Complexity

Volume 2017 (2017), Article ID 7354642, 15 pages

https://doi.org/10.1155/2017/7354642

## Empirical Analysis and Agent-Based Modeling of the Lithuanian Parliamentary Elections

Institute of Theoretical Physics and Astronomy, Vilnius University, Vilnius, Lithuania

Correspondence should be addressed to Aleksejus Kononovicius

Received 31 August 2017; Accepted 9 November 2017; Published 29 November 2017

Academic Editor: Gilberto C. Gonzalez-Parra

Copyright © 2017 Aleksejus Kononovicius. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

We analyze a parties’ vote share distribution across the polling stations during the Lithuanian parliamentary elections of 1992, 2008, and 2012. We find that the distribution is rather well fitted by the Beta distribution. To reproduce this empirical observation, we propose a simple multistate agent-based model of the voting behavior. In the proposed model, agents change the party they vote for either idiosyncratically or due to a linear recruitment mechanism. We use the model to reproduce the vote share distribution observed during the election of 1992. We discuss model extensions needed to reproduce the vote share distribution observed during the other elections.

#### 1. Introduction

While any individual vote is equally important to determine the outcome of an election, the probability for a single vote to decide the outcome is extremely small. As utility of casting a vote in this context seems to be small and as there is at least a minor associated cost, it seems that a rational choice would be simply not to vote. Yet this simplistic context may be further extended to provide sound reasoning for why people vote. Some argue that people vote to show support for the political system [1] or to avoid a risk of regret [2]; there might also be a social cost for abstention [3]. Some of the aforementioned works as well as numerous other earlier game-theoretic approaches, such as [4–6], had shown promise that game-theoretic voting models would soon provide rich and sophisticated explanation for the voting behavior. Yet further researches have shown that general game-theoretic models of the voting behavior with pure Nash equilibrium, and even mixed Nash equilibrium, might be impossible unless under certain specific conditions [7–9]. But people are rarely well informed and ideally rational, as they are not homo economicus nor are they Laplace’s demons [10–12].

The above context provides good reasoning to consider the modeling of the voting behavior from the perspective of psychology [13–20]. Usually these models appear to be very sophisticated at least if compared to the game-theoretic models. They are hard to implement numerically and, most importantly, it is usually hard to provide clear insights into the modeled phenomena. Also usually these models involve a large number of parameters, which may lead to overfitting the data or different parameter sets providing similar results. Notably, recently, a psychologically motivated model was successfully used to predict the Polish election of 2015 [17, 19].

Another possible approach to the modeling of the voting behavior has its roots in statistical physics. This perspective could be neatly summarized by quoting Boltzmann’s molecular chaos hypothesis [21]:

The molecules are like so many individuals, having the most various states of motion, and the properties of gases only remain unaltered because the number of these molecules which on the average have a given state of motion is constant.

During the last three decades, physicists have approached social and economic systems from this perspective, looking for universal laws and important statistical patterns, while proposing simple theoretical models to explain the empirical observations. This effort by numerous more or less prominent physicists became what is now known as sociophysics and econophysics [22–27]. The opinion dynamics, and the voting behavior as a proxy of opinion, is still one of the major topics in sociophysics [25–30].

This paper contributes to the understanding and description of the voting behavior from a couple of different points of view. First of all, Lithuania is a young democratic nation and the analysis of the Lithuanian parliamentary elections’ data sets seems interesting in the context of similar analyses carried out on the data sets gathered in the mature democratic nations, such as Brazil, England, Germany, France, Finland, Norway, or Switzerland [31–35]. In the political science and sociological literature, one would find numerous previous approaches to the Lithuanian parliamentary elections, for example, [36–40]. Yet most of these approaches had a quite different perspective: most of these papers discuss general electoral trends in the context of social, demographic, and economic changes. For this kind of discussion, highly aggregated (e.g., on a municipal district level) data sets prove to be sufficient, while in this paper we will consider the data on the smallest scale available (polling station level).

Another key contribution of this paper is a simple agent-based model, which is used to explain the statistical patterns uncovered during the empirical analysis. The proposed model is built upon a two-state herding model originally proposed by Kirman in [41]. In the recent years, the two-state herding model was quite frequently and rather successfully applied to reproduce the statistical patterns observed in the empirical data of the financial markets [42–48]. In this paper, we extend the two-state herding model to allow the agents to switch between more than two states. We discuss the similarity between the proposed model and the well-known Voter model [49–54].

Our approach is unique in a sense that we consider reproducing the parties’ vote share distribution observed in the Lithuanian parliamentary elections. In the previous literature, there was only a single attempt to model, and predict, popular vote (aggregated vote share) in the Lithuanian parliamentary elections using regression model (see [55]). Numerous previous sociophysics papers have mainly ignored the vote share distribution, likely due to the belief that the vote share distribution reflects electoral sensitivity to the policies promoted by the parties and less due to the endogenous interactions between the voters (a similar argument is given in [31]). To some extent, this belief is supported by game-theoretic models (see [5, 6]). Notably, there were a couple of sociophysics papers considering two-state agent-based models of the voting behavior, for example, voting for or against certain proposals in a referendum [29]. It is interesting to note that, recently, the binary models considered in [29] were used to construct a simple financial market model [56], while we start from the financial market model [47] and move towards the model of the voting behavior. While the vote share distribution was mainly ignored in the previous sociophysics papers, the other statistical patterns arising during the many different elections were considered for the empirical analysis and modeling. A branching process model was proposed to reproduce the individual candidate’s (in an open party list) vote share distribution [31]. A network model was used to explain how people decide whether to vote in the municipal elections [34]. A spatial diffusive model for the election turn-out was proposed in [33, 35]. One of more similar approaches was taken by [57], in which a generative model was proposed to reproduce the rank-size distribution of parties’ vote share. Another similar approach, taken by [54], considered the vote share distribution observed in the elections of House of Representatives in Japan. The latter approach [54] also used a mean-field Voter model to explain the empirical observations.

This paper is organized as follows. In Section 2, we discuss the Lithuanian parliamentary election system and carry out the empirical analysis. Next, in Section 3, we briefly introduce the two-state herding model and extend it to account for the multiple states. Afterwards, in Section 4, we apply the extended model to reproduce the statistical patterns uncovered during the empirical analysis. Finally, we end the paper with a discussion (see Section 5).

#### 2. Empirical Analysis of the Data from the Lithuanian Parliamentary Elections

Let us start by discussing the parliamentary voting system used in Lithuania. Lithuanian parliamentary elections are held every years. During every election, all of the parliamentary seats are distributed using two-tier voting system. Namely, seats in the parliament are taken by elected district representatives (there are electoral districts in total), while the other seats are distributed according to the popular vote among the parties that received more than of the popular vote. In other words, each individual voter is able to vote for a single candidate to represent his electoral district (the two-round voting system is used) and for an open party list (listing up to individuals from that list). Every electoral district has multiple polling stations (their number varies over the years), which further subdivide the electoral districts. Every eligible voter is assigned to a single polling station based on location of their residence. Each of the polling stations may have widely different number of the assigned voters—some of the smallest polling stations have as few as assigned voters, while the largest have up to assigned voters.

In this paper, we consider only votes cast for the open party lists in each of the local polling stations. We do not analyze ranking of the individuals on the party lists (similar analysis was carried out in, e.g., [31]), voting for the representative of electoral district (similar data was previously considered in, e.g., [54, 57]), nor turnout rates (modeling and analysis of which were previously considered in, e.g., [33, 35]). We ignore votes cast in the polling stations abroad or votes cast by post. In the analysis that follows, we consider only parties that were elected to the parliament (total vote share larger than ), while all other less successful parties were combined into a single party, which we have labeled as the “Other” party.

In this paper, we consider the three data sets from the Lithuanian parliamentary elections of 1992, 2008, and 2012. All of the original data sets were made publicly available by the Central Electoral Commission of the Republic of Lithuania (at https://www.rinkejopuslapis.lt/ataskaitu-formavimas). We have downloaded the original data sets from the website on August 31, 2016. During the preliminary phase of the empirical analysis, we have found some small inconsistencies within the original data. The original 1992 election data set had seven polling stations with incorrect total vote counts. We have identified three pairs of polling stations which were, most likely, swapped among themselves as the number of missing votes in one polling station matched the number of surplus votes in the other, while we have dealt with the remaining polling stations by simply adjusting the total vote count to match the sum of votes cast for each of the parties in that polling station. We have also found that data from (out of ) polling stations is missing (the data was filled with zeros) from the original 2008 election data set. We have not identified any issues with the original 2012 election data set. These minor inconsistencies would not impact the overall result of any of the considered elections nor the results reported in this section. We have made the modified data sets available online at https://github.com/akononovicius/lithuanian-parliamentary-election-data.

In the analysis that follows, we consider the parties’ vote share distribution across each polling station. The vote share, , is defined as total number of votes cast for the party divided by the total number of votes cast in that polling station:here index varies over the parties ( is the total number of parties participating in the election) and index varies over the polling stations. We consider the probability and rank-size distributions of across all of the polling stations during the same parliamentary election. The probability distribution is estimated using the standard probability density functions (abbr. PDFs). The rank-size distributions are often used if the data varies significantly in scale, for example, word occurrence frequency [58], earthquake magnitudes [59], city sizes [60], and cross country income distributions [61]. When using this technique, the original empirical data is sorted in descending order. Afterwards, the sorted data is plotted with the rank being the abscissa coordinate and the actual value being the ordinate coordinate. In our case, we sort the parties’ vote shares, , for each party separately to produce , for which is true. In the above, is the total number of polling stations, so that index represents the rank. Note that, in this representation, the same polling station may be ranked differently for different parties (namely, might be different for the same polling station for different ). Evidently, these two approaches, PDFs and rank-size distributions, are interrelated, but using both of them allows uncovering different statistical patterns.

##### 2.1. The Parliamentary Election of 1992

The parliamentary election of 1992 was held in local polling stations. parties competed in the parliamentary election, but only of them were able to obtain more than of popular vote. For the sake of simplicity, we will use the following abbreviations for these parties: SK, “SąjūdÂžio koalicija,” LSDP, “Lietuvos socialdemokratų partija,” LKDP, “Lietuvos KrikÂščionių demokratų partijos, Lietuvos politinių kalinių ir tremtinių sąjungos ir Lietuvos demokratų partijos jungtinis sąraÂšas,” and LDDP, “Lietuvos demokratin darbo partija.” We have combined the other parties to form the “Other” party (abbr. O) and considered the votes cast for the combined “Other” party alongside the votes cast for the main parties.

As you can see from Figures 1 and 2 and Table 1, all of the parties with a notable exception of the “Other” party are very well fitted by assuming that data is distributed according to the Beta distribution, PDF of which is given by The “Other” party stands out, because it includes “Lietuvos lenkų sąjunga” party (abbr. LLS; en. Association of Poles in Lithuania). The LLS party had heavily relied on the support of the ethnic minorities, which were spatially segregated. Namely, the representatives of ethnic minorities mostly live in larger cities and Vilnius County. The observed spatial segregation could easily cause the segregation observed in the voting data.