key: cord-0887056-epcpsc33
authors: Weibrecht, N.; Roessler, M.; Emrich, S.; Popper, N.
title: How an election can be safely planned and conducted during a pandemic: Decision support based on a discrete event model
date: 2021-07-22
journal: nan
DOI: 10.1101/2021.07.17.21260634
sha: 9d485f0d06b1098a7d06c7df3171bc42520b7a7b
doc_id: 887056
cord_uid: epcpsc33

In 2020, the ongoing COVID-19 pandemic caused major limitations for any aspect of social life and in specific for all events that require a gathering of people. While most events of this kind can be postponed or cancelled, democratic elections are key elements of any democratic regime and should be upheld if at all possible. Consequently, proper planning is required to establish the highest possible level of safety to both voters and scrutineers. In this paper, we present the novel and innovative way how the municipal council and district council elections in Vienna were planned and conducted using an agent-based simulation model. Key target of this process was to avoid queues in front of polling stations to reduce the risk of related infection clusters. In cooperation with a hygiene expert, we defined necessary precautions that should be met during the election in order to avoid the spread of COVID-19. In a next step, a simulation model was established and parametrized and validated using data from previous elections. Furthermore, the planned conditions were simulated to see whether excessive queues in front of any polling stations could form, as these could on the one hand act as an infection herd, and on the other hand, turn voters away. Our simulation identified some polling stations where long queues could emerge, however, splitting up these electoral branches resulted in a smooth election across all of Vienna. Looking back, the election did not lead to a significant increase of COVID-19 incidences. Therefore, it can be concluded that careful planning led to a safe election, despite the pandemic.

In 2020, the COVID-19-Pandemic affected almost every area of daily life, including 2 elections. On the one hand, elections necessarily cause a gathering of people, on the 3 other hand, elections are an essential part of vital democratic societies and are not 4 easily canceled or postponed. Consequently, proper planning is required to enable the 5 election process, provide the highest possible level of safety to all participants, and to 6 avoid that the election stokes the spread of the disease. 7 In Vienna, the municipal council and district council elections were scheduled for 8 October 11 th 2020. By this time, SARS-CoV-2 case numbers in Austria, especially in 9 Vienna, were on the rise and the risk of infections was high [28] . So the planning 10 committee consulted modeling and simulation experts to help them increasing the level 11 of safety to voters and scrutineers. The key question of the planning process was how to 12 avoid the development of long waiting queues in front of the polling stations, since these 13 may potentially lead to infection clusters. 14 To avoid (excessive) epidemic spread clusters forming at the polling stations, the 15 first approach was one independent of modeling and simulation. Encouraging voters to 16 use postal election was a simple but effective measure to reduce the amount of people 17 turning up at polling stations. However, not all voters can or want to vote via mail. 18 Hence, it is neither possible nor legitimate to hold elections via mail only, without the 19 option to vote in person. 20 To avoid negative impact on the spread of COVID-19 in this process, a hygiene 21 concept was developed. This hygiene concept, however, includes additional tasks during 22 the election, such as wearing a face mask which has to be removed and put back on for 23 identification, and will therefore extend the duration of the election process. 24 Consequently, next to developing the hygiene concept, it was necessary to ensure that 25 the whole process is not extended in a way such that long queues form in front of the 26 polling booths, as these would create an additional infection risk and furthermore could 27 turn voters away. [1, 2] 28 It must be stated, that, compared to other countries, waiting queues in front of 29 polling stations are comparably rare and short in Austria. Unfortunately, to the 30 authors' knowledge, there is no data on polling queues as of now. Nevertheless, in 2017, 31 when national elections took place in Austria, an article in the "Wiener Zeitung" 32 ("Vienna newspaper") stated that "there was even a short wait in front of the cabins at 33 11 a.m.", indicating that usually there are hardly any waiting queues in Austria [4] .

down the voting process, were required for the election in October, election planners 37 were afraid that it might be different this time. 38 To ensure that the hygiene measures don't cause long waiting queues, a discrete 39 event simulation (DES) model was developed to simulate the voting process including 40 the hygiene concept in each electoral branch. Thus, possible problematic districts could 41 be identified, so that additional measures like additional voting booths for these 42 districts could be applied.

In January 2020 our group developed an agent-based COVID-19 epidemic 44 model [6, 7] , which is still in heavy use for counseling of political decision makers in 45 Austria [8] . The present question revealed an interesting new chance for us. While the 46 epidemic model concentrates on the overall spread of the disease throughout the 47 Austrian population, it models the places where infections take place, like households, 48 schools, work places, or leisure facilities as chance encounters. This is of course 49 necessary due to the much larger population size. The COVID-19 model analyses the 50 spread of the disease for the whole Austrian population, and therefore uses nearly 9 51 million agents. In contrast, there were about 1.4 million people eligible to vote at the 52 present elections, from which we expected 30 -60 % to turn up at polling stations and 53 the rest to use postal votes or not vote at all. Moreover, the COVID-19 investigates a 54 much longer time frame. It predicts the spread of the virus over a time frame ranging 55 from several weeks to months, while the election takes place over the course of 10 hours. 56 The concise character of the presented problem enabled us to model the election process 57 in more detail.

In this work we show, how this DES model contributes to enabling safe election 59 processes in times of epidemics. We describe the model in detail, explain its 60 parametrization and validation process and describe how it detects potential bottlenecks 61 in an election process with respect to emergence of long queues. Furthermore, we 62 reevaluate the municipal council and district council elections in Vienna in Fall 2020 63 which have been planned using the simulation tool and identify the benefits of the usage 64 of the model. The aim of this work is to demonstrate how modelling and simulation can 65 help optimizing election processes with respect to avoiding queues and consequently also 66 avoiding infection clusters in epidemic situations.

This section describes the COVID-related methodological background, followed by a The planning process for the municipal council and district council elections in 78 October 2020 started in June and at this time, the further course of the 79 COVID-pandemic was not clear. While the number of cases was rather low in June, the 80 actual number was hard to predict, and a higher number of cases was to be expected for 81 October. To be prepared for every scenario, different hygiene measures were developed 82 in collaboration with hygiene experts, as elections usually would bear an infection risk. 83 These measures could come into effect depending on the number of COVID-cases active 84 during the election. These concepts affected every task during the election, including 85 the training of election personnel, the setup of polling stations, and the counting 86 process. To minimize the risk of election-caused COVID-19 clusters, external measures 87 such as more dates for training, more allocated time for the setup and more rooms and 88 personnel for the counting were applied. It was agreed that these measures would suffice 89 for these contexts. The assessment of measures of the actual voting process is more complex, as it not 91 only involves the voting personnel, which can be trained, but also the voters, whose 92 number is not known in advance. While the adherence to the measures within polling 93 stations can be monitored by the staff, a problem lies in the emerging queues.

Most hygiene measures that were developed for everyday life (like providing hand 95 sanitizer, keeping distance and wearing a face mask) could be applied to the election 96 too. Furthermore, the election workers didn't only wear a face mask, but also a face 97 shield. However, each voter needs to be identified before casting the vote, and this 98 contradicts with wearing a face mask during the whole process. In order to identify the 99 voters without putting anyone at risk to infect with COVID-19, two possible hygiene 100 strategies were defined (see also [5] ):

• Strategy A: Each voter is asked to maintain a safety distance to the election 102 workers, take off their face mask in order to be identified, and to put it right back 103 on afterwards.

• Strategy B: Each voter is asked to go into a perspex booth, take off the mask 105 there, wait to be identified, put the mask back on and leave the perspex booth.

It goes without saying that hygiene strategy B is safer than A, but also takes more time. 107 Clearly, both of the defined hygiene strategies might cause long queues in front of 108 the polling station, as due to them, the voting process will take longer in total. Hereby, 109 counter measures could be applied, if potential bottlenecks are known upfront: . CC-BY 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)

The copyright holder for this preprint this version posted July 22, 2021. If only few problematic polling stations were to be identified, one could think about 111 applying additional measures to these stations directly, like offering an additional 112 polling booth. Also merging or splitting of voting districts is possible. 113 Therefore, modeling and simulating the voting process and estimating the length of 114 the queue for each voting district before the actual election takes place was deemed to 115 be of great importance. features -which means different infection risks) at several hundred polling stations, the 130 macroscopic perspective is hard to neglect.

As the election takes place in a very limited time-frame only, i.e the 10 hours during 132 which the polling stations are open, it was possible to decouple these perspectives and 133 we subsequently split the problem into two: the socio-demographic aspect which assesses 134 the general epidemic situation for the Vienna metropolitan area and the logistical aspect 135 which deals with the local risks of infection at the polling stations.

With the former being not only harder to control (until today, policy makers are 137 struggling with getting a grip on the epidemic) but also much slower to affect, we chose 138 to incorporate it as a "prognosis of boundary conditions" within which the logistic part 139 of the problem had to be solved.

Modeling and analyzing the queuing times for the election, the natural choice of 141 modeling approach is a discrete event based queuing system, where the voters are the 142 entities that run through a system of servers and queues that represent the different 143 stations during the voting process. While a more detailed model using agents and their 144 individual (locally optimal) paths would have been possible (see for example [9, 10] or 145 also [11, 12] ), an agent-based approach was deemed too detailed because of the 146 sequential nature of the voting system, as there is no prioritization within the waiting 147 voters and always the first in the queue is the next to vote (i.e. there is no overtaking, 148 and therefore the individual paths of the voters are not that important).

The queuing system is typically analyzed either with classical steady state analysis 150 or with stochastic simulation. However, considering steady state analysis, the system 151 doesn't fulfill all conditions, that are required to yield reasonable results (see also 152 discussion). Therefore, the system is analyzed using stochastic simulation.

Discrete event model 154 The following section deals with the implementation of the discrete event model. First, 155 an overview over the model is provided. Next, the implemented scenarios and the 156 calibration process are described. Finally, a dashboard is shortly introduced which Modelling process 159 Our discrete event simulation model (DES) can be considered as the interface between 160 epidemiology, which is the reason for our research, and logistic, which is the solution.

Considering the different strategies of hygiene measures and assessing their impact on 162 waiting times and queues, it was necessary to extend the established models. While the 163 hygiene measures A (taking off the mask for identification with safety distance) and B 164 (taking of the mask for identification in a perspex booth) mainly affect the service times 165 for the different voting processes, the need of social distancing and the limitation of 166 voters allowed inside the polling station at any given time revealed a new challenge.

After entering the polling room, the voters must identify themselves at the electoral 168 commission and collect their ballot card. They then proceed to the polling booth. 169 Thereafter, they deposit their ballot card at the electoral commission before leaving the 170 polling room. This process is depicted in Figure 2 . As most polling stations are located 171 in schools or other public buildings and the used rooms often only have one 172 entrance/exit, voters had to wait until one of the previous voters left the room. This 173 fact was taken into account by adding another server to the model that represents the 174 entrance/exit, which created the desired blocking effect. is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted July 22, 2021. ; https://doi.org/10.1101/2021.07.17.21260634 doi: medRxiv preprint

• The age distribution in the polling station's district, as the age of a voter 191 influences the probability of their mobility being impaired.

During the simulated election process, voters appear at the polling station at 193 random following a distribution that was based on insights from previous elections and 194 pass different places within the station. These places are visualized in Figure 2 . In each 195 place, the voter spends a certain amount of time, which corresponds to an exponentially 196 distributed random number. The parameters for these random numbers are fitted in a 197 calibration process (see below).

Calibration and validation 199 As also encouraged in the literature, and in order to derive useful recommendations for 200 actions, we made substantial efforts to calibrate the model as well as possible, i.e. to set 201 the parameters reasonably.

The parameters for the arrival times of the voters are chosen according to the arrival 203 times of past elections [23, 24] . The age distribution for the district of each polling 204 station is drawn from statistical data [25, 26] . The amount of voters bringing their 205 voting information and using preferential voting corresponds to 67% and 10%, 206 respectively, according to the experts from the magistrale department 62, which is 207 responsible for elections.

The times each voter needs at each place in a polling station (to walk to the 209 electoral commission, to be identified, to vote) are drawn from an exponential 210 distribution. The parameters of these distributions were initially estimated by election 211 workers of past elections. Afterwards, these estimations were calibrated assuming a 212 voter turnout of 75% with 250, 000 postal voters, voters with limited mobility according 213 to prevalence and no hygiene strategy. This scenario corresponds approximately to the 214 conditions during the last election in Austria, which was the national council election in 215 2019. Within this scenario, the parameters were carefully adjusted using a bisection 216 algorithm, until the simulation yielded reasonable waiting queues. However, as data 217 from queues have not been measured so far, "reasonable waiting queues" were in fact 218 hard to quantify; the magistrale department 62 could not provide any data on this, 219 either. But due to their experience, they stated that the longest queue forming in front 220 of a polling station during the election day never exceeded 15 persons. Therefore, we 221 looked for a parametrization of the model such that the longest queue was lower or 222 equal to 15 in every polling station.

Via the bisection algorithm, we found a calibration which yielded maximum queues 224 of 15 people or less in 1439 of the 1456 voting districts (i.e., 98, 70%). In the remaining 225 17 stations, however, extensive queues of up to 132 persons would emerge, which clearly 226 made a closer inspection of these stations with the magistrale department 62 necessary. 227 This inspection showed that these stations were already known as potential risk stations 228 and were thus under observation. These stations, for example, belong to districts with 229 care homes; therefore, the average age is comparatively high, and the voters need 230 accordingly long to vote in the simulation. In reality, care homes offer almost 231 exclusively postal voting, which is why these stations are actually no risk stations. The 232 other stations belong to known big voting districts, and were already planned to be split 233 up into two smaller voting districts.

Via careful inspection from the planning experts using the implemented dashboard 235 (see below), the model passed general face validity tests. Since the model properly 236 displayed already known bottlenecks of a standard election process without additional 237 hygiene measures, the simulation model achieved a certain level of quantitative validity 238 as well. Note, that there is no data about queue lengths of previous elections available 239 that would allow a more detailed validation process. The model allows the simulation of several scenarios and strategies. First, the amount of 242 voters and the number of postal voters were varied, as well as the amount of people with 243 limited mobility and the number of additional polling booths. Additionally, the different 244 hygiene strategies were simulated. The impact of the scenarios on the queues can be seen in Figure 3 . Based on the 246 above mentioned baseline scenario, each of the parameters has been varied, and the 247 longest queue, that appears throughout the day in one of the polling stations in each 248 district, has been calculated. Considering these results, the following observations can 249 be made: 

• The amount of voters with limited mobility has hardly any impact on the queue 256 lengths. Therefore, in the following analysis, only "limited mobility according to 257 prevalence" will be considered.

• The difference from "no hygiene strategy" to "hygiene strategy A" is larger than 259 the difference from "hygiene strategy A" to "hygiene strategy B". Seeing this, 260 hygiene strategy B should be preferred, as it is safer without having that much 261 impact on the waiting queues.

• It happens, when comparing two scenarios, that the maximum queue is longer in a 263 scenario, where a shorter queue would have been excepted, or vice versa. For In order to visualize the scenarios and thus, to improve the decision making process, a 269 dashboard containing the simulation results was implemented. In this dashboard, it is 270 possible to set a scenario according to the values shown in Table 1 . CC-BY 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted July 22, 2021 showed, that additional voting booths in these stations don't alleviate the queues 297 sufficiently (i.e. maximum queues of 15 persons or less), as it can also be seen in Figure 298 July 18, 2021 9/15 . CC-BY 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted July 22, 2021. ; 5. This can be explained with the actual bottleneck of the election being the entrance, 299 not the voting process itself. At the entrance sits the election commission. This is a 300 group of local politicians and volunteers, that look over the whole election process. At a 301 time, only one voter can enter the voting station, as they keep all members of the 302 election commission busy. Plus, entering is the only part of the election whose duration 303 is extended due to the hygienic measures, as they lead to prolonged ID checking. Two 304 additional voting boxes hardly had any impact. is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted July 22, 2021 investigated in the US [3, [13] [14] [15] [16] [17] [18] [19] [20] but also in other countries like Nigeria [21] or Hong 342 Kong [22] . Most of these papers, especially the ones from the US, focus on the optimal 343 distribution of voting machines. This is due to the widespread use of such machines 344 there. Hence, the scarcity of these resources presents the biggest bottleneck during the 345 US voting process. Additionally, different waiting times in different voting precincts are 346 a major problem. Other papers [19, 21, 22] are more concerned on optimizing the actual 347 voting process by providing more resources such as voting booths or identification desks. 348 Big differences between the models are mainly due to varying voting processes, for 349 example in Nigeria the overall process is split into two phases, where the voters have to 350 get accredited in the morning and the actual vote is performed in the afternoon.

Technologically, the queuing system is typically analyzed in one of two ways. The first 352 approach is classical steady state analysis [15, 19] , but using steady state analysis . CC-BY 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) Fig 6. Incidences in Austria and in each federal state before and after the election date according to official data [28] . The vertical line denotes the election day.

creates a number of problems and inaccuracies for the analysis:

• Using steady state analysis requires the system to be in a steady state. Due to the 355 relatively short voting time, it is not always possible to ensure that the system 356 even reaches this state.

• If the arrival rate is greater than the servicing rate of the system, the queues 358 become unbounded, and therefore a steady state can never be reached.

• Queuing systems base their analysis on arrival rates and service times that are 360 randomly distributed, but the underlying distribution cannot change over time.

This restriction is particularly limiting for the consideration of voting processes, as 362 the arrival rates are typically dependent on the time of day, and the actual voting 363 times depend heavily on the type of voter. For example, disabilities lead to higher 364 voting times, but also voters that use preferential voting take longer than voters 365 who only vote for a political party.

These problems show that steady state analysis is not a feasible method for studying 367 voting processes, which is acknowledged in most of the literature. The second approach 368 for analyzing queuing systems is stochastic simulation, which is also the preferred 369 method in most of literature [13, 14, 16-18, 21, 22] . This ansatz enables not only a more 370 detailed stochastic analysis, but also the possibility to vary parameters over time and However, the limitations of our study need to be stated. For our simulation model, 376 the following simplifications had to be made:

• No reneging: Voters don't leave the queue if the wait is too long. This could limit 378 the application to other elections where queues are typically longer.

• No precise approximation of persons with limited mobility in each district: Our 380 estimation of the amount of people with limited mobility relies solely on the age 381 distribution in this district.

• No realistic distribution of postal voters: Our model assumes that the amount of 383 postal voters is the same across all age groups. This is, for example, not true for 384 people living in care homes, as they use postal voting almost exclusively. This 385 yielded unreliable results in districts with large care homes. Furthermore, the 386 amount of postal votes depends on the socioeconomic population structure and 387 varies within the districts. And finally, it is possible to order postal voting and 388 nevertheless enter a polling station in order to deposit the vote. This is done, for 389 example, when a voter wants to vote in a different polling district than their home 390 district. This wasn't considered either by the model.

Additionally, we had limited data for both parametrization and validation. Queue-data 392 have not been measured and collected so far, and thus, the calibration process could 393 only be validated visually, instead of quantitatively. As this work focused on identifying 394 those stations, where long queues could emerge, instead of on the actual queue lengths 395 of the single stations, the visual validation was sufficient. However, if a more precise 396 study with reliable queue length numbers is required, more data would be necessary to 397 parametrize and validate the model correctly.

In general we showed that modeling and simulation is a valid way to test new 399 conditions in an election. In this case, the precautions, that were taken in order to avoid 400 a new spread of COVID, lead to an unavoidable prolongation in the voting process. The 401 simulation showed, however, that the process was not prolonged in a way such that long 402 queues formed in front of the polling stations. Nevertheless, the model can easily be 403 adapted to simulate any other changes in the voting scheme as well.

Altogether the established strategy resulted in an election which can be considered 405 as "smooth". It should however be taken into account that this is usually the case in 406 Austria. It rarely happens, that queues in front of polling stations form at all, and if, 407 these are mostly short ones. Still, it is worth acknowledging that this condition was 408 threatened by the additional measures, but could be upheld. 409 Finally, the analysis of the reported case numbers in the city of Vienna indicated 410 that the election did not cause a temporary upswing of the epidemic. Surely, there are 411 many factors that might have prevented additional infections such as wearing face-mask, 412 large and well ventilated polling rooms, keeping the distance in the queues, low voter 413 turnout, campaigns for mail voting, or simply because voting is a quick process that 414 does not require talking. Nevertheless, it is legit to assume that the preventive measures 415 against queuing bottlenecks that were detected by the simulation model contributed to 416 avoid election related infection clusters -and this was, essentially, the uppermost goal 417 of the simulation study. 

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