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Hodler, Roland; Luechinger, Simon; Stutzer, Alois

Working Paper

The Effects of Voting Costs on the Democratic
Process and Public Finances

WWZ Discussion Paper, No. 2012/02

Provided in Cooperation with:
Center of Business and Economics (WWZ), University of Basel

Suggested Citation: Hodler, Roland; Luechinger, Simon; Stutzer, Alois (2012) : The Effects of
Voting Costs on the Democratic Process and Public Finances, WWZ Discussion Paper, No.
2012/02, University of Basel, Center of Business and Economics (WWZ), Basel

This Version is available at:
http://hdl.handle.net/10419/123432

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Wirtschaftswissenschaftliches Zentrum (WWZ) der Universität Basel 

 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

February 2012 
 
 
 
 
 
 
 

The Effects of Voting Costs on the  
Democratic Process and Public Finances 

 
 
 
 
 
 
 
WWZ Discussion Paper 2012/02 Roland Hodler, Simon Luechinger, Alois Stutzer 

 
 
 
 
 
 
 



 

 
The Author(s): 
 
 
Prof. Dr. Roland Hodler 

University of Lucerne  
Department of Economics 
Frohburgstrasse 3 
CH-6002 Lucerne 
Switzerland 

roland.hodler@unilu.ch  

 
 
 
Prof. Dr. Simon Luechinger 

University of Lucerne  
Department of Economics 
Frohburgstrasse 3 
CH-6002 Lucerne 
Switzerland 

simon.luechinger@unilu.ch  

 
 
 

Prof. Dr. Alois Stutzer 

University of Basel  
Faculty of Business and Economics 
Peter Merian-Weg 6 
CH - 4002 Basel 

alois.stutzer@unibas.ch 
 
 
 
 
 
 
 
 
 
A publication of the Center of Business and Economics (WWZ), University of Basel.  
 
 WWZ Forum 2012 and the author(s). Reproduction for other purposes than the personal use needs the 
permission of the author(s). 
 
Contact: 
WWZ Forum | Peter Merian-Weg 6 | CH-4002 Basel | forum-wwz@unibas.ch | wwz.unibas.ch 



The Effects of Voting Costs on the Democratic Process

and Public Finances

Roland Hodler∗ Simon Luechinger† Alois Stutzer‡§

January 27, 2012

Abstract

Increasing the attractiveness of voting is often seen as a remedy for unequal par-

ticipation and the influence of special-interest groups on public policy. However,

lower voting costs may also bring less informed citizens to the poll inviting efforts

to sway these voters. We substantiate this argument in a probabilistic voting model

with campaign contributions. In an empirical analysis for the 26 Swiss states, we

find that lower voting costs due to postal voting are related to higher turnout, lower

average education of participants, lower knowledge on the political issues they were

deciding on as well as lower government welfare expenditures.

JEL classification: D72, D78, H00

Keywords: Fiscal policies, political knowledge, postal voting, special-interest politics,

voter turnout, voting costs

∗University of Lucerne, Department of Economics, Frohburgstrasse 3, 6002 Lucerne, Switzerland, Email:
roland.hodler@unilu.ch.
†University of Lucerne, Department of Economics, Frohburgstrasse 3, 6002 Lucerne, Switzerland, Email:

simon.luechinger@unilu.ch.
‡University of Basel, Faculty of Business and Economics, Peter Merian-Weg 6, 4002 Basel, Switzerland,

Email: alois.stutzer@unibas.ch.
§We thank Sven Feldmann and Andrea Prat for helpful comments, and Stefan Gärtner and Sibylle Haas

for excellent research assistance. This working paper supersedes the working paper “Compulsory Voting
and Public Finance”.

1



1 Introduction

Democratic decision-making in elections and referenda is characterized by unequal turnout

as rich and well educated citizens are more likely to participate than their less privileged

compatriots.1 Many students of democracy worry that this unequal participation trans-

lates into fiscal policies that are biased towards privileged citizens (see, e.g., Lijphart 1997).

Various institutional mechanisms have been proposed to achieve a more equal representa-

tion. In these proposals, voting costs figure prominently. Incentives for participation are

expected to be higher with postal voting or some form of electronic voting involving lower

costs for citizens, or with institutional mechanisms like compulsory voting that increase

the costs of abstention.

However, voting costs might also work as a selection device bringing the confident

citizens to the poll but not the halfhearted ones. Lower voting costs may thus induce more

people to vote who only have a diffuse understanding of what their preferred alternative

is. The latter circumstances though invite efforts to influence these voters. Special-interest

groups might offer more campaign contributions allowing parties to try to sway these voters

in exchange for rents or policies tilted towards these groups. Whether lower voting costs

contribute to a better serving of citizens’ preferences is thus far from clear.

In this paper, we scrutinize the argument that lowering voting costs might have unin-

tended effects on political outcomes. We first analyze theoretically how voting costs affect

the political process and, thereby, public finances. We base this analysis on a probabilistic

voting model with campaign contributions similar to the models of Baron (1994), Gross-

man and Helpman (1996, 2001), and Persson and Tabellini (2000). In this model, political

candidates choose their policy platform, which consists of public goods provision and rent

payments to lobby groups. The latter can make campaign contributions to political candi-

1Tingsten (1937, p. 155) was one of the first to provide systematic evidence that “the voting frequency
rises with rising social standard.” Lijphart (1997) reviews many studies that document unequal turnout.

2



dates. Informed voters base their decision primarily on policy platforms, while uninformed

or impressionable citizens base their decision primarily on political advertisements paid for

by campaign contributions. Unlike in existing voting models with campaign contributions,

in our model citizens decide how much political information to acquire, and whether or not

to participate in the election. We assume that the costs of acquiring political information

are lower for citizens with good education/high incomes. Further, citizens have to bear

costs when voting, and we follow Matsusaka (1995) in assuming that the citizens’ benefit

from voting are the higher, the more confident they are of their vote choice.2

In this model citizens with good education/high incomes are more likely to take in-

formed decisions when voting, and they are also more likely to participate in the election.

The composition of participants changes if technological innovations in the electoral process

like postal voting decrease voting costs. Such innovations increase electoral participation

as well as the share of less educated and thus impressionable voters whose vote choice

depends on campaign contributions rather than policy platforms. As a consequence, can-

didates propose platforms with higher tax rates and total government spending to increase

rent payments to lobby groups (as compensation for higher campaign contributions).3 The

effect of lower voting costs on public good provision or, more generally, on expenditures

not targeted at special-interest groups is ambiguous in general, and negative with Cobb-

Douglas preferences. These changes in fiscal policies harm citizens with high incomes, and

possibly also less privileged citizens. Therefore, in contrast to what conventional wisdom

suggests, our model shows that lower voting costs benefit special-interest groups, but may

well harm all other citizens in society.

In our model, regulations that increase the costs of abstention, such as compulsory

voting, have the same effect on fiscal policies as lower voting costs. Hence they also lead to

2Lassen (2005) offers evidence from a natural experiment that better-informed people vote more.
3This result is consistent with the finding of Wegenast (2010) that interest groups are less influential

in US states with highly educated and well informed citizens.

3



higher rents and higher taxes, with the effect on public goods provision being ambiguous. In

addition, compulsory voting directly hurts all citizens who did not vote before the increase

in abstention costs.

We empirically test the predictions of the model for a procedural innovation that sig-

nificantly reduces voting costs: postal voting. We thereby exploit the natural experiment

provided by the staggered introduction of postal voting in the 26 Swiss states. This allows

us to identify the effects of reduced voting costs and to separate it from time-, issue- and

state-specific effects on political outcomes. Switzerland provides an ideal testing ground

for two additional reasons. First, frequent direct democratic decisions at the national level

allow us to observe participation decisions and changes in characteristics of participants at

a higher temporal resolution than what is normally possible. Second, Swiss states have a

high degree of fiscal autonomy which makes it possible to study effects on public finances.

The empirical analysis refers to the years 1981 to 2005. First, we establish the impact

of postal voting on participation. We find evidence for a 4 percentage point increase in

voter turnout with postal voting. Second, based on a series of post-ballot surveys, we

analyze how postal voting affects the average level of education and household income of

participants as well as the participants’ knowledge on ballot propositions (i.e., popular

initiatives and referenda). We find that postal voting is related to a systematic change in

the composition of the voting population. On average, voters have fewer years of education

and know less on the propositions they voted on. Finally, we study the correlation of postal

voting with total government and welfare expenditures. We find no systematic correlation

of the introduction of postal voting with total government expenditures. However, welfare

expenditures are lower. While the latter result might come as a surprise, it is consistent

with our model allowing for less government expenditures that are not targeted at special-

interest groups in response to lower voting costs.

This paper contributes to four different strands of the theoretical and empirical political

4



economy literature. First, it builds on the contributions of Baron (1994), Grossman and

Helpman (1996, 2001), and Persson and Tabellini (2000) on the role of campaign contri-

butions in elections. Due to its focus on fiscal policies, our model is probably closest to

Persson and Tabellini (2000). The main differences to all these contributions are that we

deviate from the assumption of full (or random) voting participation, and that we do not

take the share of informed voters as exogenous. This allows us to show that lower vot-

ing costs make campaign contributions more important and, consequently, special-interest

groups more powerful.4

Second, Meltzer and Richard (1981) contributed one of the most prominent models in

political economics linking the composition of the voting population with public finances.

Restricting government activities to redistribution financed by a proportional income tax,

their model predicts that a stronger representation of lower income citizens in the political

process leads to more redistribution. Empirical evidence for this prediction (often exploit-

ing different extensions of franchise) is rather mixed (see, e.g., Husted and Kenny 1997,

Rodriguez 1999, Alesina and Glaeser 2004, Gradstein and Milanovic 2004, Stutzer and

Kienast 2005). Our model offers a novel explanation for the lack of strong and unambigu-

ous empirical support for the Meltzer-Richard hypothesis: the inclusion of poorer and less

educated citizens may have increased the clout of special-interest groups to the detriment

of policies benefiting the general population, including the newly enfranchised citizens.

Third, voting costs are a key ingredient in the rational choice model of voting partic-

ipation (Downs 1957, Riker and Ordeshook 1968, and for a review Aldrich 1997). Our

evidence from difference-in-differences estimations contributes to a better understanding

4Strömberg (2004) endogenizes the share of informed voters in a probabilistic voting model with profit-
maximizing media. Other recent contributions building on the aforementioned models provide a micro-
foundation for the effect of political advertisement on voting decisions of imperfectly informed voters. In
Prat (2002a, 2002b) political ads are non-informative, but the amount spent on political ads serves as a
signal of the candidates’ quality. In Coate (2004a, 2004b) political ads are directly informative and the
probability that the voters understand the information increases in the amount spent on political ads. As
we focus on the effects of voting costs on fiscal policies rather than on why and how political ads work, we
leave these interesting aspects of political advertisement out.

5



of the quantitative importance of transaction costs related to voting and offers complemen-

tary evidence on the consequences of postal voting on turnout (see also Luechinger et al.

2007, Funk 2010, and for reviews, Qvortrup 2005 and Gronke et al. 2008).5 However, our

analysis goes beyond this literature by documenting effects on the composition of partic-

ipants and public finances. There are thus implications for postal voting and potentially

also for Internet voting.6

Fourth, our paper contributes to the literature on the advantages and disadvantages

of compulsory voting. So far, there have been surprisingly few theoretical contributions

to this literature. Crain and Leonard (1993) consider the effect of compulsory voting on

government spending in two separate political economy models. In line with conventional

wisdom they hypothesize that compulsory voting would lead to higher public goods provi-

sion in a median voting model in which public goods provision is the only type of public

spending, and to less rents to special-interest groups in pressure groups theories of govern-

ment. We improve upon Crain and Leonard (1993) by studying the effects of lower voting

(or higher abstention) costs on public goods provision and rents in a formal and unified

model. Börgers (2004), and Krasa and Polborn (2009) compare welfare under compulsory

and voluntary voting in costly voting models in which voters only benefit from voting if

they are pivotal. These models focus on the voters’ participation decision and their choice

between two fixed alternatives, thereby abstracting from the way candidates choose their

policy platforms and the role of special-interest groups, which are both at the heart of our

paper. In a recent contribution, Krishna and Morgan (2011) argue that compulsory vot-

ing has the drawback that preference intensities can no longer affect voting participation

5Recent alternative approaches to assess the quantitative importance of transaction costs in voting
participation are proposed in Brady and McNulty (2011) and Gibson et al. (2011). Besides transaction costs
there are, of course, also the opportunity costs of voting. A careful empirical analysis on the relationship
between employment, wages and voter turnout is provided by Charles and Stephens (2011).

6Internet voting trials have been conducted in various countries, including France, the Netherlands,
Switzerland, the United Kingdom, and the United States. In Estonia all voters could use Internet voting
in the national election in 2007 (Alvarez et al. 2009).

6



and, thereby, voting outcomes. This argument is loosely related to our general point that

postal and compulsory voting may reduce the political knowledge of the average voter and,

therefore, lead to inferior policy outcomes for the population at large.

In the following Section, we develop our voting model. Section 3 presents the data and

the results of our empirical analysis. Section 4 offers concluding remarks.

2 The Model

2.1 Setting

There are two candidates, a lobby group, and a measure-one continuum of citizens. Each

candidate P ∈ {A,B} is office-motivated and chooses his policy platform to maximize

his winning probability pP , where pA + pB = 1. Platforms consist of public goods pro-

vision gP ≥ 0 and rent payments to the lobby group rP ≥ 0. These two components of

government spending are financed with a linear income tax, and the government budget

must be balanced. Hence gP and rP determine the tax rate τP =
gP +rP

y
, where y denotes

average income. Candidates may differ in their policy platforms (gP ,rP ) as well as in some

predetermined, i.e., exogenous, positions.

The lobby group can make campaign contributions CA ≥ 0 and CB ≥ 0 to candidates

A and B at increasing marginal costs, and it receives rents rP from the elected candidate

P . Its utility is Π(rP ,CA,CB) = J(rP ) −
(CA+CB)

2

2
, where J′(rP ) > 0 and J

′′(rP ) < 0.

Citizens differ in their skills αi, which may represent educational attainments or innate

abilities. The distribution of αi is given by F(αi), with continuous density f(αi) and

mean α. For simplicity we assume F(0) = 0, F(1) = 1, and f(αi) > 0 for all αi ∈ [0, 1].

Skills αi have two effects: First they determine citizen i’s income yi = αi. Second they

determine how costly it is for citizen i to acquire political knowledge qi ∈ [0, 1]. We

assume that a citizen’s political knowledge qi measures the probability that she is informed

7



rather than impressionable, thus understanding the candidates’ platforms (gP ,rP ) and their

predetermined positions.

If candidate P is elected, the utility of citizen i is

Wi,P = W(gP ,rP ,α
i,σiP ,pi) = U(c

i
P ) + H(gP ) + σ

i
P + Ii(βqi −γ) −

q2i
2αi

. (1)

The first two terms on the right-hand side reflect citizen i’s utility from private consumption

ciP = (1 − τP )α
i and public goods provision gP , respectively. We assume U

′(ciP ) > 0,

U ′′(ciP ) ≤ 0, RR(c
i
P ) ≡ −

ci
P
U′′(ci

P
)

U′(ci
P

)
< 1, H′(gP ) > 0, and H

′′(gP ) < 0. The third term, σ
i
P ,

represents her utility from the predetermined positions of the elected candidate P . We

further assume that σi = σiB −σ
i
A is uniformly distributed in [

−1
2φ
, 1

2φ
].

The fourth term captures benefits and costs associated with voting. Ii is a dummy

variable whose value is 1 if citizen i participates in the election, and 0 if she abstains.

Some benefits from voting may well depend on the voter’s political knowledge, like the

satisfaction of being confident to have voted in one’s own interest (Matsusaka, 1995).

These benefits are βqi. For simplicity, we set β = 1. The costs of completing and casting

one’s ballot are denoted by γ. These voting costs are relatively high when ballots must

be cast at a polling station, but they decrease if postal voting or even Internet voting is

introduced. The last term captures the costs of acquiring political knowledge qi, which are

decreasing in skills αi.

Timing is as follows: First, the candidates choose their policy platforms (gP ,rP ). Sec-

ond, the lobby group can make campaign contributions. Third, elections take place. The

elected candidate then implements the announced platform.

It remains to describe the voters’ decisions.7 Informed voters vote for candidate A

if Wi,A ≥ Wi,B, and for candidate B otherwise. The electoral decisions of impressionable
7We use the term “voters” to refer to citizens who participate in the election and for whom the partic-

ipation constraint thus holds.

8



voters are driven by political advertisements and policy irrelevant candidate characteristics.

The share of impressionable voters who vote for candidate A is 1
2

+ ψ(∆C − η), where

∆C ≡ CA − CB.8 The remaining impressionable voters vote for candidate B. Note that

ψ > 0 measures the effectiveness of advertisements and, therefore, campaign contributions;

and η is a popularity shock that is uniformly distributed in [−1
2λ
, 1

2λ
].

The appropriate solution concept for this sequential game is subgame prefect Nash

equilibrium.

2.2 Discussion

We now discuss some of the assumptions made. Utility function (1) implies that the

citizens’ utility from private consumption ciP and public goods provision gP is additively

separable. The model could be solved with more general utility functions, but assuming

additive separability simplifies the analysis, and still allows for popular specifications such

as the quasi-linear preferences used by Persson and Tabellini (2000). What we need and

want, however, is for any given rP a negative relationship between a citizen’s skills α
i and

the public goods provision giP that maximizes her utility. In our setting this relationship

is strictly negative if and only if RR(c
i
P ) < 1.

9

Utility function (1) further implies that citizens derive a benefit from voting if they cast

an informed vote. Political knowledge qi benefits voters, for example, because they value

the confidence of having voted in their own interest, as suggested by Matsusaka (1995).10 In

our model higher skilled voters will optimally acquire more political knowledge because of

8Following Persson and Tabellini (2000) we could assume that impressionable voter i votes for A if and
only if ∆C > εi + η, with εi being uniformly distributed in [−1

2ψ
, 1
2ψ

].

9To see this, observe that the first-order condition −U′(ciP )
∂ciP
∂τP

∂τP
∂gP

+ H′(gP ) = 0, where
∂ciP
∂τP

= −αi

and ∂τP
∂gP

= 1
α

, determines giP for any given rP . Using the implicit function theorem, it can be shown that
∂giP
∂αi

= −U
′(ciP )[RR(c

i
P )−1]

αH′′(gP )
, which is strictly negative if and only if RR(c

i
P ) < 1.

10In general, citizens also benefit from political knowledge if they are pivotal with non-zero probability.
However, in our model where there is a continuum of voters this probability is zero.

9



lower information acquisition costs, which is consistent with empirical evidence that voters

with better education and higher incomes are better informed (e.g., Benz and Stutzer 2004,

and Lind and Rohner 2011). Again, other mechanism ensuring that higher skilled citizens

acquire more political knowledge would serve our purpose equally well. In Larcinese (2005),

for example, the effect of political knowledge on expected (future) income increases in the

citizens’ skills and income. Similarly, our results do not depend on the perfect correlation

between incomes and and the costs of acquiring political knowledge. A positive correlation

is however necessary.

Voting is probabilistic in our model, such that small changes in policy platforms (gP ,rP )

only lead to small changes in the candidates’ winning probabilities pP . Following Grossman

and Helpman (1996, 2001) and Persson and Tabellini (2000), we model probabilistic voting

by assuming that candidates differ in predetermined positions or some other exogenous

characteristics, and voters in their evaluation σi of these positions, and that a popularity

shock η affects all (impressionable) voters.11 We further follow Persson and Tabellini

(2000) in assuming that σi and η are uniformly distributed with mean zero to get simple

and tractable functional forms of the candidates’ winning probabilities.

Equation (1) includes only voting costs, but no abstention costs. Citizens may feel bad

when violating social norms and not fulfilling what might be perceived as a civic duty.

Moreover, in countries with compulsory voting laws abstention may lead to a fine or a

request to explain the failure to vote (as in Australia). We refrain from including absten-

tion costs because higher abstentions costs have exactly the same effects on participation

decisions and policy outcomes as lower voting costs. The only difference are their effects

on welfare: abstracting from changes in policies, higher abstention costs hurt all citizens

who would have abstained without the increase in abstention costs while lower voting costs

benefit all voting citizens.

11Results are virtually the same when η affects the decision of all voters as when it only affects the
decision of impressionable voters.

10



To capture lobbying in a simple way, we assume that there is only one lobby group, that

this lobby group cannot vote (or has measure zero), and that citizens do not benefit from

rents rP . However, we could derive similar results in a setting in which a non-negligible

share of the citizens belong to lobby groups, and in which all these citizens benefit from

rents and can decide whether or not to participate in the election.

2.3 Equilibrium analysis

In this section, we first derive the decisions of the citizens and the lobby group, which yield

the candidates’ objective function. We then study how changes in voting costs affect the

candidates’ policy platforms in two simplified versions of our model – one with exogenous

rents, and one with an exogenous tax rate. Finally, we look at the complete model in-

troduced above, and we discuss how changes in voting costs affect the equilibrium policy

platforms as well as the welfare of the citizens and the lobby group.

2.3.1 Decisions of citizens and lobby group

We start by looking at the citizens’ decisions of how much political knowledge qi to acquire,

and whether or not to participate in the election. For citizens who abstain from voting

acquiring political knowledge has no benefits. Hence they choose qi = 0. Citizens who

participate in the election choose qi to maximize qi −
q2i
2αi

. Hence they choose qi = α
i.

Citizens therefore acquire political knowledge qi = α
i and participate in the election if

αi − γ − (α
i)2

2αi
= α

i

2
− γ ≥ 0, i.e., if αi ≥ 2γ, while they acquire no political knowledge

and abstain from voting otherwise.12 The election participation threshold 2γ directly

determines voter turnout 1 −F(2γ). For simplicity we focus on cases in which γ ∈
(
0, 1

2

)
,

such that marginal changes in voting costs γ have an effect on voter turnout and equilibrium

policy platforms. It follows:

12As a tie-breaking rule, we assume that citizens who are indifferent participate in the election.

11



Proposition 1. Voter turnout decreases in voting costs γ.

The voters’ average skills and their average political knowledge are both given by 1
1−F(2γ)∫ 1

2γ
αif(αi)dαi. Therefore:

Proposition 2. The voters’ average skills and their average political knowledge increase

in voting costs γ.

We next derive the expected election outcome as a function of the candidates’ plat-

forms (gA,rA) and (gB,rB), and the campaign contributions CA and CB. Informed vot-

ers vote for candidate A if ∆V (αi) ≡ U(ciA) − U(c
i
B) + H(gA) − H(gB) > σ

i, and for

B otherwise. Among informed voters with skills αi ≥ 2γ, the share voting for A is

therefore 1
2

+ φ∆V (αi).13 By assumption, the share of impressionable voters voting for

A is 1
2

+ ψ(∆C − η) for any αi ≥ 2γ. As the share of voters with skills αi ≥ 2γ

who is informed equals qi = α
i, the population share who votes for A thus adds up

to πA =
∫ 1

2γ

[
1
2

+ αiφ∆V (αi) + (1 −αi)ψ(∆C −η)
]
f(αi)dαi, and the population share

who votes for B to πB = 1 − F(2γ) − πA. Candidate A therefore wins if and only if∫ 1
2γ

[αiφ∆V (αi) + (1 −αi)ψ(∆C −η)]f(αi)dαi ≥ 0. Hence his winning probability is

pA = prob

{
η ≤

φ
∫ 1

2γ
αi∆V (αi)f(αi)dαi

ψ
∫ 1

2γ
(1 −αi)f(αi)dαi

+ ∆C

}
=

1

2
+
λφ
∫ 1

2γ
αi∆V (αi)f(αi)dαi

ψ
∫ 1

2γ
(1 −αi)f(αi)dαi

+ λ∆C.

(2)

We now turn to the lobby group’s decision. The lobby group chooses campaign contri-

butions CA and CB to maximize its expected utility pAJ(rA)+(1−pA)J(rB)−12 (CA +CB)
2,

thereby anticipating the effects of CA and CB on pA. The lobby group supports no can-

didate if rents rA and rB coincide, and the candidate promising more generous rents oth-

erwise. It is easy to see that the lobby group chooses CA = max{0,λ[J(rA) − J(rB)]}
13More generally, this share is min{max{0, 1

2
+ φ∆V (αi)}, 1}, but for simplicity we assume that it is

always strictly between zero and one. We make similar (implicit) assumptions for all vote shares and
winning probabilities below.

12



and CB = max{0,λ[J(rB) − J(rA)]}, such that ∆C = λ[J(rA) − J(rB)]. Inserting this

expression for ∆C into equation (2) leads to

pA =
1

2
+
λφ
∫ 1

2γ
αi∆V (αi)f(αi)dαi

ψ
∫ 1

2γ
(1 −αi)f(αi)dαi

+ λ2[J(rA) −J(rB)]. (3)

Candidate A anticipates the behavior of the lobby group and the citizens, and chooses

his fiscal policy platform (gA,rA) to maximize his winning probability pA. Candidate B

chooses (gB,rB) to maximize pB = 1−pA. It follows from equation (3) and the definition of

∆V (αi) that each candidate’s optimal platform is independent of his opponent’s platform,

and that each candidate’s maximization problem can be written as

max
gP ,rP

∫ 1
2γ

[
αiU(ciP ) + α

iH(gP ) + (1 −αi)ΩJ(rP )
]
f(αi)dαi (4)

subject to gP ≥ 0, rP ≥ 0 and τP = gP +rPα ≤ 1, where Ω ≡
ψλ
φ

measures how sensitive

the electoral support from impressionable voters is to changes in campaign contributions

relative to how sensitive the electoral support from informed voters is to changes in policy

platforms. We assume throughout that the solution to this problem is interior. As it is

standard in this type of lobbying models, the two candidates’ platforms therefore coincide

in equilibrium, such that the lobby group makes no campaign contributions even though

the candidates offer rents rP > 0.

2.3.2 Policy platforms when rents are exogenous (or absent)

We now look at a simplified version of our model in which rents rP are exogenous and

equal to r ∈ [0,α). This simplified version includes the special case in which there are no

rents and no lobbying.14 Hence it may be close to the model that some of the proponents

14Results are identical when assuming rP = 0 as when assuming Ω = 0. In the later case each candidate
would choose rP = 0, as rents have no effect on his winning probability pP .

13



of eased voting or compulsory voting have in mind, and it indeed helps to understand why

these procedural changes could potentially benefit citizens with low incomes.

In this simplified version of the model the two endogenous fiscal policy variables, gP

and τP , are tied together by the government budget constraint. Hence candidates have

effectively only one choice, which we take to be gP , and the maximization problem (4)

reduces to

max
gP

∫ 1
2γ

αi
[
U(ciP ) + H(gP )

]
f(αi)dαi (5)

with ciP = (1 − τP )α
i and τP =

gP +r
α

. It follows:15

Proposition 3. Assume rP = r. Then public goods provision gP and the tax rate τP

decrease in voting costs γ.

The intuition for these results is as follows. Lower voting costs γ increase voter turnout

and lower the average voter’s income as well as the average informed voter’s income. Since

voters with lower incomes prefer higher public goods provision gP (because RR(c
i
P ) < 1),

the candidates respond to the lower income of the average informed voter by increasing gp.

This is very similar to the mechanism modeled in Meltzer and Richard (1981). Interestingly,

however, even if γ = 0, policy platforms would remain biased towards citizens with high

incomes, with gP and τP still being relatively low. The reason is that candidates only care

about informed voters, and that the share of informed voters always remains higher among

citizens with high incomes.

We now briefly turn to the effects of lower voting costs γ on the welfare of citizens: Lower

voting costs have a direct positive effect on the welfare of all voting citizens. Further, by

increasing gP and τP , they have indirect welfare effects that make citizens with low incomes

better off and citizens with high incomes worse off.

15Proofs of Propositions 3 to 7 are in the appendix.

14



2.3.3 Policy platforms when the tax rate is exogenous

We now look at a simplified version of our model in which the tax rate τP is exogenous

and equal to τ ∈ (0, 1]. This simplified version may reflect the situation in countries in

which governments are substantially less constrained in how they allocate public spending

than in the amount they can spend. In addition, it nicely illustrates the main mechanism

by which lower voting costs or higher costs of abstention can lead to policy changes that

make all citizens worse off.

When τP is exogenous, the two endogenous fiscal policy variables, gP and rP , are again

tied together by the government budget constraint. Hence the candidates face a simple

trade-off between high public goods provision gP and high rents rP . From their perspective,

public goods are useful to increase electoral support from informed voters, while rents

are useful to increase campaign contributions and, thereby, the electoral support from

impressionable voters. The maximization problem (4) reduces to

max
gP

∫ 1
2γ

[
αiH(gP ) + (1 −αi)ΩJ(rP )

]
f(αi)dαi (6)

with rP = τα−gP . It follows:

Proposition 4. Assume τP = τ. Then public goods provision gP increases in voting costs

γ, but decreases in Ω, while rents rP decrease in γ, but increase in Ω.

To understand these results note that for a given tax rate, all citizens have the same

policy preferences: they want public goods provision gP to be as high as possible. Hence

incentivizing more citizens to go to the polls, e.g., by lowering voting costs γ, would have

no effect on equilibrium policies if the new voters were equally well informed as those who

participated anyway. However these new voters are less skilled and, therefore, acquire

less political knowledge even when they participate in the election. As a consequence

the average voter’s political knowledge decreases. The candidates optimally respond by

15



increasing rents rP and lowering public goods provision gP , as rents serve to win votes

from impressionable voters while public goods serve to win votes from informed voters.

Not surprisingly, rents rP also increase in Ω, which measures how sensitive the electoral

support from impressionable voters is to changes in campaign contributions relative to how

sensitive the electoral support from informed voters is to changes in policy platforms.

Hence, when the tax rate is exogenous, lower voting costs γ lead to policy changes

that benefit the lobby group at the expense of all citizens. In addition, there is again

the direct positive effect on the voters’ welfare. Ironically, lower voting costs are therefore

unambiguously harmful for the poor who still abstain from voting despite the decrease in

voting costs, and they may even hurt all citizens including those encouraged to vote by the

decrease in voting costs.

2.3.4 Equilibrium policy platform

In this section, we derive the equilibrium of the complete model introduced in section 2.1 in

which public goods provision gP , rents rP and the tax rate τP =
gP +rP
α

are all endogenous.

We know that in this case the candidates’ maximization problem is given by (4).

We discuss the effects of voting and/or abstention costs on the three fiscal policy vari-

ables in turn, starting with their effects on the tax rate τP , which is proportional to the

size of government gP + rP :

Proposition 5. The tax rate τP and the size of government gP + rP decrease in the voting

costs γ, but increase in Ω.

There are two reasons why lower voting costs γ and the associated increase in the

turnout lead to a higher tax rate τP . First, as seen in Section 2.3.2, for any given rP , a

decrease in γ and the associated decrease in the average informed voter’s income make it

optimal for the candidates to choose a higher tax rate τP . This puts some upward pressure

16



on τP . Second, a decrease in γ reduces the share of informed voters among the voting

population, because less skilled voters acquire less political knowledge. A higher tax rate

τP has the advantage that it allows to increase gP or rP and, thereby, to raise electoral

support from informed or impressionable voters, respectively. But a higher τP has the

disadvantage that it lowers private consumption ciP of all citizens. This, however, only

reduces the electoral support from informed voters. Hence when the share of informed

voters decreases, the candidates become less concerned about the disadvantage of high

taxes, while the advantage of high taxes remains similarly attractive. This puts additional

upwards pressure on τP . Furthermore, the candidates choose a higher tax rate τP when

the support from impressionable voters becomes relatively more sensitive to campaign

contributions, i.e., when Ω increases.

We now turn to the effects of voting costs on the rents rP paid to the lobby group:

Proposition 6. Rents rP decrease in voting costs γ, but increase in Ω.

Some previous results are helpful to understand Proposition 6. We know from Propo-

sition 4 that a decrease in voting costs γ and the associated increase in the share of

impressionable voters increases rents rP relative to public goods provision gP for any tax

rate τP ; and from Proposition 5 that a decrease in γ increases τP . Hence lower voting costs

γ lead to more generous rents rP , because a higher share of impressionable voters tilts both

the size and the composition of public spending to the lobby group’s benefit. Proposition

6 further shows that rents rP increase in Ω, i.e., when the support from impressionable

voters becomes relatively more sensitive to campaign contributions.

We next discuss how voting costs γ affect public goods provisions gP . There are two

countervailing effects: First, candidates would like to choose higher gP when γ decreases,

because the average informed voter then earns a lower income and, therefore, prefers higher

gP for given rP (as seen in Proposition 3). Second, candidates would like to choose lower

gP when γ decreases, because informed voters also care about low tax rates τP , with the

17



marginal utility of τP being negative and decreasing, and because the decrease in γ already

puts upwards pressure on τP by increasing rents rP (as seen in Proposition 6). Any of

these two effects may dominate in general. However, for some specific utility function the

net effect is unambiguous:

Proposition 7. Public goods provision gP decreases in Ω. The effect of voting costs γ on

gP is ambiguous in general, but it holds:

(i) Assume U(ciP ) = χc
i
P with χ > 0. Then gP decreases in γ.

(ii) Assume RR(c
i
P ) = θ with θ → 1 (or θ = 1). Then gP increases in γ.

Assumption (i) in Proposition 7 leads to quasi-linear preferences over ciP and gP as in

Persson and Tabellini (2000). With these preferences, the marginal effect of an increase

in τP on U(c
i
P ) becomes independent of the levels of c

i
P and τP . Hence the second of

the countervailing effects discussed above disappears, and the candidates choose higher gP

when γ decreases.

Assumption (ii) in Proposition 7 ensures that the differences between the preferred

public goods provision giP of citizens with different incomes converge towards zero. In

this case the first of the countervailing effects discussed above becomes negligible, and the

candidates choose lower gP when γ decreases. The same also holds true when RR(c
i
P ) = 1,

as is the case with Cobb-Douglas preferences in log form over ciP and gP .

Proposition 7 further shows that the candidates choose lower public goods provision gP

when Ω increases, i.e., when the electoral support from informed voter becomes relatively

less sensitive to changes in policy platforms.

Finally, let us look at the welfare of citizens and the lobby group. The lobby group

only cares about high rents rP . As lower voting costs γ increase rP , they make the lobby

group better off. Lower voting costs γ also have a direct positive effect on the welfare of

voters. The indirect effects however are less clear-cut: Citizens prefer high public goods

18



provision gP and low tax rates τP , and the importance they assign to the former relative

to the latter decreases in their income. Lowering γ always increases τP , while the effect on

gP is ambiguous. Hence, when lowering γ reduces gP , then the associated policy changes

make all citizens worse off. But when lowering γ increases gP , then the welfare effects of

the associated policy changes depend on the citizens’ income. Citizens with low incomes

are better off as they primarily care about high gP , while citizens with high incomes are

worse off as they primarily care about low τP .

3 Empirical Analysis

In the following, we put our theoretical model to an empirical test. In particular, we study

how a reduction in voting costs due to the introduction of unrestricted optional postal

voting affected the political process and fiscal outcomes in the 26 Swiss states. The high

degree of fiscal autonomy of Swiss states makes it possible that changes in participation

decisions can translate into changes in fiscal policies. For the identification of the effects

of postal voting, we exploit the natural experiment provided by the staggered introduction

of postal voting in the states. Frequent direct democratic decisions at the national level

allow us to observe participation decisions and characteristics of the voting population more

frequently than what is normally possible. The staggered introduction of postal voting and

the frequent national ballots allow us to test Propositions 1 and 2 independently of time-,

issue- and state-specific effects. To test Proposition 1, we estimate the effect of postal

voting on turnout in national ballots. To test Proposition 2, we use post-vote surveys and

isolate the effect of postal voting on participants’ average years of education, participants’

average household income and participants’ average ballot-specific knowledge.

We do not test Propositions 3 and 4 as they prepare for Propositions 5 to 7. This

latter set of propositions is difficult to test empirically because rents to special-interest

19



groups are inherently difficult to capture. We still explore Proposition 5 as formulated in

our model and study the relationship between postal voting and total government expen-

ditures at the state level. For a test of Proposition 6 and 7, we concentrate on government

welfare expenditures as this category of government expenditures is least likely to include

rents to special-interest groups.16 Using government welfare expenditures, we explore the

possibility that lower voting costs can result in lower public goods provision, i.e., in lower

public expenditures net of rents. Importantly, government welfare expenditure is also the

expenditure category most likely to benefit poor people, the supposed beneficiaries of re-

duced voting costs and higher voting participation. Welfare expenditures are, therefore,

well suited to differentiate between our model and alternative theories, such as the Meltzer-

Richard model, which predict that higher turnout should be associated with policy changes

supporting poorer citizens.

3.1 Data

Our dependent variables are voter turnout, participants’ average years of education, partic-

ipants’ average household income, participants’ average ballot-specific knowledge, as well

as total expenditures and welfare expenditures as shares of state income. Data for these

variables come from various sources. The data on voter turnout for states and ballot dates

comes from the Federal Statistical Office (FSO). The FSO registers voter turnout for every

ballot. As there are usually several propositions at a particular date, we calculate average

turnout per state and ballot date. Voter turnout is 44% on average and ranges from 14%

to 87%.

Average years of education, average household income, and average knowledge on

proposition of the voting population are captured on the basis of post-vote surveys. Differ-

16Welfare expenditures offer limited opportunities for discretionary spending decisions and for the tar-
geting of funds to specific industries or regions.

20



ent Swiss universities together with a private research institute (Schweizerische Gesellschaft

für praktische Sozialforschung, GFS) carry out post-vote surveys after each ballot date

(VOX surveys). We use the standardized cumulative file VoxIt. The sample period starts

on June 14, 1981. The post-vote surveys contain information on whether and how respon-

dents voted, their knowledge about ballot proposals, and their socio-economic characteris-

tics.

Respondents level of education is captured by the highest degree they attained. Based

on information provided by Swiss Conference of Cantonal Ministers of Education, we trans-

late the degrees into years of education. Household income is reported in bands. Based on

this information, we estimate the distribution function of income for each year, assuming

a log-normal distribution of income, and then replace the grouped income variable by the

respective group means (in 2010 CHF). Information on household income is only available

since 1993. Respondents knowledge on the ballot proposition is expressed on a three-point

scale. The respective variable takes value 0 for respondents who remember neither the title

nor the content of the proposition, value 1 for respondents who remember one of these,

and value 2 for respondents who remember both title and content of the ballot.

Based on this information, we calculate average years of education, average household

income, and average knowledge on propositions of voting participants for all states and

ballot dates. For some states and dates there are no respondents or, alternatively, no

respondents who voted. For the characteristics education and household income, we also

calculate the average over all respondents per state and ballot date. These variables, later

called population average of outcome, capture general state developments in education and

income in a very flexible way. We do not calculate an analogous variable for knowledge on

propositions because knowledge is endogenous to the participation decision (as theoretically

modeled) whereas education and household income are exogenous to the participation

decision.

21



As can be seen from the descriptive statistics in Table 1, participants in the ballots

have a slightly higher level of education and more income (12.5 years and CHF 6,532) than

the general population (12.3 years and CHF 6,282). Average knowledge of participants is

1.6 on the three-point scale ranging from 0 to 2.

[Table 1 about here ]

Data on total expenditures and welfare expenditures in states are from an annual

publication of the Federal Finance Administration on public finances (Öffentliche Finanzen

der Schweiz, various years). On average, total state expenditures amount to 17.0% of state

income, and welfare expenditures to 2.3%.

Our main explanatory variable is a dummy variable for postal voting (Luechinger et

al. 2007).17 In our context, postal voting means that citizens get the ballot forms mailed

to their home address, and can either go to the ballot box to vote or fill out the ballot

forms and mail them back by a specified date in order to participate. The variable has

been constructed on the basis of survey information from the federal chancellery, state

corpora juris and a survey conducted with the chancelleries of the states. Since the late

1970s, Swiss states gradually introduced postal voting for all citizens without request. In

earlier years, postal voting was restricted to selected groups (e.g., hospital- or home-bound

patients) and/or only available upon request. The first state to introduce unrestricted

postal voting was Basel-Landschaft (in 1978), and the latest states were Ticino and Valais

(in 2005). In 23 out of the 26 states, the introduction of postal voting falls into our sample

period.

Control variables at the state level are income per capita, population and the rate

of unemployment. This data is from the FSO. We include these three variables both in

17Luechinger et al. (2007) provide a detailed description of the introduction of postal voting in Swiss
states, the construction of the respective dummy variable, and estimates on the effect of postal voting
on turnout. The discussion in this section abbreviates the more complete discussions of these issues in
Luechinger et al. (2007).

22



levels and in growth rates.18 Data on state income is only available until 2005. In order

to account for the population structure, we include the share of population below the

age of 16 and above the age of 64. In the government expenditure regressions, we also

include institutional and political variables that have been argued to affect spending levels

and composition. The variables are the share of left-wing party members in parliament, a

dummy for election years, a fiscal rule index, a dummy for states and years with mandatory

fiscal referenda, the signature requirement to launch a voter initiative relative to the state

population, the cabinet size and the parliament size. These institutional and political

variables are from Schaltegger and Feld (2009), except for the fiscal rule index, which is

from Feld et al. (2011).

In order to have a comparable sample across regressions, we restrict the sample period

to the years 1981 to 2005, i.e., starting with the first year of post-vote survey information

and ending with the last year with data on state income.

3.2 Estimation results

We present the results of our empirical analysis in three steps: i) voter turnout, ii) com-

position of the voting population and political knowledge, and iii) public finances.

3.2.1 Voter turnout

Table 2 shows the partial correlation between unrestricted optional postal voting and voter

turnout at the level of Swiss states on 73 dates of national ballots between 1981 and

2005. Based on ordinary least squares estimates including state-specific and ballot date-

specific effects, we find that postal voting leads to an increase in voting participation of 4.1

percentage points. The effect holds if a set of time variant control variables is included in

18As the unemployment rate was zero in the state Appenzell Inner Rhodes in eight years, we lose eight
state-years by including the growth rate of unemployment.

23



the second specification of Table 2. The estimated coefficient for the variable postal voting

now amounts to 3.9 percentage points, or 8.9% relative to the average turnout of 43.8% in

our sample. This effect is statistically highly significant (t-value=4.36) whereby standard

errors are adjusted for clustering at the state level. Of the control variables, the rate of

unemployment is statistically significantly positively correlated with turnout whereas the

other state level factors show no significant correlations. The evidence supports Proposition

1 and indicates that the reduction in voting costs due to the introduction of postal voting

significantly increased turnout.

[Table 2 about here ]

3.2.2 Composition of the voting population and political knowledge

The effects of postal voting on the composition of the voting population, i.e., participants

average years of education and household income, are estimated with two specifications

for both variables. In the baseline specifications, we include three sets of control variables.

First, time invariant state-specific effects are taken into account. Second, ballot date-

specific effects deal with issue specific mobilization of more or less educated people and of

people with lower or higher income. Third, population averages of the outcome variables

per state and ballot date control in a very flexible way for the development in the level of

education and income over time. In the extended specifications, we include a set of time

variant control variables capturing the socio-economic conditions in the states.

Table 3 presents the results. Access to voting by mail is related, on average, to a lower

education level of the participants in national ballots. The average years of education is

reduced by 0.089 or 0.085 years, respectively (with t-values of -2.23 and -1.76). While

the effect of postal voting seems small in absolute terms, it corresponds to more than one

third of the difference in the level of education of participants and non-participants in

the entire sample, which is 0.219 years (i.e., 12.509 years - 12.290 years). The finding is

24



consistent with Proposition 2 that the skill level of participants is lower with lower voting

costs. The control variable for the population average is positively related to the level of

education of the participants with a coefficient slightly larger than one. This reflects that

participants, on average, have a higher level of education than non-participants. From

the set of additional control variables, growth of state income is statistically significantly

negatively related to the participants’ level of education.

[Table 3 about here ]

Consistent with the findings for education, the average household income of participants

is lower with postal voting. The estimated coefficients amount to CHF 79.6 and CHF

89.4, respectively. This is about a third of the average difference in voters and non-voters

household income of CHF 250 (i.e., CHF 6532 - CHF 6282). However, the estimated partial

correlations are not statistically significant. There are two reason why we would expect a

low precision of the coefficient estimates. First, survey information on household income is

only available since 1993. Therefore, the household income regressions are based on both a

smaller sample size and less identifying variation in the postal voting variable. Second, we

construct the household income variable on the basis of categorized income information.

Thus, household income is measured with an error. Since we use estimated group means

rather than category midpoints, this measurement error is classical in form (Hsiao 1983).

Still, it reduces the precision of the coefficient estimates.

Finally, Table 3 reports the effect of postal voting on participants average knowledge on

propositions. We find that knowledge is statistically significantly lower by 0.051 (t-value=-

2.06) and 0.047 (t-value=-1.92), respectively, whereby the mean value of this variable is

1.619. This evidence supports Proposition 2 of our model. Moreover, it shows that lower

voting costs can have unintended side effects.19

19Remember that the estimation equation would be misspecified if we were to include the population

25



3.2.3 Public finances

Table 4 presents the results for the effects of postal voting on public finances. We estimate

three specifications for total government expenditures as a share of state income, and three

specifications for welfare expenditures as a share of state income. All estimations include

state- and year-specific effects. The specifications differ in terms of the additional control

variables. We first add the same time variant factors as in the estimations above. Second,

we add a large set of political and institutional variables that have been studied in previous

work on public finances in Swiss states (often in a cross-section context though).

We find no systematic partial correlation between postal voting and total government

expenditures across our three specifications. In fact, when controlling for time-invariant

state-specific differences and year-specific effects, the remaining variation in total govern-

ment expenditures is only related to population size of the state and aggregate income in

the state. Expenditures as a share of state income is lower with a larger population and -

not surprisingly – also with a higher aggregate income. Thus, the results for total govern-

ment expenditures support neither our model, nor other models in the spirit of Meltzer and

Richard (1981) on the relationship between the composition of the voting population and

government expenditures. We can think of two reasons for this (non-)result. First, while in

our model rents are acquired through government expenditures, in reality special-interest

groups might well benefit even more from favorable regulations allowing them to set higher

prices for goods and services that they sell to consumers (and thus “tax” them indirectly).

Second, relatively fierce tax competition between Swiss states greatly reduces the ability

of these states to increase taxes and expenditures relative to other states. Indeed, total

government expenditures in Swiss states have been found to mimic expenditure patterns of

neighboring states (Schaltegger and Küttel 2002, Schaltegger 2004). In comparison, Swiss

average of knowledge on propositions as an additional control variable. Knowledge is endogenous to
the participation decision (as theoretically modeled) whereas income and education are exogenous to the
participation decision.

26



states have considerably more leeway in deciding on the composition than on the level of

government expenditures, similarly to the situation modeled in Section 2.3.3.

[Table 4 about here ]

According to the second set of estimations in Table 4, postal voting is statistically

significantly negatively correlated with welfare expenditures. Welfare expenditures as a

share of aggregate income in the state are lower by between 0.13 and 0.19 percentage

points depending on the specification. Given that state government welfare expenditures

are an expenditure category that is likely not to include rents for special-interest groups,

we see the evidence as consistent with the – probably most controversial – second case in

Proposition 7 that lower voting costs decrease public expenditures net of rents.20

4 Conclusions

There is a common concern that voting costs with traditional voluntary voting at the poll

put many citizens off participating in the process of democratic decision-making. Moreover,

these costs contribute to an unequal representation with the better educated being more

likely to participate. Accordingly, the plea is for lower voting costs (or higher costs of

abstention, e.g., induced by compulsory voting). However, lower voting costs involve a

trade-off: While they may reduce the representation bias, they may simultaneously lower

the average participants’ political knowledge and increase the bias from interest-group

politics.

We substantiate this argument offering a theoretical model and some first evidence.

In particular, we study how lower voting costs affect public goods provision and rents to

20We have argued above that the model with exogenous total government expenditures (Section 2.3.3)
might be more relevant in the Swiss context than our general model (Section 2.3.4). Proposition 4 shows
that the prediction of lower public goods provision in response to lower voting costs is unambiguous in
this context.

27



special-interest groups in a probabilistic voting model with campaign contributions. This

model is fairly standard except that we allow the citizens to decide how much political

knowledge to acquire, and whether or not to participate in the election. We show that

lower voting costs (or higher costs of abstention) increase the share of uninformed voters,

thereby making special-interest groups more influential. These groups thus receive more

generous rents. Furthermore, we show that total government spending and taxes are higher

with lower voting costs, while public goods provision may be higher or lower. Lower voting

costs may thus well lead to policies that make even less privileged citizens worse off.

Consistent with the main propositions of our model, we find in an empirical analysis for

26 Swiss states that lower voting costs due to postal voting are related to higher turnout

and lower average education of participants as well as lower knowledge on the political

issues they were deciding on. Moreover, we observe that the introduction of postal voting

is related to lower - and not higher - government welfare expenditures.

Overall, we want to submit that high participation in democratic decision-making is

not a value in itself. Rather participants’ knowledge on the political decisions at stake is

crucial. Lowering voting costs to increase participation might have rather negative side

effects when special-interest groups are attracted that try to influence the less well informed

in the voting population.

28



Appendix: Proofs

Proof of Proposition 3: The interior solution of maximization problem (5) must satisfy the

first-order condition ∫ 1
2γ
αi
[
−αi

α
U ′(ciP ) + H

′(gP )

]
f(αi)dαi = 0, (7)

where ciP = (1−τP )α
i and τP =

gP +r
α

. It is straightforward to show that the second-order condi-

tion holds. Denote the left-hand side of (7) by kr. Note that
∂kr
∂gP

=
∫ 1

2γ
αi
[(
−αi
α

)2
U ′′(ciP ) + H

′′(gP )

]
f(αi)dαi < 0. It follows from Leibniz’s rule that ∂kr

∂γ
= −4γ

[
−2γ
α
U ′(ĉP ) + H

′(gP )
]
f(2γ), where

ĉP = (1−τP )2γ. Observe that
∂
[
−αi
α
U′(ci

P
)+H′(gP )

]
∂αi

= −1
α

[U ′(ciP )+c
i
PU
′′(ciP )] =

1
α
U ′(ciP )[RR(c

i
P )−

1] < 0, where the inequality follows from our assumption that RR(c
i
P ) < 1 for all c

i
P . Therefore

it follows from (7) and 2γ < 1 that
[
−2γ
α
U ′(ĉP ) + H

′(gP )
]
> 0 and, consequently, that ∂kr

∂γ
< 0.

The implicit function theorem then implies
∂gP
∂γ

= −
∂kr
∂γ
∂kr
∂gP

< 0, which implies ∂rP
∂γ

> 0. �

Proof of Proposition 4: The interior solution of maximization problem (6) must satisfy the

first-order condition

∫ 1
2γ

[
αiH′(gP ) − (1 −αi)ΩJ′(rP )

]
f(αi)dαi = 0. (8)

It is straightforward to show that the second-order condition holds. Denote the left-hand side of

(8) by kτ . Note that
∂kτ
∂gP

=
∫ 1

2γ

[
αiH′′(gP ) + (1 −αi)ΩJ′′(rP )

]
f(αi)dαi < 0, and ∂kτ

∂Ω
= −

∫ 1
2γ

(1−

αi)J′(rP )f(α
i)dαi < 0. It follows from Leibniz’s rule that ∂kτ

∂γ
= −2 [2γH′(gP ) − (1 − 2γ)ΩJ′(rP )]

f(2γ). Observe that
∂[αiH′(gP )−(1−αi)ΩJ′(rP )]

∂αi
= H′(gP ) + ΩJ

′(rP ) > 0. Therefore it follows from

(8) and 2γ < 1 that [2γH′(gP ) − (1 − 2γ)ΩJ′(rP )] < 0 and, consequently, ∂kτ∂γ > 0. The implicit

function theorem then implies
∂gP
∂Ω

< 0 and
∂gP
∂γ

> 0. It follows that ∂rP
∂Ω

> 0 and ∂rP
∂γ

< 0. �

Proof of Proposition 5: The interior solution of maximization problem (4) must satisfy the

first-order conditions ∫ 1
2γ

[
−(αi)2

α
U ′(ciP ) + α

iH′(gP )

]
f(αi)dαi = 0 (9)

29



and ∫ 1
2γ

[
−(αi)2

α
U ′(ciP ) + (1 −α

i)ΩJ′(rP )

]
f(αi)dαi = 0. (10)

It is straightforward to show that the second-order conditions hold. Denote the left-hand side of

(9) by k1, and the left-hand side of (10) by k2. It follows that
∂k1
∂gP

= KU +KH,
∂k2
∂gP

= ∂k1
∂rP

= KU ,

and ∂k2
∂rP

= KU + KJ, where KU ≡
∫ 1

2γ
(αi)3

α2
U ′′(ciP )f(α

i)dαi ≤ 0, KH ≡ H′′(gP )
∫ 1

2γ
αif(αi)dαi <

0, and KJ ≡ ΩJ′′(rP )
∫ 1

2γ
(1 − αi)f(αi)dαi < 0. Further it holds that ∂k1

∂Ω
= 0 and ∂k2

∂Ω
>

0; and it follows from Leibniz’s rule that ∂k1
∂γ

= −2[−4γ
2

α
U ′(ĉP ) + 2γH

′(gP )]f(2γ) and
∂k2
∂γ

=

−2[−4γ
2

α
U ′(ĉP ) + (1 − 2γ)ΩJ′(rP )]f(2γ).

The implicit function theorem states that


 ∂gP∂γ

∂rP
∂γ


 = −B


 ∂k2∂rP − ∂k1∂rP
−∂k2
∂gP

∂k1
∂gP




 ∂k1∂γ

∂k2
∂γ




with B ≡
[
∂k1
∂gP

∂k2
∂rP
− ∂k1

∂rP
∂k2
∂gP

]−1
. Hence

∂gP
∂γ

= 2Bf(2γ)

{
KU

[
2γH′(gP ) − (1 − 2γ)ΩJ′(rP )

]
+ KJ

[
−4γ2

α
U ′(ĉP ) + 2γH

′(gP )

]}
, (11)

∂rP
∂γ

= 2Bf(2γ)

{
KU [(1 − 2γ)ΩJ′(rP ) − 2γH′(gP )] + KH

[
−4γ2

α
U ′(ĉP ) + (1 − 2γ)ΩJ′(rP )

]}
,

(12)

and, consequently,

∂(gP + rP )

∂γ
= 2Bf(2γ)

{
KJ

[
−4γ2

α
U ′(ĉP ) + 2γH

′(gP )

]
+ KH

[
−4γ2

α
U ′(ĉP ) + (1 − 2γ)ΩJ′(rP )

]}
.

(13)

We know that KJ < 0 and KH < 0, and it is easy to show that B > 0. Hence it re-

mains to determine whether the two terms in square brackets in (13) are positive or neg-

ative. As shown in the proof of Proposition 3, it holds that
∂
[
−αi
α
U′(ci

P
)+H′(gP )

]
∂αi

< 0. It

then follows from (9) and 2γ < 1 that
[
−4γ2
α
U ′(ĉP ) + 2γH

′(gP )
]
> 0. It further holds that

30



∂

[
−(αi)2
α

U′(ci
P

)+(1−αi)ΩJ′(rP )
]

∂αi
= −α

i

α
[2U ′(ciP ) + c

i
PU
′′(ciP )] − ΩJ

′(rP ) < 0, where the inequality

holds since RR(c
i
P ) < 1 implies U

′(ciP ) + c
i
PU
′′(ciP ) > 0. It then follows from (10) and 2γ < 1

that
[
−4γ2
α
U ′(ĉP ) + (1 − 2γ)ΩJ′(rP )

]
> 0. Together with (13), these results imply

∂(gP +rP )
∂γ

< 0.

Consequently, ∂τP
∂γ

< 0.

The implicit function theorem further implies
∂gP
∂Ω

= B ∂k1
∂rP

∂k2
∂Ω
≤ 0, ∂rP

∂Ω
= −B ∂k1

∂gP
∂k2
∂Ω

> 0,

and
∂(gP +rP )

∂Ω
= B

[
∂k1
∂rP
− ∂k1

∂gP

]
∂k2
∂Ω

= −BKH ∂k2∂Ω > 0, where all inequalities directly follow from

results derived above. Consequently, ∂τP
∂Ω

> 0. �

Proof of Proposition 6: It is shown in the proof of Proposition 5 that ∂rP
∂Ω

< 0. There I further

show that B > 0, KU ≤ 0, KH < 0, and
[
−4γ2
α
U ′(ĉP ) + (1 − 2γ)ΩJ′(rP )

]
> 0. Therefore it

follows from (12) that ∂rP
∂γ

< 0 if [(1 − 2γ)ΩJ′(rP ) −γH′(gP )] ≥ 0. It follows from conditions (9)

and (10) that ∫ 1
2γ

[
(1 −αi)ΩJ′(rP ) −αiH′(gP )

]
f(αi)dαi = 0. (14)

Observe that
∂[(1−αi)ΩJ′(rP )−αiH′(gP )]

∂αi
= −ΩJ′(rP ) − H′(gP ) < 0. Therefore condition (14) and

2γ < 1 imply [(1 − 2γ)ΩJ′(rP ) − 2γH′(gP )] > 0. Consequently, ∂rP∂γ < 0. �

Proof of Proposition 7: It is shown in the proof of Proposition 5 that
∂gP
∂Ω
≤ 0.

Assume for the moment that U(ciP ) = χc
i
P with χ > 0. Then U

′′(ciP ) = 0, such that KU = 0.

Hence (11) reduces to
∂gP
∂γ

= 2Bf(2γ)KJ

[
−4γ2
α
U ′(ĉP ) + 2γH

′(gP )
]
. It is shown in the proof of

Proposition 5 that B > 0, KJ < 0, and
[
−4γ2
α
U ′(ĉP ) + 2γH

′(gP )
]
> 0. It follows that

∂gP
∂γ

< 0.

Assume now that RR(c
i
P ) = θ with θ → 1 (or θ = 1). Then

∂
[
−αi
α
U′(ci

P
)+H′(gP )

]
∂αi

→ 0,

such that
[
−4γ2
α
U ′(ĉP ) + 2γH

′(gP )
]
→ 0. Hence it follows from (11) that ∂gP

∂γ
→ 2Bf(2γ)KU

[2γH′(gP ) − (1 − 2γ)ΩJ′(rP )]. It is shown in the proofs of Propositions 5 and 6 that B > 0 and

[2γH′(gP ) − (1 − 2γ)ΩJ′(rP )] < 0, respectively. Further, RR(ciP ) > 0 implies U
′′(ciP ) < 0 and,

consequently, KU < 0. It follows that
∂gP
∂γ

> 0. �

31



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36



Table 1: Descriptive statistics

No. of obs. Mean Std. dev. Min. Max.

A. Turnout regressions

Turnout 1870 0.438 0.118 0.138 0.872
Postal voting 1870 0.489 0.500 0.000 1.000

B. Education and knowledge regressions

Avrg. years of education
of participants 1394 12.509 0.998 9.000 17.000
of general population 1394 12.290 0.825 9.000 17.000

Avrg. knowledge on propositions
of participants 1394 1.619 0.288 0.000 2.000

Postal voting 1394 0.604 0.489 0.000 1.000

C. Income regressions

Avrg. household income
of participants 910 6532 1346 2487 12639
of general population 910 6282 1069 2553 12561

Postal voting 910 0.793 0.405 0.000 1.000

D. Expenditure regressions

Total expenditures (% of state inc.) 639 0.170 0.057 0.044 0.358
Welfare expenditures (% of state inc.) 639 0.023 0.013 5.0E-4 0.066
Postal voting 639 0.473 0.500 0.000 1.000
Population 639 271201 279351 14145 1292481
Growth of population 639 0.007 0.007 -0.010 0.070
Share under 16 639 0.188 0.024 0.116 0.247
Share over 64 639 0.151 0.021 0.105 0.214
State income p.c. 639 40416 13508 19168 115180
Growth of state income p.c. 639 0.036 0.043 -0.170 0.420
Unemployment rate 639 2.077 1.791 0.030 7.810
Growth of unemployment rate 639 0.268 0.683 -0.590 3.630
Share of left-wingers in parliament 639 0.228 0.127 0.000 0.530
Election year 639 0.260 0.439 0.000 1.000
Fiscal rule index 639 0.397 0.900 0.000 3.000
Mandatory fiscal referendum 639 0.643 0.479 0.000 1.000
Signature requirement initiative, relative 639 0.015 0.010 1.8E-5 0.039
Cabinet size 639 6.277 1.118 5.000 9.000
Parliament size 639 116 47 46 200

Notes: Data refers to the sample period 1981 to 2005. Observations in panels A, B and C are at

the state-ballot date level while those in panel D are at the state-year level.

Data sources: Luechinger et al. (2007), Schaltegger and Feld (2009), Feld et al. (2011), Swiss

Federal Statistical Office, Swiss Federal Finance Administration, and VoxIt.

37



Table 2: Postal voting and voter turnout in federal ballots in Switzerland for 1981 to 2005

Dependant variable Turnout
(I) (II)

Postal voting 0.041*** 0.039***
(0.009) (0.009)

Population in 1’000’000 –0.042
(0.332)

Growth of population 0.188
(0.226)

Share under 16 0.756
(0.720)

Share over 64 –0.268
(0.579)

State income p.c. in 100’000 –0.010
(0.059)

Growth of state income p.c. 0.004
(0.048)

Unemployment rate 0.007*
(0.004)

Growth of unemployment rate 0.006
(0.005)

State-specific effects Yes Yes
Ballot date-specific effects Yes Yes

No. of obs. 1870 1870
No. of clusters 26 26
R2 within 0.75 0.75

Notes: OLS estimations. Robust standard errors in parentheses. Standard errors are adjusted

for clustering at the level of states. ***, **, and * indicate significance level at 1%, 5%, and 10%,

respectively.

Data sources: Luechinger et al. (2007), and Swiss Federal Statistical Office.

38



Table 3: Postal voting, the composition of the voting population and political knowledge
in federal ballots in Switzerland for 1981 to 2005

Dependent variable Avrg. years Avrg. household Avrg. knowledge
of education income on propositions

of participants of participantsa) of participantsb)

(I) (II) (I) (II) (I) (II)

Postal voting –0.089** –0.085* –79.610 –89.484 –0.051* –0.047*
(0.040) (0.048) (94.249) (92.618) (0.025) (0.024)

Population avrg. 1.031*** 1.026*** 1.069*** 1.071***
of outcome (0.022) (0.023) (0.027) (0.029)

Population –0.050 –11.232 0.741*
in 1’000’000 (0.824) (2.1E+4) (0.413)

Growth of pop. –0.394 1.7E+3 –0.442
(2.575) (5.1E+3) (0.824)

Share under 16 –3.074 –9.2E+3 –2.711*
(3.323) (7.9E+3) (1.434)

Share over 64 0.504 –1.7E+04 –0.329
(2.151) (1.4E+4) (1.525)

State income p.c. 0.197 –683.130 0.195
in 100’000 (0.296) (760.215) (0.144)

Growth of state –1.073*** 446.698 –0.040
income p.c. (0.372) (830.392) (0.164)

Unemployment rate –0.020 –31.244 0.005
(0.025) (44.466) (0.013)

Growth of unempl. 0.089 330.065 0.012
rate (0.074) (265.717) (0.025)

State-specific effects Yes Yes Yes Yes Yes Yes
Ballot date-specific effects Yes Yes Yes Yes Yes Yes

No. of obs. 1394 1394 910 910 1394 1394
No. of clusters 26 26 26 26 26 26
R2 within 0.74 0.74 0.69 0.69 0.59 0.60

General notes: OLS estimations. Robust standard errors in parentheses. Standard errors are

adjusted for clustering at the level of states. The regressions based on the survey data have fewer

observations than the turnout regressions in Table 2 because for some ballot dates, surveys do

not contain respondents from all states. ***, **, and * indicate significance level at 1%, 5%, and

10%, respectively.

Specific notes: a) Information is only available since 1993. Household income is reported in

categories. We use this information to estimate the distribution function of income and then

replace the grouped income variable by the respective group means (in 2010 CHF). b) Since

knowledge of the proposition is clearly endogenous, it makes no sense in this case to include avrg.

knowledge of the population at large.

Data sources: Luechinger et al. (2007), Swiss Federal Statistical Office, and VoxIt.

39



Table 4: Postal voting and public expenditures of Swiss states for 1981 to 2005

Dependent variable Total expenditures Welfare expenditures
(I) (II) (III) (I) (II) (III)

Postal voting –0.003 0.001 –0.001 –0.002** –0.001* –0.001**
(0.005) (0.003) (0.003) (0.001) (0.001) (0.001)

Population –0.274* –0.325* –0.052** –0.059***
in 1’000’000 (0.156) (0.188) (0.021) (0.019)

Growth of population 0.055 0.085 0.033 0.032
(0.142) (0.144) (0.025) (0.024)

Share under 16 0.065 0.031 0.121** 0.115**
(0.215) (0.272) (0.044) (0.049)

Share over 64 0.089 0.059 0.066** 0.061*
(0.205) (0.199) (0.031) (0.032)

State income p.c. –0.281*** –0.286*** –0.048*** –0.049***
in 100’000 (0.050) (0.050) (0.006) (0.006)

Growth of state –0.016 –0.013 –0.007 –0.007
income p.c. (0.014) (0.014) (0.004) (0.004)

Unemployment rate 0.003 0.003 0.001** 0.001**
(0.003) (0.003) (3.9E-4) (4.0E-4)

Growth of –0.001 –0.002 –2.3E-4 –2.6E-4
unemployment rate (0.003) (0.003) (3.3E-4) (3.3E-4)

Share of left-wingers 0.049 0.003
in parliament (0.037) (0.007)

Election year 0.001 –2.0E-5
(0.001) (1.6E-4)

Fiscal rule index 0.001 2.2E-4
(0.002) (4.8E-4)

Mandatory fiscal –0.003 –0.001*
referendum (0.009) (0.001)

Signature requirement –0.864 –0.149
initiative, relative (0.899) (0.114)

Cabinet size –0.004 –0.001
(0.004) (3.9E-4)

Parliament size –5.8E-5 1.9E-5
(1.4E-4) (2.2E-5)

State-specific effects Yes Yes Yes Yes Yes Yes
Year-specific effects Yes Yes Yes Yes Yes Yes

No. of obs. 639 639 639 639 639 639
No. of clusters 26 26 26 26 26 26
R2 within 0.57 0.72 0.73 0.84 0.91 0.91

Notes: OLS estimations. Standard errors are adjusted for clustering at the level of states. ***, **, and *

indicate significance level at 1%, 5%, and 10%, respectively.

Data sources: Luechinger et al. (2007), Schaltegger and Feld (2009), Feld et al. (2011), Swiss Federal

Statistical Office, and Swiss Federal Finance Administration.

40