 587 34 binomial binomial JJ work_ln56cwsp7ffppl4wxeq7osqfuu 587 35 distribution distribution NN work_ln56cwsp7ffppl4wxeq7osqfuu 587 36 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 587 37 i.e. i.e. FW work_ln56cwsp7ffppl4wxeq7osqfuu 587 38 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 587 39 .25 .25 NFP work_ln56cwsp7ffppl4wxeq7osqfuu 587 40 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 587 41 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 588 1 This this DT work_ln56cwsp7ffppl4wxeq7osqfuu 588 2 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 588 3 a a DT work_ln56cwsp7ffppl4wxeq7osqfuu 588 4 conservative conservative JJ work_ln56cwsp7ffppl4wxeq7osqfuu 588 5 method method NN work_ln56cwsp7ffppl4wxeq7osqfuu 588 6 to to TO work_ln56cwsp7ffppl4wxeq7osqfuu 588 7 compare compare VB work_ln56cwsp7ffppl4wxeq7osqfuu 588 8 significant significant JJ work_ln56cwsp7ffppl4wxeq7osqfuu 588 9 differences difference NNS work_ln56cwsp7ffppl4wxeq7osqfuu 588 10 across across IN work_ln56cwsp7ffppl4wxeq7osqfuu 588 11 scoring score VBG work_ln56cwsp7ffppl4wxeq7osqfuu 588 12 rules.12 rules.12 NNP work_ln56cwsp7ffppl4wxeq7osqfuu 588 13 For for IN work_ln56cwsp7ffppl4wxeq7osqfuu 588 14 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 588 15 α−index α−index JJR work_ln56cwsp7ffppl4wxeq7osqfuu 588 16 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 588 17 we -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 588 18 estimate estimate VBP work_ln56cwsp7ffppl4wxeq7osqfuu 588 19 both both CC work_ln56cwsp7ffppl4wxeq7osqfuu 588 20 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 588 21 value value NN work_ln56cwsp7ffppl4wxeq7osqfuu 588 22 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 588 23 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 588 24 index index NN work_ln56cwsp7ffppl4wxeq7osqfuu 588 25 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 588 26 its -PRON- PRP$ work_ln56cwsp7ffppl4wxeq7osqfuu 588 27 variance variance NN work_ln56cwsp7ffppl4wxeq7osqfuu 588 28 in in IN work_ln56cwsp7ffppl4wxeq7osqfuu 588 29 order order NN work_ln56cwsp7ffppl4wxeq7osqfuu 588 30 to to TO work_ln56cwsp7ffppl4wxeq7osqfuu 588 31 construct construct VB work_ln56cwsp7ffppl4wxeq7osqfuu 588 32 confidence confidence NN work_ln56cwsp7ffppl4wxeq7osqfuu 588 33 intervals interval NNS work_ln56cwsp7ffppl4wxeq7osqfuu 588 34 that that WDT work_ln56cwsp7ffppl4wxeq7osqfuu 588 35 depend depend VBP work_ln56cwsp7ffppl4wxeq7osqfuu 588 36 on on IN work_ln56cwsp7ffppl4wxeq7osqfuu 588 37 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 588 38 estimated estimate VBN work_ln56cwsp7ffppl4wxeq7osqfuu 588 39 variance.13 variance.13 NNP work_ln56cwsp7ffppl4wxeq7osqfuu 588 40 The the DT work_ln56cwsp7ffppl4wxeq7osqfuu 588 41 simulations simulation NNS work_ln56cwsp7ffppl4wxeq7osqfuu 588 42 complement complement VBP work_ln56cwsp7ffppl4wxeq7osqfuu 588 43 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 588 44 theoretical theoretical JJ work_ln56cwsp7ffppl4wxeq7osqfuu 588 45 results result NNS work_ln56cwsp7ffppl4wxeq7osqfuu 588 46 obtained obtain VBN work_ln56cwsp7ffppl4wxeq7osqfuu 588 47 in in IN work_ln56cwsp7ffppl4wxeq7osqfuu 588 48 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 588 49 text text NN work_ln56cwsp7ffppl4wxeq7osqfuu 588 50 by by IN work_ln56cwsp7ffppl4wxeq7osqfuu 588 51 studying study VBG work_ln56cwsp7ffppl4wxeq7osqfuu 588 52 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 588 53 following follow VBG work_ln56cwsp7ffppl4wxeq7osqfuu 588 54 cases case NNS work_ln56cwsp7ffppl4wxeq7osqfuu 588 55 : : : work_ln56cwsp7ffppl4wxeq7osqfuu 588 56 • • VB work_ln56cwsp7ffppl4wxeq7osqfuu 588 57 Utilitarianism utilitarianism NN work_ln56cwsp7ffppl4wxeq7osqfuu 588 58 : : : work_ln56cwsp7ffppl4wxeq7osqfuu 588 59 βUT βut NN work_ln56cwsp7ffppl4wxeq7osqfuu 588 60 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 588 61 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 588 62 uniform uniform NN work_ln56cwsp7ffppl4wxeq7osqfuu 588 63 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 588 64 normal normal JJ work_ln56cwsp7ffppl4wxeq7osqfuu 588 65 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 588 66 exponential exponential JJ work_ln56cwsp7ffppl4wxeq7osqfuu 588 67 distributions distribution NNS work_ln56cwsp7ffppl4wxeq7osqfuu 588 68 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 588 69 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 588 70 γUT γUT NNP work_ln56cwsp7ffppl4wxeq7osqfuu 588 71 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 588 72 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 588 73 exponential exponential JJ work_ln56cwsp7ffppl4wxeq7osqfuu 588 74 distribution distribution NN work_ln56cwsp7ffppl4wxeq7osqfuu 588 75 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 589 1 10We 10we CD work_ln56cwsp7ffppl4wxeq7osqfuu 589 2 are be VBP work_ln56cwsp7ffppl4wxeq7osqfuu 589 3 grateful grateful JJ work_ln56cwsp7ffppl4wxeq7osqfuu 589 4 to to IN work_ln56cwsp7ffppl4wxeq7osqfuu 589 5 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 589 6 Advanced Advanced NNP work_ln56cwsp7ffppl4wxeq7osqfuu 589 7 Computing Computing NNP work_ln56cwsp7ffppl4wxeq7osqfuu 589 8 Center Center NNP work_ln56cwsp7ffppl4wxeq7osqfuu 589 9 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 589 10 Research Research NNP work_ln56cwsp7ffppl4wxeq7osqfuu 589 11 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 589 12 Education Education NNP work_ln56cwsp7ffppl4wxeq7osqfuu 589 13 at at IN work_ln56cwsp7ffppl4wxeq7osqfuu 589 14 Vanderbilt Vanderbilt NNP work_ln56cwsp7ffppl4wxeq7osqfuu 589 15 University University NNP work_ln56cwsp7ffppl4wxeq7osqfuu 589 16 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 589 17 providing provide VBG work_ln56cwsp7ffppl4wxeq7osqfuu 589 18 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 589 19 necessary necessary JJ work_ln56cwsp7ffppl4wxeq7osqfuu 589 20 computing computing NN work_ln56cwsp7ffppl4wxeq7osqfuu 589 21 resources resource NNS work_ln56cwsp7ffppl4wxeq7osqfuu 589 22 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 590 1 11To 11to CD work_ln56cwsp7ffppl4wxeq7osqfuu 590 2 determine determine VBP work_ln56cwsp7ffppl4wxeq7osqfuu 590 3 that that IN work_ln56cwsp7ffppl4wxeq7osqfuu 590 4 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 590 5 difference difference NN work_ln56cwsp7ffppl4wxeq7osqfuu 590 6 between between IN work_ln56cwsp7ffppl4wxeq7osqfuu 590 7 two two CD work_ln56cwsp7ffppl4wxeq7osqfuu 590 8 values value NNS work_ln56cwsp7ffppl4wxeq7osqfuu 590 9 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 590 10 significantly significantly RB work_ln56cwsp7ffppl4wxeq7osqfuu 590 11 different different JJ work_ln56cwsp7ffppl4wxeq7osqfuu 590 12 than than IN work_ln56cwsp7ffppl4wxeq7osqfuu 590 13 zero zero CD work_ln56cwsp7ffppl4wxeq7osqfuu 590 14 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 590 15 this this DT work_ln56cwsp7ffppl4wxeq7osqfuu 590 16 method method NN work_ln56cwsp7ffppl4wxeq7osqfuu 590 17 provides provide VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 590 18 a a DT work_ln56cwsp7ffppl4wxeq7osqfuu 590 19 confidence confidence NN work_ln56cwsp7ffppl4wxeq7osqfuu 590 20 interval interval NN work_ln56cwsp7ffppl4wxeq7osqfuu 590 21 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 590 22 length length NN work_ln56cwsp7ffppl4wxeq7osqfuu 590 23 .001 .001 CD work_ln56cwsp7ffppl4wxeq7osqfuu 590 24 × × NNS work_ln56cwsp7ffppl4wxeq7osqfuu 590 25 21/2 21/2 CD work_ln56cwsp7ffppl4wxeq7osqfuu 590 26 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 590 27 such such JJ work_ln56cwsp7ffppl4wxeq7osqfuu 590 28 difference difference NN work_ln56cwsp7ffppl4wxeq7osqfuu 590 29 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 591 1 12The 12the CD work_ln56cwsp7ffppl4wxeq7osqfuu 591 2 use use NN work_ln56cwsp7ffppl4wxeq7osqfuu 591 3 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 591 4 this this DT work_ln56cwsp7ffppl4wxeq7osqfuu 591 5 method method NN work_ln56cwsp7ffppl4wxeq7osqfuu 591 6 might may MD work_ln56cwsp7ffppl4wxeq7osqfuu 591 7 provide provide VB work_ln56cwsp7ffppl4wxeq7osqfuu 591 8 unnecessarily unnecessarily RB work_ln56cwsp7ffppl4wxeq7osqfuu 591 9 wide wide JJ work_ln56cwsp7ffppl4wxeq7osqfuu 591 10 intervals interval NNS work_ln56cwsp7ffppl4wxeq7osqfuu 591 11 ; ; : work_ln56cwsp7ffppl4wxeq7osqfuu 591 12 however however RB work_ln56cwsp7ffppl4wxeq7osqfuu 591 13 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 591 14 it -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 591 15 allows allow VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 591 16 us -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 591 17 to to TO work_ln56cwsp7ffppl4wxeq7osqfuu 591 18 find find VB work_ln56cwsp7ffppl4wxeq7osqfuu 591 19 significant significant JJ work_ln56cwsp7ffppl4wxeq7osqfuu 591 20 differences difference NNS work_ln56cwsp7ffppl4wxeq7osqfuu 591 21 across across IN work_ln56cwsp7ffppl4wxeq7osqfuu 591 22 scoring score VBG work_ln56cwsp7ffppl4wxeq7osqfuu 591 23 rules rule NNS work_ln56cwsp7ffppl4wxeq7osqfuu 591 24 without without IN work_ln56cwsp7ffppl4wxeq7osqfuu 591 25 having have VBG work_ln56cwsp7ffppl4wxeq7osqfuu 591 26 to to TO work_ln56cwsp7ffppl4wxeq7osqfuu 591 27 estimate estimate VB work_ln56cwsp7ffppl4wxeq7osqfuu 591 28 their -PRON- PRP$ work_ln56cwsp7ffppl4wxeq7osqfuu 591 29 covariance covariance NN work_ln56cwsp7ffppl4wxeq7osqfuu 591 30 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 592 1 13Given 13given CD work_ln56cwsp7ffppl4wxeq7osqfuu 592 2 our -PRON- PRP$ work_ln56cwsp7ffppl4wxeq7osqfuu 592 3 sample sample NN work_ln56cwsp7ffppl4wxeq7osqfuu 592 4 size size NN work_ln56cwsp7ffppl4wxeq7osqfuu 592 5 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 592 6 with with IN work_ln56cwsp7ffppl4wxeq7osqfuu 592 7 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 592 8 exponential exponential JJ work_ln56cwsp7ffppl4wxeq7osqfuu 592 9 distribution distribution NN work_ln56cwsp7ffppl4wxeq7osqfuu 592 10 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 592 11 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 592 12 normal normal JJ work_ln56cwsp7ffppl4wxeq7osqfuu 592 13 distribution distribution NN work_ln56cwsp7ffppl4wxeq7osqfuu 592 14 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 592 15 length length NN work_ln56cwsp7ffppl4wxeq7osqfuu 592 16 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 592 17 these these DT work_ln56cwsp7ffppl4wxeq7osqfuu 592 18 intervals interval NNS work_ln56cwsp7ffppl4wxeq7osqfuu 592 19 varies vary VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 592 20 between between IN work_ln56cwsp7ffppl4wxeq7osqfuu 592 21 .002 .002 CD work_ln56cwsp7ffppl4wxeq7osqfuu 592 22 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 592 23 .004 .004 CD work_ln56cwsp7ffppl4wxeq7osqfuu 592 24 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 592 25 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 592 26 case case NN work_ln56cwsp7ffppl4wxeq7osqfuu 592 27 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 592 28 maximax maximax NNP work_ln56cwsp7ffppl4wxeq7osqfuu 592 29 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 592 30 between between IN work_ln56cwsp7ffppl4wxeq7osqfuu 592 31 .0002 .0002 NNP work_ln56cwsp7ffppl4wxeq7osqfuu 592 32 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 592 33 .002 .002 CD work_ln56cwsp7ffppl4wxeq7osqfuu 592 34 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 592 35 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 592 36 case case NN work_ln56cwsp7ffppl4wxeq7osqfuu 592 37 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 592 38 maximin maximin NN work_ln56cwsp7ffppl4wxeq7osqfuu 592 39 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 593 1 With with IN work_ln56cwsp7ffppl4wxeq7osqfuu 593 2 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 593 3 uniform uniform JJ work_ln56cwsp7ffppl4wxeq7osqfuu 593 4 distribution distribution NN work_ln56cwsp7ffppl4wxeq7osqfuu 593 5 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 593 6 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 593 7 length length NN work_ln56cwsp7ffppl4wxeq7osqfuu 593 8 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 593 9 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 593 10 interval interval NN work_ln56cwsp7ffppl4wxeq7osqfuu 593 11 varies varie NNS work_ln56cwsp7ffppl4wxeq7osqfuu 593 12 between between IN work_ln56cwsp7ffppl4wxeq7osqfuu 593 13 .00001 .00001 NNP work_ln56cwsp7ffppl4wxeq7osqfuu 593 14 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 593 15 .0005 .0005 NNP work_ln56cwsp7ffppl4wxeq7osqfuu 593 16 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 594 1 Note note VB work_ln56cwsp7ffppl4wxeq7osqfuu 594 2 that that IN work_ln56cwsp7ffppl4wxeq7osqfuu 594 3 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 594 4 differences difference NNS work_ln56cwsp7ffppl4wxeq7osqfuu 594 5 across across IN work_ln56cwsp7ffppl4wxeq7osqfuu 594 6 distributions distribution NNS work_ln56cwsp7ffppl4wxeq7osqfuu 594 7 are be VBP work_ln56cwsp7ffppl4wxeq7osqfuu 594 8 due due JJ work_ln56cwsp7ffppl4wxeq7osqfuu 594 9 to to IN work_ln56cwsp7ffppl4wxeq7osqfuu 594 10 their -PRON- PRP$ work_ln56cwsp7ffppl4wxeq7osqfuu 594 11 different different JJ work_ln56cwsp7ffppl4wxeq7osqfuu 594 12 ranges range NNS work_ln56cwsp7ffppl4wxeq7osqfuu 594 13 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 595 1 24 24 CD work_ln56cwsp7ffppl4wxeq7osqfuu 595 2 • • NN work_ln56cwsp7ffppl4wxeq7osqfuu 595 3 Maximax Maximax NNP work_ln56cwsp7ffppl4wxeq7osqfuu 595 4 : : : work_ln56cwsp7ffppl4wxeq7osqfuu 595 5 αMX αmx XX work_ln56cwsp7ffppl4wxeq7osqfuu 595 6 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 595 7 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 595 8 uniform uniform NN work_ln56cwsp7ffppl4wxeq7osqfuu 595 9 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 595 10 with with IN work_ln56cwsp7ffppl4wxeq7osqfuu 595 11 k k NNP work_ln56cwsp7ffppl4wxeq7osqfuu 595 12 > > NNP work_ln56cwsp7ffppl4wxeq7osqfuu 595 13 3 3 CD work_ln56cwsp7ffppl4wxeq7osqfuu 595 14 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 595 15 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 595 16 normal normal JJ work_ln56cwsp7ffppl4wxeq7osqfuu 595 17 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 595 18 exponential exponential JJ work_ln56cwsp7ffppl4wxeq7osqfuu 595 19 distri- distri- JJ work_ln56cwsp7ffppl4wxeq7osqfuu 595 20 butions bution NNS work_ln56cwsp7ffppl4wxeq7osqfuu 595 21 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 595 22 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 595 23 γMX γMX VBD work_ln56cwsp7ffppl4wxeq7osqfuu 595 24 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 595 25 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 595 26 exponential exponential JJ work_ln56cwsp7ffppl4wxeq7osqfuu 595 27 distribution distribution NN work_ln56cwsp7ffppl4wxeq7osqfuu 595 28 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 596 1 • • NNP work_ln56cwsp7ffppl4wxeq7osqfuu 596 2 Maximin Maximin NNP work_ln56cwsp7ffppl4wxeq7osqfuu 596 3 : : : work_ln56cwsp7ffppl4wxeq7osqfuu 596 4 βMN βmn ADD work_ln56cwsp7ffppl4wxeq7osqfuu 596 5 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 596 6 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 596 7 uniform uniform NN work_ln56cwsp7ffppl4wxeq7osqfuu 596 8 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 596 9 normal normal JJ work_ln56cwsp7ffppl4wxeq7osqfuu 596 10 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 596 11 exponential exponential JJ work_ln56cwsp7ffppl4wxeq7osqfuu 596 12 distributions distribution NNS work_ln56cwsp7ffppl4wxeq7osqfuu 596 13 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 596 14 αMN αmn XX work_ln56cwsp7ffppl4wxeq7osqfuu 596 15 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 596 16 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 596 17 exponential exponential JJ work_ln56cwsp7ffppl4wxeq7osqfuu 596 18 distribution distribution NN work_ln56cwsp7ffppl4wxeq7osqfuu 596 19 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 596 20 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 596 21 γMN γMN NNP work_ln56cwsp7ffppl4wxeq7osqfuu 596 22 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 596 23 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 596 24 exponential exponential JJ work_ln56cwsp7ffppl4wxeq7osqfuu 596 25 distribution distribution NN work_ln56cwsp7ffppl4wxeq7osqfuu 596 26 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 597 1 Table table NN work_ln56cwsp7ffppl4wxeq7osqfuu 597 2 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 597 3 reports report VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 597 4 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 597 5 βUT βut NN work_ln56cwsp7ffppl4wxeq7osqfuu 597 6 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 597 7 γUT γut JJ work_ln56cwsp7ffppl4wxeq7osqfuu 597 8 values value NNS work_ln56cwsp7ffppl4wxeq7osqfuu 597 9 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 597 10 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 597 11 optimal optimal JJ work_ln56cwsp7ffppl4wxeq7osqfuu 597 12 scoring score VBG work_ln56cwsp7ffppl4wxeq7osqfuu 597 13 rules rule NNS work_ln56cwsp7ffppl4wxeq7osqfuu 597 14 according accord VBG work_ln56cwsp7ffppl4wxeq7osqfuu 597 15 to to IN work_ln56cwsp7ffppl4wxeq7osqfuu 597 16 Theorem Theorem NNP work_ln56cwsp7ffppl4wxeq7osqfuu 597 17 3.1 3.1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 597 18 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 598 1 Moreover moreover RB work_ln56cwsp7ffppl4wxeq7osqfuu 598 2 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 598 3 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 598 4 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 598 5 sake sake NN work_ln56cwsp7ffppl4wxeq7osqfuu 598 6 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 598 7 comparison comparison NN work_ln56cwsp7ffppl4wxeq7osqfuu 598 8 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 598 9 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 598 10 table table NN work_ln56cwsp7ffppl4wxeq7osqfuu 598 11 also also RB work_ln56cwsp7ffppl4wxeq7osqfuu 598 12 includes include VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 598 13 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 598 14 βUT βut NN work_ln56cwsp7ffppl4wxeq7osqfuu 598 15 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 598 16 γUT γUT NNS work_ln56cwsp7ffppl4wxeq7osqfuu 598 17 -values -values : work_ln56cwsp7ffppl4wxeq7osqfuu 598 18 that that IN work_ln56cwsp7ffppl4wxeq7osqfuu 598 19 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 598 20 three three CD work_ln56cwsp7ffppl4wxeq7osqfuu 598 21 most most RBS work_ln56cwsp7ffppl4wxeq7osqfuu 598 22 prominent prominent JJ work_ln56cwsp7ffppl4wxeq7osqfuu 598 23 scoring score VBG work_ln56cwsp7ffppl4wxeq7osqfuu 598 24 rules rule NNS work_ln56cwsp7ffppl4wxeq7osqfuu 598 25 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 598 26 plurality plurality NN work_ln56cwsp7ffppl4wxeq7osqfuu 598 27 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 598 28 Borda Borda NNP work_ln56cwsp7ffppl4wxeq7osqfuu 598 29 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 598 30 neg- neg- RB work_ln56cwsp7ffppl4wxeq7osqfuu 598 31 ative ative JJ work_ln56cwsp7ffppl4wxeq7osqfuu 598 32 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 598 33 attain attain VB work_ln56cwsp7ffppl4wxeq7osqfuu 598 34 in in IN work_ln56cwsp7ffppl4wxeq7osqfuu 598 35 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 598 36 simulations simulation NNS work_ln56cwsp7ffppl4wxeq7osqfuu 598 37 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 599 1 Accordingly accordingly RB work_ln56cwsp7ffppl4wxeq7osqfuu 599 2 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 599 3 Tables Tables NNP work_ln56cwsp7ffppl4wxeq7osqfuu 599 4 2 2 CD work_ln56cwsp7ffppl4wxeq7osqfuu 599 5 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 599 6 3 3 CD work_ln56cwsp7ffppl4wxeq7osqfuu 599 7 report report VB work_ln56cwsp7ffppl4wxeq7osqfuu 599 8 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 599 9 corresponding correspond VBG work_ln56cwsp7ffppl4wxeq7osqfuu 599 10 values value NNS work_ln56cwsp7ffppl4wxeq7osqfuu 599 11 attained attain VBN work_ln56cwsp7ffppl4wxeq7osqfuu 599 12 by by IN work_ln56cwsp7ffppl4wxeq7osqfuu 599 13 plurality plurality NN work_ln56cwsp7ffppl4wxeq7osqfuu 599 14 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 599 15 Borda Borda NNP work_ln56cwsp7ffppl4wxeq7osqfuu 599 16 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 599 17 negative negative JJ work_ln56cwsp7ffppl4wxeq7osqfuu 599 18 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 600 1 As as IN work_ln56cwsp7ffppl4wxeq7osqfuu 600 2 shown show VBN work_ln56cwsp7ffppl4wxeq7osqfuu 600 3 in in IN work_ln56cwsp7ffppl4wxeq7osqfuu 600 4 Tables Tables NNP work_ln56cwsp7ffppl4wxeq7osqfuu 600 5 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 600 6 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 600 7 2 2 CD work_ln56cwsp7ffppl4wxeq7osqfuu 600 8 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 600 9 3 3 CD work_ln56cwsp7ffppl4wxeq7osqfuu 600 10 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 600 11 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 600 12 each each DT work_ln56cwsp7ffppl4wxeq7osqfuu 600 13 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 600 14 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 600 15 three three CD work_ln56cwsp7ffppl4wxeq7osqfuu 600 16 ideals ideal NNS work_ln56cwsp7ffppl4wxeq7osqfuu 600 17 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 600 18 justice justice NN work_ln56cwsp7ffppl4wxeq7osqfuu 600 19 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 600 20 each each DT work_ln56cwsp7ffppl4wxeq7osqfuu 600 21 probability probability NN work_ln56cwsp7ffppl4wxeq7osqfuu 600 22 distributions distribution NNS work_ln56cwsp7ffppl4wxeq7osqfuu 600 23 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 600 24 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 600 25 each each DT work_ln56cwsp7ffppl4wxeq7osqfuu 600 26 performance performance NN work_ln56cwsp7ffppl4wxeq7osqfuu 600 27 index index NN work_ln56cwsp7ffppl4wxeq7osqfuu 600 28 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 600 29 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 600 30 scoring score VBG work_ln56cwsp7ffppl4wxeq7osqfuu 600 31 rule rule NN work_ln56cwsp7ffppl4wxeq7osqfuu 600 32 that that WDT work_ln56cwsp7ffppl4wxeq7osqfuu 600 33 provides provide VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 600 34 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 600 35 highest high JJS work_ln56cwsp7ffppl4wxeq7osqfuu 600 36 value value NN work_ln56cwsp7ffppl4wxeq7osqfuu 600 37 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 600 38 generally generally RB work_ln56cwsp7ffppl4wxeq7osqfuu 600 39 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 600 40 one one NN work_ln56cwsp7ffppl4wxeq7osqfuu 600 41 predicted predict VBD work_ln56cwsp7ffppl4wxeq7osqfuu 600 42 in in IN work_ln56cwsp7ffppl4wxeq7osqfuu 600 43 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 600 44 theoretical theoretical JJ work_ln56cwsp7ffppl4wxeq7osqfuu 600 45 results result NNS work_ln56cwsp7ffppl4wxeq7osqfuu 600 46 presented present VBN work_ln56cwsp7ffppl4wxeq7osqfuu 600 47 in in IN work_ln56cwsp7ffppl4wxeq7osqfuu 600 48 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 600 49 text text NN work_ln56cwsp7ffppl4wxeq7osqfuu 600 50 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 601 1 This this DT work_ln56cwsp7ffppl4wxeq7osqfuu 601 2 means mean VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 601 3 that that IN work_ln56cwsp7ffppl4wxeq7osqfuu 601 4 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 601 5 scoring score VBG work_ln56cwsp7ffppl4wxeq7osqfuu 601 6 rule rule NN work_ln56cwsp7ffppl4wxeq7osqfuu 601 7 determined determine VBN work_ln56cwsp7ffppl4wxeq7osqfuu 601 8 by by IN work_ln56cwsp7ffppl4wxeq7osqfuu 601 9 Theorem theorem NN work_ln56cwsp7ffppl4wxeq7osqfuu 601 10 3.1 3.1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 601 11 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 601 12 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 601 13 best good JJS work_ln56cwsp7ffppl4wxeq7osqfuu 601 14 in in IN work_ln56cwsp7ffppl4wxeq7osqfuu 601 15 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 601 16 case case NN work_ln56cwsp7ffppl4wxeq7osqfuu 601 17 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 601 18 utilitarianism utilitarianism NN work_ln56cwsp7ffppl4wxeq7osqfuu 601 19 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 601 20 plurality plurality NN work_ln56cwsp7ffppl4wxeq7osqfuu 601 21 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 601 22 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 601 23 best good JJS work_ln56cwsp7ffppl4wxeq7osqfuu 601 24 in in IN work_ln56cwsp7ffppl4wxeq7osqfuu 601 25 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 601 26 case case NN work_ln56cwsp7ffppl4wxeq7osqfuu 601 27 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 601 28 maximax maximax NNP work_ln56cwsp7ffppl4wxeq7osqfuu 601 29 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 601 30 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 601 31 negative negative JJ work_ln56cwsp7ffppl4wxeq7osqfuu 601 32 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 601 33 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 601 34 best good JJS work_ln56cwsp7ffppl4wxeq7osqfuu 601 35 in in IN work_ln56cwsp7ffppl4wxeq7osqfuu 601 36 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 601 37 case case NN work_ln56cwsp7ffppl4wxeq7osqfuu 601 38 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 601 39 maximin maximin NN work_ln56cwsp7ffppl4wxeq7osqfuu 601 40 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 601 41 across across IN work_ln56cwsp7ffppl4wxeq7osqfuu 601 42 probability probability NN work_ln56cwsp7ffppl4wxeq7osqfuu 601 43 distributions distribution NNS work_ln56cwsp7ffppl4wxeq7osqfuu 601 44 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 602 1 There there EX work_ln56cwsp7ffppl4wxeq7osqfuu 602 2 are be VBP work_ln56cwsp7ffppl4wxeq7osqfuu 602 3 only only RB work_ln56cwsp7ffppl4wxeq7osqfuu 602 4 some some DT work_ln56cwsp7ffppl4wxeq7osqfuu 602 5 exceptions exception NNS work_ln56cwsp7ffppl4wxeq7osqfuu 602 6 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 602 7 small small JJ work_ln56cwsp7ffppl4wxeq7osqfuu 602 8 society society NN work_ln56cwsp7ffppl4wxeq7osqfuu 602 9 sizes size NNS work_ln56cwsp7ffppl4wxeq7osqfuu 602 10 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 602 11 in in IN work_ln56cwsp7ffppl4wxeq7osqfuu 602 12 which which WDT work_ln56cwsp7ffppl4wxeq7osqfuu 602 13 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 602 14 frequency frequency NN work_ln56cwsp7ffppl4wxeq7osqfuu 602 15 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 602 16 ties tie NNS work_ln56cwsp7ffppl4wxeq7osqfuu 602 17 in in IN work_ln56cwsp7ffppl4wxeq7osqfuu 602 18 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 602 19 number number NN work_ln56cwsp7ffppl4wxeq7osqfuu 602 20 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 602 21 points point NNS work_ln56cwsp7ffppl4wxeq7osqfuu 602 22 sometimes sometimes RB work_ln56cwsp7ffppl4wxeq7osqfuu 602 23 causes cause VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 602 24 distortions distortion NNS work_ln56cwsp7ffppl4wxeq7osqfuu 602 25 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 603 1 More more RBR work_ln56cwsp7ffppl4wxeq7osqfuu 603 2 specifically specifically RB work_ln56cwsp7ffppl4wxeq7osqfuu 603 3 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 603 4 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 603 5 utilitarianism utilitarianism NN work_ln56cwsp7ffppl4wxeq7osqfuu 603 6 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 603 7 scoring score VBG work_ln56cwsp7ffppl4wxeq7osqfuu 603 8 rule rule NN work_ln56cwsp7ffppl4wxeq7osqfuu 603 9 predicted predict VBD work_ln56cwsp7ffppl4wxeq7osqfuu 603 10 in in IN work_ln56cwsp7ffppl4wxeq7osqfuu 603 11 Theorem theorem NN work_ln56cwsp7ffppl4wxeq7osqfuu 603 12 3.1 3.1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 603 13 pro- pro- NN work_ln56cwsp7ffppl4wxeq7osqfuu 603 14 vides vide VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 603 15 a a DT work_ln56cwsp7ffppl4wxeq7osqfuu 603 16 higher high JJR work_ln56cwsp7ffppl4wxeq7osqfuu 603 17 value value NN work_ln56cwsp7ffppl4wxeq7osqfuu 603 18 than than IN work_ln56cwsp7ffppl4wxeq7osqfuu 603 19 not not RB work_ln56cwsp7ffppl4wxeq7osqfuu 603 20 only only RB work_ln56cwsp7ffppl4wxeq7osqfuu 603 21 plurality plurality NN work_ln56cwsp7ffppl4wxeq7osqfuu 603 22 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 603 23 negative negative JJ work_ln56cwsp7ffppl4wxeq7osqfuu 603 24 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 603 25 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 603 26 Borda Borda NNP work_ln56cwsp7ffppl4wxeq7osqfuu 603 27 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 603 28 when when WRB work_ln56cwsp7ffppl4wxeq7osqfuu 603 29 Borda Borda NNP work_ln56cwsp7ffppl4wxeq7osqfuu 603 30 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 603 31 not not RB work_ln56cwsp7ffppl4wxeq7osqfuu 603 32 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 603 33 S∗ s∗ NN work_ln56cwsp7ffppl4wxeq7osqfuu 603 34 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 603 35 but but CC work_ln56cwsp7ffppl4wxeq7osqfuu 603 36 also also RB work_ln56cwsp7ffppl4wxeq7osqfuu 603 37 than than IN work_ln56cwsp7ffppl4wxeq7osqfuu 603 38 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 603 39 best good JJS work_ln56cwsp7ffppl4wxeq7osqfuu 603 40 randomly randomly RB work_ln56cwsp7ffppl4wxeq7osqfuu 603 41 - - HYPH work_ln56cwsp7ffppl4wxeq7osqfuu 603 42 generated generate VBN work_ln56cwsp7ffppl4wxeq7osqfuu 603 43 scoring score VBG work_ln56cwsp7ffppl4wxeq7osqfuu 603 44 rule rule NN work_ln56cwsp7ffppl4wxeq7osqfuu 603 45 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 604 1 In in IN work_ln56cwsp7ffppl4wxeq7osqfuu 604 2 addition addition NN work_ln56cwsp7ffppl4wxeq7osqfuu 604 3 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 604 4 we -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 604 5 find find VBP work_ln56cwsp7ffppl4wxeq7osqfuu 604 6 that that IN work_ln56cwsp7ffppl4wxeq7osqfuu 604 7 S∗ s∗ NN work_ln56cwsp7ffppl4wxeq7osqfuu 604 8 can can MD work_ln56cwsp7ffppl4wxeq7osqfuu 604 9 not not RB work_ln56cwsp7ffppl4wxeq7osqfuu 604 10 be be VB work_ln56cwsp7ffppl4wxeq7osqfuu 604 11 rejected reject VBN work_ln56cwsp7ffppl4wxeq7osqfuu 604 12 as as IN work_ln56cwsp7ffppl4wxeq7osqfuu 604 13 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 604 14 best well RBS work_ln56cwsp7ffppl4wxeq7osqfuu 604 15 - - HYPH work_ln56cwsp7ffppl4wxeq7osqfuu 604 16 performing perform VBG work_ln56cwsp7ffppl4wxeq7osqfuu 604 17 scoring score VBG work_ln56cwsp7ffppl4wxeq7osqfuu 604 18 rule.14 rule.14 NNP work_ln56cwsp7ffppl4wxeq7osqfuu 604 19 For for IN work_ln56cwsp7ffppl4wxeq7osqfuu 604 20 maximax maximax NNP work_ln56cwsp7ffppl4wxeq7osqfuu 604 21 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 604 22 plurality plurality NN work_ln56cwsp7ffppl4wxeq7osqfuu 604 23 has have VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 604 24 a a DT work_ln56cwsp7ffppl4wxeq7osqfuu 604 25 significantly significantly RB work_ln56cwsp7ffppl4wxeq7osqfuu 604 26 higher high JJR work_ln56cwsp7ffppl4wxeq7osqfuu 604 27 expected expect VBN work_ln56cwsp7ffppl4wxeq7osqfuu 604 28 value value NN work_ln56cwsp7ffppl4wxeq7osqfuu 604 29 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 604 30 a a DT work_ln56cwsp7ffppl4wxeq7osqfuu 604 31 significantly significantly RB work_ln56cwsp7ffppl4wxeq7osqfuu 604 32 higher high JJR work_ln56cwsp7ffppl4wxeq7osqfuu 604 33 probability probability NN work_ln56cwsp7ffppl4wxeq7osqfuu 604 34 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 604 35 not not RB work_ln56cwsp7ffppl4wxeq7osqfuu 604 36 selecting select VBG work_ln56cwsp7ffppl4wxeq7osqfuu 604 37 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 604 38 worst bad JJS work_ln56cwsp7ffppl4wxeq7osqfuu 604 39 alternative alternative NN work_ln56cwsp7ffppl4wxeq7osqfuu 604 40 than than IN work_ln56cwsp7ffppl4wxeq7osqfuu 604 41 Borda Borda NNP work_ln56cwsp7ffppl4wxeq7osqfuu 604 42 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 604 43 negative negative JJ work_ln56cwsp7ffppl4wxeq7osqfuu 604 44 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 604 45 as as IN work_ln56cwsp7ffppl4wxeq7osqfuu 604 46 predicted predict VBN work_ln56cwsp7ffppl4wxeq7osqfuu 604 47 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 605 1 There there EX work_ln56cwsp7ffppl4wxeq7osqfuu 605 2 are be VBP work_ln56cwsp7ffppl4wxeq7osqfuu 605 3 only only RB work_ln56cwsp7ffppl4wxeq7osqfuu 605 4 a a DT work_ln56cwsp7ffppl4wxeq7osqfuu 605 5 few few JJ work_ln56cwsp7ffppl4wxeq7osqfuu 605 6 exceptions exception NNS work_ln56cwsp7ffppl4wxeq7osqfuu 605 7 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 605 8 small small JJ work_ln56cwsp7ffppl4wxeq7osqfuu 605 9 societies society NNS work_ln56cwsp7ffppl4wxeq7osqfuu 605 10 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 605 11 wherein wherein WRB work_ln56cwsp7ffppl4wxeq7osqfuu 605 12 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 605 13 frequency frequency NN work_ln56cwsp7ffppl4wxeq7osqfuu 605 14 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 605 15 ties tie NNS work_ln56cwsp7ffppl4wxeq7osqfuu 605 16 causes cause VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 605 17 distortions distortion NNS work_ln56cwsp7ffppl4wxeq7osqfuu 605 18 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 606 1 In in IN work_ln56cwsp7ffppl4wxeq7osqfuu 606 2 addition addition NN work_ln56cwsp7ffppl4wxeq7osqfuu 606 3 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 606 4 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 606 5 best good JJS work_ln56cwsp7ffppl4wxeq7osqfuu 606 6 randomly randomly RB work_ln56cwsp7ffppl4wxeq7osqfuu 606 7 - - HYPH work_ln56cwsp7ffppl4wxeq7osqfuu 606 8 generated generate VBN work_ln56cwsp7ffppl4wxeq7osqfuu 606 9 scoring score VBG work_ln56cwsp7ffppl4wxeq7osqfuu 606 10 rule rule NN work_ln56cwsp7ffppl4wxeq7osqfuu 606 11 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 606 12 in in IN work_ln56cwsp7ffppl4wxeq7osqfuu 606 13 a a DT work_ln56cwsp7ffppl4wxeq7osqfuu 606 14 neighborhood neighborhood NN work_ln56cwsp7ffppl4wxeq7osqfuu 606 15 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 606 16 plurality plurality NN work_ln56cwsp7ffppl4wxeq7osqfuu 606 17 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 607 1 Moreover moreover RB work_ln56cwsp7ffppl4wxeq7osqfuu 607 2 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 607 3 as as IN work_ln56cwsp7ffppl4wxeq7osqfuu 607 4 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 607 5 size size NN work_ln56cwsp7ffppl4wxeq7osqfuu 607 6 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 607 7 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 607 8 society society NN work_ln56cwsp7ffppl4wxeq7osqfuu 607 9 increases increase NNS work_ln56cwsp7ffppl4wxeq7osqfuu 607 10 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 607 11 i.e. i.e. FW work_ln56cwsp7ffppl4wxeq7osqfuu 607 12 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 607 13 as as IN work_ln56cwsp7ffppl4wxeq7osqfuu 607 14 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 607 15 probability probability NN work_ln56cwsp7ffppl4wxeq7osqfuu 607 16 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 607 17 ties tie NNS work_ln56cwsp7ffppl4wxeq7osqfuu 607 18 decreases decrease VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 607 19 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 607 20 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 607 21 values value NNS work_ln56cwsp7ffppl4wxeq7osqfuu 607 22 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 607 23 plurality plurality NN work_ln56cwsp7ffppl4wxeq7osqfuu 607 24 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 607 25 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 607 26 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 607 27 best good JJS work_ln56cwsp7ffppl4wxeq7osqfuu 607 28 randomly- randomly- NN work_ln56cwsp7ffppl4wxeq7osqfuu 607 29 generated generate VBN work_ln56cwsp7ffppl4wxeq7osqfuu 607 30 scoring score VBG work_ln56cwsp7ffppl4wxeq7osqfuu 607 31 rule rule NN work_ln56cwsp7ffppl4wxeq7osqfuu 607 32 converge converge NN work_ln56cwsp7ffppl4wxeq7osqfuu 607 33 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 608 1 In in IN work_ln56cwsp7ffppl4wxeq7osqfuu 608 2 particular particular JJ work_ln56cwsp7ffppl4wxeq7osqfuu 608 3 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 608 4 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 608 5 societies society NNS work_ln56cwsp7ffppl4wxeq7osqfuu 608 6 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 608 7 100 100 CD work_ln56cwsp7ffppl4wxeq7osqfuu 608 8 individuals individual NNS work_ln56cwsp7ffppl4wxeq7osqfuu 608 9 we -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 608 10 find find VBP work_ln56cwsp7ffppl4wxeq7osqfuu 608 11 that that IN work_ln56cwsp7ffppl4wxeq7osqfuu 608 12 plurality plurality NN work_ln56cwsp7ffppl4wxeq7osqfuu 608 13 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 608 14 significantly significantly RB work_ln56cwsp7ffppl4wxeq7osqfuu 608 15 better well JJR work_ln56cwsp7ffppl4wxeq7osqfuu 608 16 than than IN work_ln56cwsp7ffppl4wxeq7osqfuu 608 17 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 608 18 best good JJS work_ln56cwsp7ffppl4wxeq7osqfuu 608 19 randomly randomly RB work_ln56cwsp7ffppl4wxeq7osqfuu 608 20 - - HYPH work_ln56cwsp7ffppl4wxeq7osqfuu 608 21 generated generate VBN work_ln56cwsp7ffppl4wxeq7osqfuu 608 22 scoring score VBG work_ln56cwsp7ffppl4wxeq7osqfuu 608 23 rule rule NN work_ln56cwsp7ffppl4wxeq7osqfuu 608 24 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 609 1 For for IN work_ln56cwsp7ffppl4wxeq7osqfuu 609 2 maximin maximin NN work_ln56cwsp7ffppl4wxeq7osqfuu 609 3 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 609 4 when when WRB work_ln56cwsp7ffppl4wxeq7osqfuu 609 5 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 609 6 number number NN work_ln56cwsp7ffppl4wxeq7osqfuu 609 7 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 609 8 individuals individual NNS work_ln56cwsp7ffppl4wxeq7osqfuu 609 9 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 609 10 larger large JJR work_ln56cwsp7ffppl4wxeq7osqfuu 609 11 than than IN work_ln56cwsp7ffppl4wxeq7osqfuu 609 12 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 609 13 number number NN work_ln56cwsp7ffppl4wxeq7osqfuu 609 14 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 609 15 alter- alter- JJ work_ln56cwsp7ffppl4wxeq7osqfuu 609 16 natives native NNS work_ln56cwsp7ffppl4wxeq7osqfuu 609 17 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 609 18 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 609 19 results result NNS work_ln56cwsp7ffppl4wxeq7osqfuu 609 20 are be VBP work_ln56cwsp7ffppl4wxeq7osqfuu 609 21 analogous analogous JJ work_ln56cwsp7ffppl4wxeq7osqfuu 609 22 to to IN work_ln56cwsp7ffppl4wxeq7osqfuu 609 23 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 609 24 case case NN work_ln56cwsp7ffppl4wxeq7osqfuu 609 25 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 609 26 maximax maximax NNP work_ln56cwsp7ffppl4wxeq7osqfuu 609 27 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 610 1 That that RB work_ln56cwsp7ffppl4wxeq7osqfuu 610 2 is is RB work_ln56cwsp7ffppl4wxeq7osqfuu 610 3 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 610 4 negative negative JJ work_ln56cwsp7ffppl4wxeq7osqfuu 610 5 has have VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 610 6 a a DT work_ln56cwsp7ffppl4wxeq7osqfuu 610 7 significantly significantly RB work_ln56cwsp7ffppl4wxeq7osqfuu 610 8 higher high JJR work_ln56cwsp7ffppl4wxeq7osqfuu 610 9 expected expect VBN work_ln56cwsp7ffppl4wxeq7osqfuu 610 10 value value NN work_ln56cwsp7ffppl4wxeq7osqfuu 610 11 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 610 12 a a DT work_ln56cwsp7ffppl4wxeq7osqfuu 610 13 significantly significantly RB work_ln56cwsp7ffppl4wxeq7osqfuu 610 14 higher high JJR work_ln56cwsp7ffppl4wxeq7osqfuu 610 15 probability probability NN work_ln56cwsp7ffppl4wxeq7osqfuu 610 16 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 610 17 selecting select VBG work_ln56cwsp7ffppl4wxeq7osqfuu 610 18 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 610 19 best good JJS work_ln56cwsp7ffppl4wxeq7osqfuu 610 20 alternative alternative NN work_ln56cwsp7ffppl4wxeq7osqfuu 610 21 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 610 22 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 610 23 a a DT work_ln56cwsp7ffppl4wxeq7osqfuu 610 24 significantly significantly RB work_ln56cwsp7ffppl4wxeq7osqfuu 610 25 higher high JJR work_ln56cwsp7ffppl4wxeq7osqfuu 610 26 probability probability NN work_ln56cwsp7ffppl4wxeq7osqfuu 610 27 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 610 28 not not RB work_ln56cwsp7ffppl4wxeq7osqfuu 610 29 selecting select VBG work_ln56cwsp7ffppl4wxeq7osqfuu 610 30 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 610 31 worst bad JJS work_ln56cwsp7ffppl4wxeq7osqfuu 610 32 alter- alter- JJ work_ln56cwsp7ffppl4wxeq7osqfuu 610 33 native native JJ work_ln56cwsp7ffppl4wxeq7osqfuu 610 34 than than IN work_ln56cwsp7ffppl4wxeq7osqfuu 610 35 Borda Borda NNP work_ln56cwsp7ffppl4wxeq7osqfuu 610 36 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 610 37 plurality plurality NN work_ln56cwsp7ffppl4wxeq7osqfuu 610 38 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 611 1 Furthermore furthermore RB work_ln56cwsp7ffppl4wxeq7osqfuu 611 2 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 611 3 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 611 4 best good JJS work_ln56cwsp7ffppl4wxeq7osqfuu 611 5 randomly randomly RB work_ln56cwsp7ffppl4wxeq7osqfuu 611 6 - - HYPH work_ln56cwsp7ffppl4wxeq7osqfuu 611 7 generated generate VBN work_ln56cwsp7ffppl4wxeq7osqfuu 611 8 scoring score VBG work_ln56cwsp7ffppl4wxeq7osqfuu 611 9 rule rule NN work_ln56cwsp7ffppl4wxeq7osqfuu 611 10 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 611 11 in in IN work_ln56cwsp7ffppl4wxeq7osqfuu 611 12 a a DT work_ln56cwsp7ffppl4wxeq7osqfuu 611 13 neighborhood neighborhood NN work_ln56cwsp7ffppl4wxeq7osqfuu 611 14 around around IN work_ln56cwsp7ffppl4wxeq7osqfuu 611 15 negative negative JJ work_ln56cwsp7ffppl4wxeq7osqfuu 611 16 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 612 1 In in IN work_ln56cwsp7ffppl4wxeq7osqfuu 612 2 contrast contrast NN work_ln56cwsp7ffppl4wxeq7osqfuu 612 3 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 612 4 notice notice VB work_ln56cwsp7ffppl4wxeq7osqfuu 612 5 that that IN work_ln56cwsp7ffppl4wxeq7osqfuu 612 6 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 612 7 societies society NNS work_ln56cwsp7ffppl4wxeq7osqfuu 612 8 with with IN work_ln56cwsp7ffppl4wxeq7osqfuu 612 9 n n CC work_ln56cwsp7ffppl4wxeq7osqfuu 612 10 below below IN work_ln56cwsp7ffppl4wxeq7osqfuu 612 11 or or CC work_ln56cwsp7ffppl4wxeq7osqfuu 612 12 around around RB work_ln56cwsp7ffppl4wxeq7osqfuu 612 13 k k NN work_ln56cwsp7ffppl4wxeq7osqfuu 612 14 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 612 15 it -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 612 16 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 612 17 likely likely JJ work_ln56cwsp7ffppl4wxeq7osqfuu 612 18 than than IN work_ln56cwsp7ffppl4wxeq7osqfuu 612 19 more more JJR work_ln56cwsp7ffppl4wxeq7osqfuu 612 20 that that IN work_ln56cwsp7ffppl4wxeq7osqfuu 612 21 one one CD work_ln56cwsp7ffppl4wxeq7osqfuu 612 22 alternative alternative NN work_ln56cwsp7ffppl4wxeq7osqfuu 612 23 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 612 24 not not RB work_ln56cwsp7ffppl4wxeq7osqfuu 612 25 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 612 26 worst bad JJS work_ln56cwsp7ffppl4wxeq7osqfuu 612 27 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 612 28 any any DT work_ln56cwsp7ffppl4wxeq7osqfuu 612 29 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 612 30 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 612 31 individuals individual NNS work_ln56cwsp7ffppl4wxeq7osqfuu 612 32 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 613 1 In in IN work_ln56cwsp7ffppl4wxeq7osqfuu 613 2 such such JJ work_ln56cwsp7ffppl4wxeq7osqfuu 613 3 cases case NNS work_ln56cwsp7ffppl4wxeq7osqfuu 613 4 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 613 5 negative negative JJ work_ln56cwsp7ffppl4wxeq7osqfuu 613 6 chooses choose NNS work_ln56cwsp7ffppl4wxeq7osqfuu 613 7 randomly randomly RB work_ln56cwsp7ffppl4wxeq7osqfuu 613 8 between between IN work_ln56cwsp7ffppl4wxeq7osqfuu 613 9 these these DT work_ln56cwsp7ffppl4wxeq7osqfuu 613 10 alternatives alternative NNS work_ln56cwsp7ffppl4wxeq7osqfuu 613 11 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 613 12 which which WDT work_ln56cwsp7ffppl4wxeq7osqfuu 613 13 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 613 14 not not RB work_ln56cwsp7ffppl4wxeq7osqfuu 613 15 necessarily necessarily RB work_ln56cwsp7ffppl4wxeq7osqfuu 613 16 optimal optimal JJ work_ln56cwsp7ffppl4wxeq7osqfuu 613 17 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 613 18 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 613 19 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 613 20 cause cause NN work_ln56cwsp7ffppl4wxeq7osqfuu 613 21 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 613 22 some some DT work_ln56cwsp7ffppl4wxeq7osqfuu 613 23 distortions distortion NNS work_ln56cwsp7ffppl4wxeq7osqfuu 613 24 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 614 1 As as IN work_ln56cwsp7ffppl4wxeq7osqfuu 614 2 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 614 3 size size NN work_ln56cwsp7ffppl4wxeq7osqfuu 614 4 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 614 5 14We 14we CD work_ln56cwsp7ffppl4wxeq7osqfuu 614 6 find find VBP work_ln56cwsp7ffppl4wxeq7osqfuu 614 7 a a DT work_ln56cwsp7ffppl4wxeq7osqfuu 614 8 few few JJ work_ln56cwsp7ffppl4wxeq7osqfuu 614 9 exceptions exception NNS work_ln56cwsp7ffppl4wxeq7osqfuu 614 10 in in IN work_ln56cwsp7ffppl4wxeq7osqfuu 614 11 small small JJ work_ln56cwsp7ffppl4wxeq7osqfuu 614 12 societies society NNS work_ln56cwsp7ffppl4wxeq7osqfuu 614 13 due due IN work_ln56cwsp7ffppl4wxeq7osqfuu 614 14 to to IN work_ln56cwsp7ffppl4wxeq7osqfuu 614 15 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 614 16 frequency frequency NN work_ln56cwsp7ffppl4wxeq7osqfuu 614 17 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 614 18 ties tie NNS work_ln56cwsp7ffppl4wxeq7osqfuu 614 19 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 615 1 25 25 CD work_ln56cwsp7ffppl4wxeq7osqfuu 615 2 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 615 3 society society NN work_ln56cwsp7ffppl4wxeq7osqfuu 615 4 increases increase NNS work_ln56cwsp7ffppl4wxeq7osqfuu 615 5 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 615 6 this this DT work_ln56cwsp7ffppl4wxeq7osqfuu 615 7 effect effect NN work_ln56cwsp7ffppl4wxeq7osqfuu 615 8 vanishes vanish VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 615 9 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 616 1 In in IN work_ln56cwsp7ffppl4wxeq7osqfuu 616 2 particular particular JJ work_ln56cwsp7ffppl4wxeq7osqfuu 616 3 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 616 4 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 616 5 societies society NNS work_ln56cwsp7ffppl4wxeq7osqfuu 616 6 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 616 7 100 100 CD work_ln56cwsp7ffppl4wxeq7osqfuu 616 8 individuals individual NNS work_ln56cwsp7ffppl4wxeq7osqfuu 616 9 we -PRON- PRP work_ln56cwsp7ffppl4wxeq7osqfuu 616 10 find find VBP work_ln56cwsp7ffppl4wxeq7osqfuu 616 11 that that IN work_ln56cwsp7ffppl4wxeq7osqfuu 616 12 negative negative JJ work_ln56cwsp7ffppl4wxeq7osqfuu 616 13 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 616 14 significantly significantly RB work_ln56cwsp7ffppl4wxeq7osqfuu 616 15 better well JJR work_ln56cwsp7ffppl4wxeq7osqfuu 616 16 than than IN work_ln56cwsp7ffppl4wxeq7osqfuu 616 17 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 616 18 best good JJS work_ln56cwsp7ffppl4wxeq7osqfuu 616 19 randomly randomly RB work_ln56cwsp7ffppl4wxeq7osqfuu 616 20 - - HYPH work_ln56cwsp7ffppl4wxeq7osqfuu 616 21 generated generate VBN work_ln56cwsp7ffppl4wxeq7osqfuu 616 22 scoring score VBG work_ln56cwsp7ffppl4wxeq7osqfuu 616 23 rule rule NN work_ln56cwsp7ffppl4wxeq7osqfuu 616 24 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 617 1 26 26 CD work_ln56cwsp7ffppl4wxeq7osqfuu 617 2 T t NN work_ln56cwsp7ffppl4wxeq7osqfuu 617 3 a a DT work_ln56cwsp7ffppl4wxeq7osqfuu 617 4 b b NN work_ln56cwsp7ffppl4wxeq7osqfuu 617 5 l l NN work_ln56cwsp7ffppl4wxeq7osqfuu 617 6 e e NN work_ln56cwsp7ffppl4wxeq7osqfuu 617 7 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 617 8 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 618 1 U U NNP work_ln56cwsp7ffppl4wxeq7osqfuu 618 2 ti ti NNP work_ln56cwsp7ffppl4wxeq7osqfuu 618 3 li li NNP work_ln56cwsp7ffppl4wxeq7osqfuu 618 4 ta ta NNP work_ln56cwsp7ffppl4wxeq7osqfuu 618 5 ri ri NNP work_ln56cwsp7ffppl4wxeq7osqfuu 618 6 a a DT work_ln56cwsp7ffppl4wxeq7osqfuu 618 7 n n NN work_ln56cwsp7ffppl4wxeq7osqfuu 618 8 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 618 9 m m NN work_ln56cwsp7ffppl4wxeq7osqfuu 618 10 : : : work_ln56cwsp7ffppl4wxeq7osqfuu 618 11 V V NNP work_ln56cwsp7ffppl4wxeq7osqfuu 618 12 a a DT work_ln56cwsp7ffppl4wxeq7osqfuu 618 13 lu lu NN work_ln56cwsp7ffppl4wxeq7osqfuu 618 14 es es NN work_ln56cwsp7ffppl4wxeq7osqfuu 618 15 o o XX work_ln56cwsp7ffppl4wxeq7osqfuu 618 16 f f NNP work_ln56cwsp7ffppl4wxeq7osqfuu 618 17 th th NNP 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work_ln56cwsp7ffppl4wxeq7osqfuu 738 1572 .2 .2 CD work_ln56cwsp7ffppl4wxeq7osqfuu 738 1573 2 2 CD work_ln56cwsp7ffppl4wxeq7osqfuu 738 1574 2 2 CD work_ln56cwsp7ffppl4wxeq7osqfuu 738 1575 3 3 CD work_ln56cwsp7ffppl4wxeq7osqfuu 738 1576 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 738 1577 .2 .2 CD work_ln56cwsp7ffppl4wxeq7osqfuu 738 1578 6 6 CD work_ln56cwsp7ffppl4wxeq7osqfuu 738 1579 3 3 CD work_ln56cwsp7ffppl4wxeq7osqfuu 738 1580 3 3 CD work_ln56cwsp7ffppl4wxeq7osqfuu 738 1581 5 5 CD work_ln56cwsp7ffppl4wxeq7osqfuu 738 1582 .2 .2 CD work_ln56cwsp7ffppl4wxeq7osqfuu 738 1583 9 9 CD work_ln56cwsp7ffppl4wxeq7osqfuu 738 1584 2 2 CD work_ln56cwsp7ffppl4wxeq7osqfuu 738 1585 3 3 CD work_ln56cwsp7ffppl4wxeq7osqfuu 738 1586 2 2 CD work_ln56cwsp7ffppl4wxeq7osqfuu 738 1587 .2 .2 CD work_ln56cwsp7ffppl4wxeq7osqfuu 738 1588 2 2 CD work_ln56cwsp7ffppl4wxeq7osqfuu 738 1589 2 2 CD work_ln56cwsp7ffppl4wxeq7osqfuu 738 1590 7 7 CD work_ln56cwsp7ffppl4wxeq7osqfuu 738 1591 4 4 CD work_ln56cwsp7ffppl4wxeq7osqfuu 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work_ln56cwsp7ffppl4wxeq7osqfuu 738 1613 5 5 CD work_ln56cwsp7ffppl4wxeq7osqfuu 738 1614 0 0 CD work_ln56cwsp7ffppl4wxeq7osqfuu 738 1615 6 6 CD work_ln56cwsp7ffppl4wxeq7osqfuu 738 1616 5 5 CD work_ln56cwsp7ffppl4wxeq7osqfuu 738 1617 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 738 1618 0 0 CD work_ln56cwsp7ffppl4wxeq7osqfuu 738 1619 0 0 CD work_ln56cwsp7ffppl4wxeq7osqfuu 738 1620 × × NN work_ln56cwsp7ffppl4wxeq7osqfuu 738 1621 7 7 CD work_ln56cwsp7ffppl4wxeq7osqfuu 738 1622 .0 .0 CD work_ln56cwsp7ffppl4wxeq7osqfuu 738 1623 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 738 1624 0 0 CD work_ln56cwsp7ffppl4wxeq7osqfuu 738 1625 6 6 CD work_ln56cwsp7ffppl4wxeq7osqfuu 738 1626 4 4 CD work_ln56cwsp7ffppl4wxeq7osqfuu 738 1627 .0 .0 CD work_ln56cwsp7ffppl4wxeq7osqfuu 738 1628 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 738 1629 2 2 CD work_ln56cwsp7ffppl4wxeq7osqfuu 738 1630 3 3 CD work_ln56cwsp7ffppl4wxeq7osqfuu 738 1631 7 7 CD work_ln56cwsp7ffppl4wxeq7osqfuu 738 1632 .0 .0 CD work_ln56cwsp7ffppl4wxeq7osqfuu 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work_ln56cwsp7ffppl4wxeq7osqfuu 738 1654 0 0 CD work_ln56cwsp7ffppl4wxeq7osqfuu 738 1655 2 2 CD work_ln56cwsp7ffppl4wxeq7osqfuu 738 1656 9 9 CD work_ln56cwsp7ffppl4wxeq7osqfuu 738 1657 .2 .2 CD work_ln56cwsp7ffppl4wxeq7osqfuu 738 1658 0 0 CD work_ln56cwsp7ffppl4wxeq7osqfuu 738 1659 7 7 CD work_ln56cwsp7ffppl4wxeq7osqfuu 738 1660 9 9 CD work_ln56cwsp7ffppl4wxeq7osqfuu 738 1661 0 0 CD work_ln56cwsp7ffppl4wxeq7osqfuu 738 1662 .2 .2 CD work_ln56cwsp7ffppl4wxeq7osqfuu 738 1663 5 5 CD work_ln56cwsp7ffppl4wxeq7osqfuu 738 1664 5 5 CD work_ln56cwsp7ffppl4wxeq7osqfuu 738 1665 7 7 CD work_ln56cwsp7ffppl4wxeq7osqfuu 738 1666 7 7 CD work_ln56cwsp7ffppl4wxeq7osqfuu 738 1667 .1 .1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 738 1668 5 5 CD work_ln56cwsp7ffppl4wxeq7osqfuu 738 1669 9 9 CD work_ln56cwsp7ffppl4wxeq7osqfuu 738 1670 9 9 CD work_ln56cwsp7ffppl4wxeq7osqfuu 738 1671 3 3 CD work_ln56cwsp7ffppl4wxeq7osqfuu 738 1672 .2 .2 CD work_ln56cwsp7ffppl4wxeq7osqfuu 738 1673 0 0 CD work_ln56cwsp7ffppl4wxeq7osqfuu 738 1674 7 7 CD work_ln56cwsp7ffppl4wxeq7osqfuu 738 1675 7 7 CD work_ln56cwsp7ffppl4wxeq7osqfuu 738 1676 5 5 CD work_ln56cwsp7ffppl4wxeq7osqfuu 738 1677 .2 .2 CD work_ln56cwsp7ffppl4wxeq7osqfuu 738 1678 5 5 CD work_ln56cwsp7ffppl4wxeq7osqfuu 738 1679 5 5 CD work_ln56cwsp7ffppl4wxeq7osqfuu 738 1680 4 4 CD work_ln56cwsp7ffppl4wxeq7osqfuu 738 1681 3 3 CD work_ln56cwsp7ffppl4wxeq7osqfuu 738 1682 .8 .8 CD work_ln56cwsp7ffppl4wxeq7osqfuu 738 1683 6 6 CD work_ln56cwsp7ffppl4wxeq7osqfuu 738 1684 6 6 CD work_ln56cwsp7ffppl4wxeq7osqfuu 738 1685 0 0 CD work_ln56cwsp7ffppl4wxeq7osqfuu 738 1686 5 5 CD work_ln56cwsp7ffppl4wxeq7osqfuu 738 1687 .8 .8 SYM work_ln56cwsp7ffppl4wxeq7osqfuu 738 1688 8 8 CD work_ln56cwsp7ffppl4wxeq7osqfuu 738 1689 7 7 CD work_ln56cwsp7ffppl4wxeq7osqfuu 738 1690 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 738 1691 7 7 CD work_ln56cwsp7ffppl4wxeq7osqfuu 738 1692 .9 .9 CD work_ln56cwsp7ffppl4wxeq7osqfuu 738 1693 0 0 CD work_ln56cwsp7ffppl4wxeq7osqfuu 738 1694 5 5 CD work_ln56cwsp7ffppl4wxeq7osqfuu 738 1695 9 9 CD work_ln56cwsp7ffppl4wxeq7osqfuu 738 1696 2 2 CD work_ln56cwsp7ffppl4wxeq7osqfuu 738 1697 † † NN work_ln56cwsp7ffppl4wxeq7osqfuu 738 1698 S S NNP work_ln56cwsp7ffppl4wxeq7osqfuu 738 1699 P p NN work_ln56cwsp7ffppl4wxeq7osqfuu 738 1700 l l NN work_ln56cwsp7ffppl4wxeq7osqfuu 738 1701 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 738 1702 S S NNP work_ln56cwsp7ffppl4wxeq7osqfuu 738 1703 B B NNP work_ln56cwsp7ffppl4wxeq7osqfuu 738 1704 d d NNP work_ln56cwsp7ffppl4wxeq7osqfuu 738 1705 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 738 1706 S S NNP work_ln56cwsp7ffppl4wxeq7osqfuu 738 1707 N N NNP work_ln56cwsp7ffppl4wxeq7osqfuu 738 1708 g g NNP work_ln56cwsp7ffppl4wxeq7osqfuu 738 1709 d d NNP work_ln56cwsp7ffppl4wxeq7osqfuu 738 1710 en en FW work_ln56cwsp7ffppl4wxeq7osqfuu 738 1711 ot ot NN work_ln56cwsp7ffppl4wxeq7osqfuu 738 1712 e e NNP work_ln56cwsp7ffppl4wxeq7osqfuu 738 1713 p p NNP work_ln56cwsp7ffppl4wxeq7osqfuu 738 1714 lu lu NNP work_ln56cwsp7ffppl4wxeq7osqfuu 738 1715 ra ra NNP work_ln56cwsp7ffppl4wxeq7osqfuu 738 1716 li li NNP work_ln56cwsp7ffppl4wxeq7osqfuu 738 1717 ty ty NNP work_ln56cwsp7ffppl4wxeq7osqfuu 738 1718 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 738 1719 B b NN work_ln56cwsp7ffppl4wxeq7osqfuu 738 1720 or or CC work_ln56cwsp7ffppl4wxeq7osqfuu 738 1721 d d NNP work_ln56cwsp7ffppl4wxeq7osqfuu 738 1722 a a NNP work_ln56cwsp7ffppl4wxeq7osqfuu 738 1723 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 738 1724 an an DT work_ln56cwsp7ffppl4wxeq7osqfuu 738 1725 d d NNP work_ln56cwsp7ffppl4wxeq7osqfuu 738 1726 n n NN work_ln56cwsp7ffppl4wxeq7osqfuu 738 1727 eg eg NNP work_ln56cwsp7ffppl4wxeq7osqfuu 738 1728 at at IN work_ln56cwsp7ffppl4wxeq7osqfuu 738 1729 iv iv NNP work_ln56cwsp7ffppl4wxeq7osqfuu 738 1730 e e NNP work_ln56cwsp7ffppl4wxeq7osqfuu 738 1731 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 738 1732 re re IN work_ln56cwsp7ffppl4wxeq7osqfuu 738 1733 sp sp NNP work_ln56cwsp7ffppl4wxeq7osqfuu 738 1734 ec ec NNP work_ln56cwsp7ffppl4wxeq7osqfuu 738 1735 ti ti NNP work_ln56cwsp7ffppl4wxeq7osqfuu 738 1736 ve ve NNP work_ln56cwsp7ffppl4wxeq7osqfuu 738 1737 ly ly XX work_ln56cwsp7ffppl4wxeq7osqfuu 738 1738 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 739 1 29 29 CD work_ln56cwsp7ffppl4wxeq7osqfuu 739 2 References reference NNS work_ln56cwsp7ffppl4wxeq7osqfuu 739 3 [ [ -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 739 4 1 1 CD work_ln56cwsp7ffppl4wxeq7osqfuu 739 5 ] ] -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 739 6 Balakrishnan Balakrishnan NNP work_ln56cwsp7ffppl4wxeq7osqfuu 739 7 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 739 8 N. N. NNP work_ln56cwsp7ffppl4wxeq7osqfuu 739 9 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 739 10 K.S. K.S. NNP work_ln56cwsp7ffppl4wxeq7osqfuu 740 1 Sultan Sultan NNP work_ln56cwsp7ffppl4wxeq7osqfuu 740 2 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 740 3 1998 1998 CD work_ln56cwsp7ffppl4wxeq7osqfuu 740 4 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 740 5 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 740 6 “ " `` work_ln56cwsp7ffppl4wxeq7osqfuu 740 7 Recurrence Recurrence NNP work_ln56cwsp7ffppl4wxeq7osqfuu 740 8 Relations Relations NNPS work_ln56cwsp7ffppl4wxeq7osqfuu 740 9 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 740 10 Identities Identities NNPS work_ln56cwsp7ffppl4wxeq7osqfuu 740 11 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 740 12 Moments Moments NNPS work_ln56cwsp7ffppl4wxeq7osqfuu 740 13 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 740 14 Order Order NNP work_ln56cwsp7ffppl4wxeq7osqfuu 740 15 Statistics Statistics NNPS work_ln56cwsp7ffppl4wxeq7osqfuu 740 16 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 740 17 ” " '' work_ln56cwsp7ffppl4wxeq7osqfuu 740 18 in in IN work_ln56cwsp7ffppl4wxeq7osqfuu 740 19 N. N. NNP work_ln56cwsp7ffppl4wxeq7osqfuu 740 20 Balakrishnan Balakrishnan NNP work_ln56cwsp7ffppl4wxeq7osqfuu 740 21 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 740 22 C.R. C.R. NNP work_ln56cwsp7ffppl4wxeq7osqfuu 741 1 Rao Rao NNP work_ln56cwsp7ffppl4wxeq7osqfuu 741 2 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 741 3 eds eds NN work_ln56cwsp7ffppl4wxeq7osqfuu 741 4 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 741 5 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 742 1 Handbook Handbook NNP work_ln56cwsp7ffppl4wxeq7osqfuu 742 2 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 742 3 Statistics statistic NNS work_ln56cwsp7ffppl4wxeq7osqfuu 742 4 16 16 CD work_ln56cwsp7ffppl4wxeq7osqfuu 742 5 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 742 6 North- North- NNP work_ln56cwsp7ffppl4wxeq7osqfuu 742 7 Holland Holland NNP work_ln56cwsp7ffppl4wxeq7osqfuu 742 8 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 743 1 [ [ -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 743 2 2 2 LS work_ln56cwsp7ffppl4wxeq7osqfuu 743 3 ] ] -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 743 4 Barbera Barbera NNP work_ln56cwsp7ffppl4wxeq7osqfuu 743 5 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 743 6 S. S. NNP work_ln56cwsp7ffppl4wxeq7osqfuu 743 7 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 743 8 M. M. NNP work_ln56cwsp7ffppl4wxeq7osqfuu 743 9 Jackson Jackson NNP work_ln56cwsp7ffppl4wxeq7osqfuu 743 10 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 743 11 2004 2004 CD work_ln56cwsp7ffppl4wxeq7osqfuu 743 12 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 743 13 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 743 14 “ " `` work_ln56cwsp7ffppl4wxeq7osqfuu 743 15 Choosing choose VBG work_ln56cwsp7ffppl4wxeq7osqfuu 743 16 How how WRB work_ln56cwsp7ffppl4wxeq7osqfuu 743 17 to to TO work_ln56cwsp7ffppl4wxeq7osqfuu 743 18 Choose choose VB work_ln56cwsp7ffppl4wxeq7osqfuu 743 19 : : : work_ln56cwsp7ffppl4wxeq7osqfuu 743 20 Self self NN work_ln56cwsp7ffppl4wxeq7osqfuu 743 21 - - HYPH work_ln56cwsp7ffppl4wxeq7osqfuu 743 22 Stable stable JJ work_ln56cwsp7ffppl4wxeq7osqfuu 743 23 Majority Majority NNP work_ln56cwsp7ffppl4wxeq7osqfuu 743 24 Rules Rules NNPS work_ln56cwsp7ffppl4wxeq7osqfuu 743 25 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 743 26 Constitutions Constitutions NNPS work_ln56cwsp7ffppl4wxeq7osqfuu 743 27 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 743 28 ” " '' work_ln56cwsp7ffppl4wxeq7osqfuu 743 29 Quarterly Quarterly NNP work_ln56cwsp7ffppl4wxeq7osqfuu 743 30 Journal Journal NNP work_ln56cwsp7ffppl4wxeq7osqfuu 743 31 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 743 32 Economics Economics NNP work_ln56cwsp7ffppl4wxeq7osqfuu 743 33 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 743 34 119:1011 119:1011 NNP work_ln56cwsp7ffppl4wxeq7osqfuu 743 35 - - SYM work_ln56cwsp7ffppl4wxeq7osqfuu 743 36 1048 1048 CD work_ln56cwsp7ffppl4wxeq7osqfuu 743 37 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 744 1 [ [ -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 744 2 3 3 LS work_ln56cwsp7ffppl4wxeq7osqfuu 744 3 ] ] -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 744 4 Barbera Barbera NNP work_ln56cwsp7ffppl4wxeq7osqfuu 744 5 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 744 6 S. S. NNP work_ln56cwsp7ffppl4wxeq7osqfuu 744 7 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 744 8 M. M. NNP work_ln56cwsp7ffppl4wxeq7osqfuu 744 9 Jackson Jackson NNP work_ln56cwsp7ffppl4wxeq7osqfuu 744 10 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 744 11 2006 2006 CD work_ln56cwsp7ffppl4wxeq7osqfuu 744 12 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 744 13 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 744 14 “ " `` work_ln56cwsp7ffppl4wxeq7osqfuu 744 15 On on IN work_ln56cwsp7ffppl4wxeq7osqfuu 744 16 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 744 17 Weights Weights NNPS work_ln56cwsp7ffppl4wxeq7osqfuu 744 18 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 744 19 Nations Nations NNPS work_ln56cwsp7ffppl4wxeq7osqfuu 744 20 : : : work_ln56cwsp7ffppl4wxeq7osqfuu 744 21 Assigning Assigning NNP work_ln56cwsp7ffppl4wxeq7osqfuu 744 22 Voting Voting NNP work_ln56cwsp7ffppl4wxeq7osqfuu 744 23 Weights Weights NNPS work_ln56cwsp7ffppl4wxeq7osqfuu 744 24 in in IN work_ln56cwsp7ffppl4wxeq7osqfuu 744 25 a a DT work_ln56cwsp7ffppl4wxeq7osqfuu 744 26 Heterogeneous Heterogeneous NNP work_ln56cwsp7ffppl4wxeq7osqfuu 744 27 Union Union NNP work_ln56cwsp7ffppl4wxeq7osqfuu 744 28 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 744 29 ” " '' work_ln56cwsp7ffppl4wxeq7osqfuu 744 30 Journal Journal NNP work_ln56cwsp7ffppl4wxeq7osqfuu 744 31 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 744 32 Political Political NNP work_ln56cwsp7ffppl4wxeq7osqfuu 744 33 Economy Economy NNP work_ln56cwsp7ffppl4wxeq7osqfuu 744 34 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 744 35 114:317 114:317 CD work_ln56cwsp7ffppl4wxeq7osqfuu 744 36 - - SYM work_ln56cwsp7ffppl4wxeq7osqfuu 744 37 339 339 CD work_ln56cwsp7ffppl4wxeq7osqfuu 744 38 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 745 1 [ [ -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 745 2 4 4 CD work_ln56cwsp7ffppl4wxeq7osqfuu 745 3 ] ] -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 745 4 Barnett Barnett NNP work_ln56cwsp7ffppl4wxeq7osqfuu 745 5 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 745 6 V.D. V.D. NNP work_ln56cwsp7ffppl4wxeq7osqfuu 746 1 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 746 2 1966 1966 CD work_ln56cwsp7ffppl4wxeq7osqfuu 746 3 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 746 4 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 746 5 “ " `` work_ln56cwsp7ffppl4wxeq7osqfuu 746 6 Order Order NNP work_ln56cwsp7ffppl4wxeq7osqfuu 746 7 Statistics Statistics NNPS work_ln56cwsp7ffppl4wxeq7osqfuu 746 8 Estimators Estimators NNPS work_ln56cwsp7ffppl4wxeq7osqfuu 746 9 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 746 10 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 746 11 Location Location NNP work_ln56cwsp7ffppl4wxeq7osqfuu 746 12 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 746 13 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 746 14 Cauchy Cauchy NNP work_ln56cwsp7ffppl4wxeq7osqfuu 746 15 Distribution Distribution NNP work_ln56cwsp7ffppl4wxeq7osqfuu 746 16 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 746 17 ” " '' work_ln56cwsp7ffppl4wxeq7osqfuu 746 18 Journal Journal NNP work_ln56cwsp7ffppl4wxeq7osqfuu 746 19 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 746 20 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 746 21 American American NNP work_ln56cwsp7ffppl4wxeq7osqfuu 746 22 Statistical Statistical NNP work_ln56cwsp7ffppl4wxeq7osqfuu 746 23 Association Association NNP work_ln56cwsp7ffppl4wxeq7osqfuu 746 24 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 746 25 61:1205 61:1205 CD work_ln56cwsp7ffppl4wxeq7osqfuu 746 26 - - SYM work_ln56cwsp7ffppl4wxeq7osqfuu 746 27 1218 1218 CD work_ln56cwsp7ffppl4wxeq7osqfuu 746 28 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 747 1 [ [ -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 747 2 5 5 CD work_ln56cwsp7ffppl4wxeq7osqfuu 747 3 ] ] -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 747 4 Benoit Benoit NNP work_ln56cwsp7ffppl4wxeq7osqfuu 747 5 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 747 6 J.P. J.P. NNP work_ln56cwsp7ffppl4wxeq7osqfuu 747 7 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 747 8 L.A. L.A. NNP work_ln56cwsp7ffppl4wxeq7osqfuu 747 9 Kornhauser Kornhauser NNP work_ln56cwsp7ffppl4wxeq7osqfuu 747 10 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 747 11 2007 2007 CD work_ln56cwsp7ffppl4wxeq7osqfuu 747 12 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 747 13 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 747 14 “ " `` work_ln56cwsp7ffppl4wxeq7osqfuu 747 15 Only only RB work_ln56cwsp7ffppl4wxeq7osqfuu 747 16 a a DT work_ln56cwsp7ffppl4wxeq7osqfuu 747 17 Dictatorship dictatorship NN work_ln56cwsp7ffppl4wxeq7osqfuu 747 18 is be VBZ work_ln56cwsp7ffppl4wxeq7osqfuu 747 19 Efficient efficient JJ work_ln56cwsp7ffppl4wxeq7osqfuu 747 20 or or CC work_ln56cwsp7ffppl4wxeq7osqfuu 747 21 Neutral neutral JJ work_ln56cwsp7ffppl4wxeq7osqfuu 747 22 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 747 23 ” " '' work_ln56cwsp7ffppl4wxeq7osqfuu 747 24 mimeo mimeo NNP work_ln56cwsp7ffppl4wxeq7osqfuu 747 25 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 747 26 LBS LBS NNP work_ln56cwsp7ffppl4wxeq7osqfuu 747 27 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 748 1 [ [ -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 748 2 6 6 CD work_ln56cwsp7ffppl4wxeq7osqfuu 748 3 ] ] -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 748 4 Börgers Börgers NNP work_ln56cwsp7ffppl4wxeq7osqfuu 748 5 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 748 6 T. T. NNP work_ln56cwsp7ffppl4wxeq7osqfuu 748 7 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 748 8 P. P. NNP work_ln56cwsp7ffppl4wxeq7osqfuu 748 9 Postl Postl NNP work_ln56cwsp7ffppl4wxeq7osqfuu 748 10 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 748 11 2007 2007 CD work_ln56cwsp7ffppl4wxeq7osqfuu 748 12 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 748 13 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 748 14 “ " `` work_ln56cwsp7ffppl4wxeq7osqfuu 748 15 Efficient Efficient NNP work_ln56cwsp7ffppl4wxeq7osqfuu 748 16 Compromising Compromising NNP work_ln56cwsp7ffppl4wxeq7osqfuu 748 17 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 748 18 ” " '' work_ln56cwsp7ffppl4wxeq7osqfuu 748 19 mimeo mimeo NNP work_ln56cwsp7ffppl4wxeq7osqfuu 748 20 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 748 21 University University NNP work_ln56cwsp7ffppl4wxeq7osqfuu 748 22 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 748 23 Michigan Michigan NNP work_ln56cwsp7ffppl4wxeq7osqfuu 748 24 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 749 1 [ [ -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 749 2 7 7 CD work_ln56cwsp7ffppl4wxeq7osqfuu 749 3 ] ] -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 749 4 Black Black NNP work_ln56cwsp7ffppl4wxeq7osqfuu 749 5 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 749 6 D. D. NNP work_ln56cwsp7ffppl4wxeq7osqfuu 749 7 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 749 8 1958 1958 CD work_ln56cwsp7ffppl4wxeq7osqfuu 749 9 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 749 10 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 749 11 The the DT work_ln56cwsp7ffppl4wxeq7osqfuu 749 12 Theory Theory NNP work_ln56cwsp7ffppl4wxeq7osqfuu 749 13 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 749 14 Committees Committees NNPS work_ln56cwsp7ffppl4wxeq7osqfuu 749 15 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 749 16 Elections Elections NNPS work_ln56cwsp7ffppl4wxeq7osqfuu 749 17 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 750 1 Cambridge Cambridge NNP work_ln56cwsp7ffppl4wxeq7osqfuu 750 2 : : : work_ln56cwsp7ffppl4wxeq7osqfuu 750 3 Cambridge Cambridge NNP work_ln56cwsp7ffppl4wxeq7osqfuu 750 4 University University NNP work_ln56cwsp7ffppl4wxeq7osqfuu 750 5 Press Press NNP work_ln56cwsp7ffppl4wxeq7osqfuu 750 6 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 751 1 [ [ -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 751 2 8 8 CD work_ln56cwsp7ffppl4wxeq7osqfuu 751 3 ] ] -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 751 4 Brams Brams NNP work_ln56cwsp7ffppl4wxeq7osqfuu 751 5 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 751 6 S.J. S.J. NNP work_ln56cwsp7ffppl4wxeq7osqfuu 752 1 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 752 2 P.C. P.C. NNP work_ln56cwsp7ffppl4wxeq7osqfuu 753 1 Fishburn Fishburn NNP work_ln56cwsp7ffppl4wxeq7osqfuu 753 2 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 753 3 1978 1978 CD work_ln56cwsp7ffppl4wxeq7osqfuu 753 4 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 753 5 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 753 6 “ " `` work_ln56cwsp7ffppl4wxeq7osqfuu 753 7 Approval Approval NNP work_ln56cwsp7ffppl4wxeq7osqfuu 753 8 Voting voting NN work_ln56cwsp7ffppl4wxeq7osqfuu 753 9 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 753 10 ” " '' work_ln56cwsp7ffppl4wxeq7osqfuu 753 11 American American NNP work_ln56cwsp7ffppl4wxeq7osqfuu 753 12 Political Political NNP work_ln56cwsp7ffppl4wxeq7osqfuu 753 13 Science Science NNP work_ln56cwsp7ffppl4wxeq7osqfuu 753 14 Review Review NNP work_ln56cwsp7ffppl4wxeq7osqfuu 753 15 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 753 16 72:831 72:831 CD work_ln56cwsp7ffppl4wxeq7osqfuu 753 17 - - SYM work_ln56cwsp7ffppl4wxeq7osqfuu 753 18 847 847 CD work_ln56cwsp7ffppl4wxeq7osqfuu 753 19 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 754 1 [ [ -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 754 2 9 9 CD work_ln56cwsp7ffppl4wxeq7osqfuu 754 3 ] ] -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 754 4 Bordley Bordley NNP work_ln56cwsp7ffppl4wxeq7osqfuu 754 5 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 754 6 R.F. R.F. NNP work_ln56cwsp7ffppl4wxeq7osqfuu 755 1 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 755 2 1983 1983 CD work_ln56cwsp7ffppl4wxeq7osqfuu 755 3 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 755 4 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 755 5 “ " `` work_ln56cwsp7ffppl4wxeq7osqfuu 755 6 A a DT work_ln56cwsp7ffppl4wxeq7osqfuu 755 7 Pragmatic pragmatic JJ work_ln56cwsp7ffppl4wxeq7osqfuu 755 8 Method method NN work_ln56cwsp7ffppl4wxeq7osqfuu 755 9 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 755 10 Evaluating evaluate VBG work_ln56cwsp7ffppl4wxeq7osqfuu 755 11 Election election NN work_ln56cwsp7ffppl4wxeq7osqfuu 755 12 Schemes Schemes NNPS work_ln56cwsp7ffppl4wxeq7osqfuu 755 13 through through IN work_ln56cwsp7ffppl4wxeq7osqfuu 755 14 Simula- Simula- NNP work_ln56cwsp7ffppl4wxeq7osqfuu 755 15 tion tion NN work_ln56cwsp7ffppl4wxeq7osqfuu 755 16 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 755 17 ” " '' work_ln56cwsp7ffppl4wxeq7osqfuu 755 18 American American NNP work_ln56cwsp7ffppl4wxeq7osqfuu 755 19 Political Political NNP work_ln56cwsp7ffppl4wxeq7osqfuu 755 20 Science Science NNP work_ln56cwsp7ffppl4wxeq7osqfuu 755 21 Review Review NNP work_ln56cwsp7ffppl4wxeq7osqfuu 755 22 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 755 23 77:123 77:123 CD work_ln56cwsp7ffppl4wxeq7osqfuu 755 24 - - SYM work_ln56cwsp7ffppl4wxeq7osqfuu 755 25 141 141 CD work_ln56cwsp7ffppl4wxeq7osqfuu 755 26 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 756 1 [ [ -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 756 2 10 10 CD work_ln56cwsp7ffppl4wxeq7osqfuu 756 3 ] ] -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 756 4 Caplin Caplin NNP work_ln56cwsp7ffppl4wxeq7osqfuu 756 5 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 756 6 A. a. NN work_ln56cwsp7ffppl4wxeq7osqfuu 756 7 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 756 8 B. B. NNP work_ln56cwsp7ffppl4wxeq7osqfuu 756 9 Nalebuff Nalebuff NNP work_ln56cwsp7ffppl4wxeq7osqfuu 756 10 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 756 11 1988 1988 CD work_ln56cwsp7ffppl4wxeq7osqfuu 756 12 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 756 13 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 756 14 “ " `` work_ln56cwsp7ffppl4wxeq7osqfuu 756 15 On on IN work_ln56cwsp7ffppl4wxeq7osqfuu 756 16 64%-Majority 64%-Majority NNP work_ln56cwsp7ffppl4wxeq7osqfuu 756 17 Rule Rule NNP work_ln56cwsp7ffppl4wxeq7osqfuu 756 18 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 756 19 ” " '' work_ln56cwsp7ffppl4wxeq7osqfuu 756 20 Econometrica Econometrica NNP work_ln56cwsp7ffppl4wxeq7osqfuu 756 21 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 756 22 56:787 56:787 CD work_ln56cwsp7ffppl4wxeq7osqfuu 756 23 - - HYPH work_ln56cwsp7ffppl4wxeq7osqfuu 756 24 814 814 CD work_ln56cwsp7ffppl4wxeq7osqfuu 756 25 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 757 1 [ [ -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 757 2 11 11 CD work_ln56cwsp7ffppl4wxeq7osqfuu 757 3 ] ] -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 757 4 Dasgupta Dasgupta NNP work_ln56cwsp7ffppl4wxeq7osqfuu 757 5 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 757 6 P P NNP work_ln56cwsp7ffppl4wxeq7osqfuu 757 7 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 757 8 E. E. NNP work_ln56cwsp7ffppl4wxeq7osqfuu 757 9 Maskin Maskin NNP work_ln56cwsp7ffppl4wxeq7osqfuu 757 10 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 757 11 2008 2008 CD work_ln56cwsp7ffppl4wxeq7osqfuu 757 12 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 757 13 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 757 14 “ " `` work_ln56cwsp7ffppl4wxeq7osqfuu 757 15 On on IN work_ln56cwsp7ffppl4wxeq7osqfuu 757 16 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 757 17 Robustness Robustness NNP work_ln56cwsp7ffppl4wxeq7osqfuu 757 18 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 757 19 Majority Majority NNP work_ln56cwsp7ffppl4wxeq7osqfuu 757 20 Rule Rule NNP work_ln56cwsp7ffppl4wxeq7osqfuu 757 21 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 757 22 ” " '' work_ln56cwsp7ffppl4wxeq7osqfuu 757 23 Journal Journal NNP work_ln56cwsp7ffppl4wxeq7osqfuu 757 24 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 757 25 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 757 26 European European NNP work_ln56cwsp7ffppl4wxeq7osqfuu 757 27 Economic Economic NNP work_ln56cwsp7ffppl4wxeq7osqfuu 757 28 Association Association NNP work_ln56cwsp7ffppl4wxeq7osqfuu 757 29 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 757 30 forthcoming forthcoming JJ work_ln56cwsp7ffppl4wxeq7osqfuu 757 31 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 758 1 [ [ -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 758 2 12 12 CD work_ln56cwsp7ffppl4wxeq7osqfuu 758 3 ] ] -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 758 4 DeMeyer DeMeyer NNP work_ln56cwsp7ffppl4wxeq7osqfuu 758 5 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 758 6 F. F. NNP work_ln56cwsp7ffppl4wxeq7osqfuu 758 7 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 758 8 C.R. C.R. NNP work_ln56cwsp7ffppl4wxeq7osqfuu 759 1 Plott Plott NNP work_ln56cwsp7ffppl4wxeq7osqfuu 759 2 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 759 3 1970 1970 CD work_ln56cwsp7ffppl4wxeq7osqfuu 759 4 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 759 5 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 759 6 “ " `` work_ln56cwsp7ffppl4wxeq7osqfuu 759 7 The the DT work_ln56cwsp7ffppl4wxeq7osqfuu 759 8 Probability Probability NNP work_ln56cwsp7ffppl4wxeq7osqfuu 759 9 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 759 10 a a DT work_ln56cwsp7ffppl4wxeq7osqfuu 759 11 Cyclical Cyclical NNP work_ln56cwsp7ffppl4wxeq7osqfuu 759 12 Majority Majority NNP work_ln56cwsp7ffppl4wxeq7osqfuu 759 13 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 759 14 ” " '' work_ln56cwsp7ffppl4wxeq7osqfuu 759 15 Econometrica Econometrica NNP work_ln56cwsp7ffppl4wxeq7osqfuu 759 16 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 759 17 38:345 38:345 CD work_ln56cwsp7ffppl4wxeq7osqfuu 759 18 - - SYM work_ln56cwsp7ffppl4wxeq7osqfuu 759 19 354 354 CD work_ln56cwsp7ffppl4wxeq7osqfuu 759 20 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 760 1 [ [ -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 760 2 13 13 CD work_ln56cwsp7ffppl4wxeq7osqfuu 760 3 ] ] -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 760 4 Gehrlein Gehrlein NNP work_ln56cwsp7ffppl4wxeq7osqfuu 760 5 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 760 6 W.V. W.V. NNP work_ln56cwsp7ffppl4wxeq7osqfuu 761 1 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 761 2 1997 1997 CD work_ln56cwsp7ffppl4wxeq7osqfuu 761 3 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 761 4 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 761 5 “ " `` work_ln56cwsp7ffppl4wxeq7osqfuu 761 6 Condorcet Condorcet NNP work_ln56cwsp7ffppl4wxeq7osqfuu 761 7 ’s ’s POS work_ln56cwsp7ffppl4wxeq7osqfuu 761 8 Paradox Paradox NNP work_ln56cwsp7ffppl4wxeq7osqfuu 761 9 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 761 10 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 761 11 Condorcet Condorcet NNP work_ln56cwsp7ffppl4wxeq7osqfuu 761 12 Efficiency Efficiency NNP work_ln56cwsp7ffppl4wxeq7osqfuu 761 13 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 761 14 Voting Voting NNP work_ln56cwsp7ffppl4wxeq7osqfuu 761 15 Rules Rules NNPS work_ln56cwsp7ffppl4wxeq7osqfuu 761 16 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 761 17 ” " '' work_ln56cwsp7ffppl4wxeq7osqfuu 761 18 Mathematica Mathematica NNP work_ln56cwsp7ffppl4wxeq7osqfuu 761 19 Japonica Japonica NNP work_ln56cwsp7ffppl4wxeq7osqfuu 761 20 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 761 21 45 45 CD work_ln56cwsp7ffppl4wxeq7osqfuu 761 22 : : SYM work_ln56cwsp7ffppl4wxeq7osqfuu 761 23 173 173 CD work_ln56cwsp7ffppl4wxeq7osqfuu 761 24 - - SYM work_ln56cwsp7ffppl4wxeq7osqfuu 761 25 199 199 CD work_ln56cwsp7ffppl4wxeq7osqfuu 761 26 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 762 1 [ [ -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 762 2 14 14 CD work_ln56cwsp7ffppl4wxeq7osqfuu 762 3 ] ] -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 762 4 Kamps Kamps NNP work_ln56cwsp7ffppl4wxeq7osqfuu 762 5 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 762 6 U. U. NNP work_ln56cwsp7ffppl4wxeq7osqfuu 763 1 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 763 2 1991 1991 CD work_ln56cwsp7ffppl4wxeq7osqfuu 763 3 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 763 4 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 763 5 “ " `` work_ln56cwsp7ffppl4wxeq7osqfuu 763 6 A a DT work_ln56cwsp7ffppl4wxeq7osqfuu 763 7 General General NNP work_ln56cwsp7ffppl4wxeq7osqfuu 763 8 Recurrence Recurrence NNP work_ln56cwsp7ffppl4wxeq7osqfuu 763 9 Relation Relation NNP work_ln56cwsp7ffppl4wxeq7osqfuu 763 10 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 763 11 Moments Moments NNPS work_ln56cwsp7ffppl4wxeq7osqfuu 763 12 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 763 13 Order Order NNP work_ln56cwsp7ffppl4wxeq7osqfuu 763 14 Statistics Statistics NNPS work_ln56cwsp7ffppl4wxeq7osqfuu 763 15 in in IN work_ln56cwsp7ffppl4wxeq7osqfuu 763 16 a a DT work_ln56cwsp7ffppl4wxeq7osqfuu 763 17 Class Class NNP work_ln56cwsp7ffppl4wxeq7osqfuu 763 18 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 763 19 Probability Probability NNP work_ln56cwsp7ffppl4wxeq7osqfuu 763 20 Distributions Distributions NNPS work_ln56cwsp7ffppl4wxeq7osqfuu 763 21 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 763 22 Characterizations Characterizations NNPS work_ln56cwsp7ffppl4wxeq7osqfuu 763 23 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 763 24 ” " '' work_ln56cwsp7ffppl4wxeq7osqfuu 763 25 Metrika Metrika NNP work_ln56cwsp7ffppl4wxeq7osqfuu 763 26 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 763 27 38:215 38:215 CD work_ln56cwsp7ffppl4wxeq7osqfuu 763 28 - - SYM work_ln56cwsp7ffppl4wxeq7osqfuu 763 29 225 225 CD work_ln56cwsp7ffppl4wxeq7osqfuu 763 30 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 764 1 [ [ -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 764 2 15 15 CD work_ln56cwsp7ffppl4wxeq7osqfuu 764 3 ] ] -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 764 4 Kamps Kamps NNP work_ln56cwsp7ffppl4wxeq7osqfuu 764 5 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 764 6 U. U. NNP work_ln56cwsp7ffppl4wxeq7osqfuu 765 1 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 765 2 1992 1992 CD work_ln56cwsp7ffppl4wxeq7osqfuu 765 3 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 765 4 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 765 5 “ " `` work_ln56cwsp7ffppl4wxeq7osqfuu 765 6 Identities identity NNS work_ln56cwsp7ffppl4wxeq7osqfuu 765 7 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 765 8 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 765 9 Difference Difference NNP work_ln56cwsp7ffppl4wxeq7osqfuu 765 10 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 765 11 Moments Moments NNPS work_ln56cwsp7ffppl4wxeq7osqfuu 765 12 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 765 13 Successive Successive NNP work_ln56cwsp7ffppl4wxeq7osqfuu 765 14 Order Order NNP work_ln56cwsp7ffppl4wxeq7osqfuu 765 15 Statistics Statistics NNPS work_ln56cwsp7ffppl4wxeq7osqfuu 765 16 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 765 17 Record Record NNP work_ln56cwsp7ffppl4wxeq7osqfuu 765 18 Values value NNS work_ln56cwsp7ffppl4wxeq7osqfuu 765 19 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 765 20 ” " '' work_ln56cwsp7ffppl4wxeq7osqfuu 765 21 Metron Metron NNP work_ln56cwsp7ffppl4wxeq7osqfuu 765 22 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 765 23 50:179 50:179 CD work_ln56cwsp7ffppl4wxeq7osqfuu 765 24 - - SYM work_ln56cwsp7ffppl4wxeq7osqfuu 765 25 187 187 CD work_ln56cwsp7ffppl4wxeq7osqfuu 765 26 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 766 1 [ [ -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 766 2 16 16 CD work_ln56cwsp7ffppl4wxeq7osqfuu 766 3 ] ] -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 766 4 Levin Levin NNP work_ln56cwsp7ffppl4wxeq7osqfuu 766 5 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 766 6 J. J. NNP work_ln56cwsp7ffppl4wxeq7osqfuu 766 7 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 766 8 B. B. NNP work_ln56cwsp7ffppl4wxeq7osqfuu 766 9 Nalebuff Nalebuff NNP work_ln56cwsp7ffppl4wxeq7osqfuu 766 10 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 766 11 1995 1995 CD work_ln56cwsp7ffppl4wxeq7osqfuu 766 12 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 766 13 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 766 14 “ " `` work_ln56cwsp7ffppl4wxeq7osqfuu 766 15 An an DT work_ln56cwsp7ffppl4wxeq7osqfuu 766 16 Introduction introduction NN work_ln56cwsp7ffppl4wxeq7osqfuu 766 17 to to TO work_ln56cwsp7ffppl4wxeq7osqfuu 766 18 Vote vote VB work_ln56cwsp7ffppl4wxeq7osqfuu 766 19 - - HYPH work_ln56cwsp7ffppl4wxeq7osqfuu 766 20 Counting Counting NNP work_ln56cwsp7ffppl4wxeq7osqfuu 766 21 Schemes Schemes NNPS work_ln56cwsp7ffppl4wxeq7osqfuu 766 22 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 766 23 ” " '' work_ln56cwsp7ffppl4wxeq7osqfuu 766 24 Journal Journal NNP work_ln56cwsp7ffppl4wxeq7osqfuu 766 25 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 766 26 Economic Economic NNP work_ln56cwsp7ffppl4wxeq7osqfuu 766 27 Perspectives Perspectives NNPS work_ln56cwsp7ffppl4wxeq7osqfuu 766 28 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 766 29 9:3 9:3 CD work_ln56cwsp7ffppl4wxeq7osqfuu 766 30 - - SYM work_ln56cwsp7ffppl4wxeq7osqfuu 766 31 26 26 CD work_ln56cwsp7ffppl4wxeq7osqfuu 766 32 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 767 1 [ [ -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 767 2 17 17 CD work_ln56cwsp7ffppl4wxeq7osqfuu 767 3 ] ] -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 767 4 Maggi Maggi NNP work_ln56cwsp7ffppl4wxeq7osqfuu 767 5 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 767 6 G. G. NNP work_ln56cwsp7ffppl4wxeq7osqfuu 767 7 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 767 8 M. M. NNP work_ln56cwsp7ffppl4wxeq7osqfuu 767 9 Morelli Morelli NNP work_ln56cwsp7ffppl4wxeq7osqfuu 767 10 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 767 11 2006 2006 CD work_ln56cwsp7ffppl4wxeq7osqfuu 767 12 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 767 13 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 767 14 “ " `` work_ln56cwsp7ffppl4wxeq7osqfuu 767 15 Self self NN work_ln56cwsp7ffppl4wxeq7osqfuu 767 16 - - HYPH work_ln56cwsp7ffppl4wxeq7osqfuu 767 17 Enforcing enforce VBG work_ln56cwsp7ffppl4wxeq7osqfuu 767 18 Voting Voting NNP work_ln56cwsp7ffppl4wxeq7osqfuu 767 19 in in IN work_ln56cwsp7ffppl4wxeq7osqfuu 767 20 International International NNP work_ln56cwsp7ffppl4wxeq7osqfuu 767 21 Organizations Organizations NNP work_ln56cwsp7ffppl4wxeq7osqfuu 767 22 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 767 23 ” " '' work_ln56cwsp7ffppl4wxeq7osqfuu 767 24 Amer- amer- JJ work_ln56cwsp7ffppl4wxeq7osqfuu 767 25 ican ican JJ work_ln56cwsp7ffppl4wxeq7osqfuu 767 26 Economic Economic NNP work_ln56cwsp7ffppl4wxeq7osqfuu 767 27 Review Review NNP work_ln56cwsp7ffppl4wxeq7osqfuu 767 28 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 767 29 Vol Vol NNP work_ln56cwsp7ffppl4wxeq7osqfuu 767 30 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 768 1 96 96 CD work_ln56cwsp7ffppl4wxeq7osqfuu 768 2 - - HYPH work_ln56cwsp7ffppl4wxeq7osqfuu 768 3 4:1137 4:1137 CD work_ln56cwsp7ffppl4wxeq7osqfuu 768 4 - - SYM work_ln56cwsp7ffppl4wxeq7osqfuu 768 5 58 58 CD work_ln56cwsp7ffppl4wxeq7osqfuu 768 6 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 769 1 [ [ -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 769 2 18 18 CD work_ln56cwsp7ffppl4wxeq7osqfuu 769 3 ] ] -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 769 4 Merrill Merrill NNP work_ln56cwsp7ffppl4wxeq7osqfuu 769 5 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 769 6 S. S. NNP work_ln56cwsp7ffppl4wxeq7osqfuu 769 7 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 769 8 1984 1984 CD work_ln56cwsp7ffppl4wxeq7osqfuu 769 9 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 769 10 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 769 11 “ " `` work_ln56cwsp7ffppl4wxeq7osqfuu 769 12 A a DT work_ln56cwsp7ffppl4wxeq7osqfuu 769 13 Comparison Comparison NNP work_ln56cwsp7ffppl4wxeq7osqfuu 769 14 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 769 15 Efficiency Efficiency NNP work_ln56cwsp7ffppl4wxeq7osqfuu 769 16 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 769 17 Multicandidate Multicandidate NNP work_ln56cwsp7ffppl4wxeq7osqfuu 769 18 Electoral Electoral NNP work_ln56cwsp7ffppl4wxeq7osqfuu 769 19 Systems Systems NNPS work_ln56cwsp7ffppl4wxeq7osqfuu 769 20 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 769 21 ” " '' work_ln56cwsp7ffppl4wxeq7osqfuu 769 22 American American NNP work_ln56cwsp7ffppl4wxeq7osqfuu 769 23 Journal Journal NNP work_ln56cwsp7ffppl4wxeq7osqfuu 769 24 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 769 25 Political Political NNP work_ln56cwsp7ffppl4wxeq7osqfuu 769 26 Science Science NNP work_ln56cwsp7ffppl4wxeq7osqfuu 769 27 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 769 28 28:23 28:23 CD work_ln56cwsp7ffppl4wxeq7osqfuu 769 29 - - SYM work_ln56cwsp7ffppl4wxeq7osqfuu 769 30 48 48 CD work_ln56cwsp7ffppl4wxeq7osqfuu 769 31 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 770 1 [ [ -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 770 2 19 19 CD work_ln56cwsp7ffppl4wxeq7osqfuu 770 3 ] ] -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 770 4 Myerson Myerson NNP work_ln56cwsp7ffppl4wxeq7osqfuu 770 5 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 770 6 R. R. NNP work_ln56cwsp7ffppl4wxeq7osqfuu 770 7 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 770 8 2002),“Comparison 2002),“comparison CD work_ln56cwsp7ffppl4wxeq7osqfuu 770 9 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 770 10 Scoring Scoring NNP work_ln56cwsp7ffppl4wxeq7osqfuu 770 11 Rules Rules NNPS work_ln56cwsp7ffppl4wxeq7osqfuu 770 12 in in IN work_ln56cwsp7ffppl4wxeq7osqfuu 770 13 Poisson Poisson NNP work_ln56cwsp7ffppl4wxeq7osqfuu 770 14 Voting Voting NNP work_ln56cwsp7ffppl4wxeq7osqfuu 770 15 Games Games NNPS work_ln56cwsp7ffppl4wxeq7osqfuu 770 16 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 770 17 ” " '' work_ln56cwsp7ffppl4wxeq7osqfuu 770 18 Journal Journal NNP work_ln56cwsp7ffppl4wxeq7osqfuu 770 19 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 770 20 Eco- Eco- NNP work_ln56cwsp7ffppl4wxeq7osqfuu 770 21 nomic nomic JJ work_ln56cwsp7ffppl4wxeq7osqfuu 770 22 Theory Theory NNP work_ln56cwsp7ffppl4wxeq7osqfuu 770 23 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 770 24 103:219 103:219 CD work_ln56cwsp7ffppl4wxeq7osqfuu 770 25 - - SYM work_ln56cwsp7ffppl4wxeq7osqfuu 770 26 251 251 CD work_ln56cwsp7ffppl4wxeq7osqfuu 770 27 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 771 1 [ [ -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 771 2 20 20 CD work_ln56cwsp7ffppl4wxeq7osqfuu 771 3 ] ] -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 771 4 Nurmi Nurmi NNP work_ln56cwsp7ffppl4wxeq7osqfuu 771 5 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 771 6 H. H. NNP work_ln56cwsp7ffppl4wxeq7osqfuu 771 7 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 771 8 1983 1983 CD work_ln56cwsp7ffppl4wxeq7osqfuu 771 9 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 771 10 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 771 11 “ " `` work_ln56cwsp7ffppl4wxeq7osqfuu 771 12 Voting Voting NNP work_ln56cwsp7ffppl4wxeq7osqfuu 771 13 Procedures Procedures NNPS work_ln56cwsp7ffppl4wxeq7osqfuu 771 14 : : : work_ln56cwsp7ffppl4wxeq7osqfuu 771 15 A a DT work_ln56cwsp7ffppl4wxeq7osqfuu 771 16 Summary Summary NNP work_ln56cwsp7ffppl4wxeq7osqfuu 771 17 Analysis Analysis NNP work_ln56cwsp7ffppl4wxeq7osqfuu 771 18 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 771 19 ” " '' work_ln56cwsp7ffppl4wxeq7osqfuu 771 20 British British NNP work_ln56cwsp7ffppl4wxeq7osqfuu 771 21 Journal Journal NNP work_ln56cwsp7ffppl4wxeq7osqfuu 771 22 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 771 23 Political Political NNP work_ln56cwsp7ffppl4wxeq7osqfuu 771 24 Science Science NNP work_ln56cwsp7ffppl4wxeq7osqfuu 771 25 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 771 26 13:181 13:181 CD work_ln56cwsp7ffppl4wxeq7osqfuu 771 27 - - CD work_ln56cwsp7ffppl4wxeq7osqfuu 771 28 208 208 CD work_ln56cwsp7ffppl4wxeq7osqfuu 771 29 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 772 1 [ [ -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 772 2 21 21 CD work_ln56cwsp7ffppl4wxeq7osqfuu 772 3 ] ] -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 772 4 Rae Rae NNP work_ln56cwsp7ffppl4wxeq7osqfuu 772 5 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 772 6 D. D. NNP work_ln56cwsp7ffppl4wxeq7osqfuu 772 7 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 772 8 1969 1969 CD work_ln56cwsp7ffppl4wxeq7osqfuu 772 9 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 772 10 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 772 11 “ " `` work_ln56cwsp7ffppl4wxeq7osqfuu 772 12 Decision decision NN work_ln56cwsp7ffppl4wxeq7osqfuu 772 13 Rules rule NNS work_ln56cwsp7ffppl4wxeq7osqfuu 772 14 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 772 15 Individual individual JJ work_ln56cwsp7ffppl4wxeq7osqfuu 772 16 Values value NNS work_ln56cwsp7ffppl4wxeq7osqfuu 772 17 in in IN work_ln56cwsp7ffppl4wxeq7osqfuu 772 18 Constitutional Constitutional NNP work_ln56cwsp7ffppl4wxeq7osqfuu 772 19 Choice Choice NNP work_ln56cwsp7ffppl4wxeq7osqfuu 772 20 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 772 21 ” " '' work_ln56cwsp7ffppl4wxeq7osqfuu 772 22 American American NNP work_ln56cwsp7ffppl4wxeq7osqfuu 772 23 Political Political NNP work_ln56cwsp7ffppl4wxeq7osqfuu 772 24 Science Science NNP work_ln56cwsp7ffppl4wxeq7osqfuu 772 25 Review Review NNP work_ln56cwsp7ffppl4wxeq7osqfuu 772 26 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 772 27 63:40 63:40 CD work_ln56cwsp7ffppl4wxeq7osqfuu 772 28 - - SYM work_ln56cwsp7ffppl4wxeq7osqfuu 772 29 56 56 CD work_ln56cwsp7ffppl4wxeq7osqfuu 772 30 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 773 1 [ [ -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 773 2 22 22 CD work_ln56cwsp7ffppl4wxeq7osqfuu 773 3 ] ] -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 773 4 Saari Saari NNP work_ln56cwsp7ffppl4wxeq7osqfuu 773 5 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 773 6 D.G. D.G. NNP work_ln56cwsp7ffppl4wxeq7osqfuu 774 1 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 774 2 1999 1999 CD work_ln56cwsp7ffppl4wxeq7osqfuu 774 3 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 774 4 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 774 5 “ " `` work_ln56cwsp7ffppl4wxeq7osqfuu 774 6 Explaining explain VBG work_ln56cwsp7ffppl4wxeq7osqfuu 774 7 All all DT work_ln56cwsp7ffppl4wxeq7osqfuu 774 8 Three three CD work_ln56cwsp7ffppl4wxeq7osqfuu 774 9 - - HYPH work_ln56cwsp7ffppl4wxeq7osqfuu 774 10 Alternative Alternative NNP work_ln56cwsp7ffppl4wxeq7osqfuu 774 11 Voting Voting NNP work_ln56cwsp7ffppl4wxeq7osqfuu 774 12 Outcomes Outcomes NNPS work_ln56cwsp7ffppl4wxeq7osqfuu 774 13 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 774 14 ” " '' work_ln56cwsp7ffppl4wxeq7osqfuu 774 15 Journal Journal NNP work_ln56cwsp7ffppl4wxeq7osqfuu 774 16 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 774 17 Economic Economic NNP work_ln56cwsp7ffppl4wxeq7osqfuu 774 18 Theory Theory NNP work_ln56cwsp7ffppl4wxeq7osqfuu 774 19 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 774 20 87:313 87:313 CD work_ln56cwsp7ffppl4wxeq7osqfuu 774 21 - - SYM work_ln56cwsp7ffppl4wxeq7osqfuu 774 22 355 355 CD work_ln56cwsp7ffppl4wxeq7osqfuu 774 23 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 775 1 30 30 CD work_ln56cwsp7ffppl4wxeq7osqfuu 775 2 [ [ -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 775 3 23 23 CD work_ln56cwsp7ffppl4wxeq7osqfuu 775 4 ] ] -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 775 5 Teichroew Teichroew NNP work_ln56cwsp7ffppl4wxeq7osqfuu 775 6 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 775 7 D. D. NNP work_ln56cwsp7ffppl4wxeq7osqfuu 775 8 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 775 9 1956 1956 CD work_ln56cwsp7ffppl4wxeq7osqfuu 775 10 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 775 11 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 775 12 “ " `` work_ln56cwsp7ffppl4wxeq7osqfuu 775 13 Tables table NNS work_ln56cwsp7ffppl4wxeq7osqfuu 775 14 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 775 15 Expected expected JJ work_ln56cwsp7ffppl4wxeq7osqfuu 775 16 Values value NNS work_ln56cwsp7ffppl4wxeq7osqfuu 775 17 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 775 18 Order order NN work_ln56cwsp7ffppl4wxeq7osqfuu 775 19 Statistics Statistics NNPS work_ln56cwsp7ffppl4wxeq7osqfuu 775 20 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 775 21 Products Products NNPS work_ln56cwsp7ffppl4wxeq7osqfuu 775 22 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 775 23 Or- Or- NNP work_ln56cwsp7ffppl4wxeq7osqfuu 775 24 der der NN work_ln56cwsp7ffppl4wxeq7osqfuu 775 25 Statistics statistic NNS work_ln56cwsp7ffppl4wxeq7osqfuu 775 26 for for IN work_ln56cwsp7ffppl4wxeq7osqfuu 775 27 Samples sample NNS work_ln56cwsp7ffppl4wxeq7osqfuu 775 28 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 775 29 Size Size NNP work_ln56cwsp7ffppl4wxeq7osqfuu 775 30 Twenty Twenty NNP work_ln56cwsp7ffppl4wxeq7osqfuu 775 31 and and CC work_ln56cwsp7ffppl4wxeq7osqfuu 775 32 Less Less JJR work_ln56cwsp7ffppl4wxeq7osqfuu 775 33 from from IN work_ln56cwsp7ffppl4wxeq7osqfuu 775 34 the the DT work_ln56cwsp7ffppl4wxeq7osqfuu 775 35 Normal Normal NNP work_ln56cwsp7ffppl4wxeq7osqfuu 775 36 Distribution Distribution NNP work_ln56cwsp7ffppl4wxeq7osqfuu 775 37 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 775 38 ” " '' work_ln56cwsp7ffppl4wxeq7osqfuu 775 39 Annals Annals NNPS work_ln56cwsp7ffppl4wxeq7osqfuu 775 40 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 775 41 Mathematical Mathematical NNP work_ln56cwsp7ffppl4wxeq7osqfuu 775 42 Statistics Statistics NNPS work_ln56cwsp7ffppl4wxeq7osqfuu 775 43 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 775 44 27:410 27:410 CD work_ln56cwsp7ffppl4wxeq7osqfuu 775 45 - - SYM work_ln56cwsp7ffppl4wxeq7osqfuu 775 46 426 426 CD work_ln56cwsp7ffppl4wxeq7osqfuu 775 47 . . . work_ln56cwsp7ffppl4wxeq7osqfuu 776 1 [ [ -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 776 2 24 24 CD work_ln56cwsp7ffppl4wxeq7osqfuu 776 3 ] ] -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 776 4 Weber Weber NNP work_ln56cwsp7ffppl4wxeq7osqfuu 776 5 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 776 6 R.J R.J NNP work_ln56cwsp7ffppl4wxeq7osqfuu 776 7 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 776 8 ( ( -LRB- work_ln56cwsp7ffppl4wxeq7osqfuu 776 9 1978 1978 CD work_ln56cwsp7ffppl4wxeq7osqfuu 776 10 ) ) -RRB- work_ln56cwsp7ffppl4wxeq7osqfuu 776 11 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 776 12 “ " `` work_ln56cwsp7ffppl4wxeq7osqfuu 776 13 Comparison Comparison NNP work_ln56cwsp7ffppl4wxeq7osqfuu 776 14 of of IN work_ln56cwsp7ffppl4wxeq7osqfuu 776 15 Voting Voting NNP work_ln56cwsp7ffppl4wxeq7osqfuu 776 16 Systems Systems NNPS work_ln56cwsp7ffppl4wxeq7osqfuu 776 17 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 776 18 ” " '' work_ln56cwsp7ffppl4wxeq7osqfuu 776 19 mimeo mimeo FW work_ln56cwsp7ffppl4wxeq7osqfuu 776 20 , , , work_ln56cwsp7ffppl4wxeq7osqfuu 776 21 Cowles Cowles NNP work_ln56cwsp7ffppl4wxeq7osqfuu 776 22 Foundation Foundation NNP work_ln56cwsp7ffppl4wxeq7osqfuu 776 23 . . .