Evidence from Hungary

Strategic Voting, Mixed and Runoff Elections: Evidence from Hungary Daniel Prinz March 30, 2013 Abstract Iattempttoquantifystrategicvotingusingthemixed(proportional and plurality) dual ballot election system in Hungary. The main finding is that there is a moderate amount of desertion of third parties. The smaller the likelihood of a second round, and the closer the large parties are, the more pronounced the desertion, consistent with a hypothesis of strategic voting. IthankChishioFurukawa,BrianKnight,GáborSimonovitsandNeilThakralfortheircomments. 1

1 Introduction Whether people vote sincerely (for their most preferred candidate) or strategically (taking into account factors such as the plausibility of candidates) is an important question in political economy, with implications for the design of electoral rules and systems, as well as other policies. In an election with more than two candidates, voters who care about the policies that will be implemented after the elections face some incentives to vote for a candidate other than their favorite. However, whether these incentives actually make people vote strategically isanempiricalquestion.becausethereare competing incentives (people might derive consumption benefits from voting for their favorite candidate), information might be lacking (it is unclear who the top candidatesare) orpeoplemightnot care about strategy, it is far from obvious that strategic voting will actually occur. Nevertheless, some predictions have been made regarding the likely outcome of elections. One of these predictions, made by Duverger (1967) is that in a single ballot system, third-party candidates will be deserted, while a dual-ballot system is advantageous for third parties. Most studies on strategic voting are plagued by at least two important identification problems. The first and most basic problem of any study of real-world voting behavior is that data on individuallevel voting is unlikely to be available from any contemporary, functioning democratic country, due to the principle of secret ballot. Therefore, as discussed below, studies either rely on aggregate voting data or on surveys. Both aggregate data and surveys have limitations: aggregate data may obscure individual-level trends, while in surveys people do not necessarily report their true voting behavior. The second important identification problem is that situations where a behavior can clearly be called strategic voting, as opposed to sincere voting according to some preference relation, are not easy to come by. In this paper I use disaggregated (ballot station level) data on vote shares, and a situation where voters cast two votes at the same time, one of which is expected to be sincere and one that could either be sincere or strategic to try to identify strategic voting. To be clear, the situation that is used to try to understand strategic voting is a particular electoral 2

set-up, a mixed, dual ballot system. The Hungarian general elections offer an opportunity for identifying the presence of strategic voting, because they are both mixed and dual ballot: a portion of representatives is elected through a single-ballot proportional (PR) system, another portion is elected in a dual-ballot plurality system. It is in order to explain each of the terms used to characterize the Hungarian system of elections. Aproportionalsystemisoneunderwhichtheseatsreceivedbyapartyareproportionaltothe votes they receive. For example, if a party receives 27% of votes, they will receive roughly 27% of the seats. Naturally, the system cannot be completely proportional as fractions of seats cannot be given out. Apluralitysystemisoneunderwhichtheseat(inasingle-member district) or the seats (in a multi-member district) are received exclusively by the winner. For example, in the U.S. presidential elections, in the District of Columbia and 48 of the states, all electoral seats go to the candidate who gets the most votes. A single-ballot system is one with one round of voting, while in a dual-ballot system, there is a runoff. Typically, the top two candidates participate in the second round (e.g., French presidential elections), but in Hungary, the top three candidates qualify for the second ballot. The Hungarian elections mix the above elements in a particular way. Each voter has three votes: in the first round of the elections, they can vote for a single member district (SMD) candidate and a party list (PR), and if a second round is held (no candidate received more than 50% of the votes in the first round), they can vote for a SMD candidate that survived the first round. In the PR system, people have less of an incentive to desert their most preferred parties, while in the plurality system, these incentives are greater. Therefore, the difference in PR andsmdvotesreceivedbypartiescould indicate strategic voting. There are several reasons besides strategic voting that could lead to people voting for different parties with their votes: people might want to diversify their vote (strategic power sharing), like two parties equally or have different opinions abouttheindividualcandidateandthe party list of the same party. To make a credible claim about strategic voting, I will explore these 3

competing hypotheses as well. The main finding of this paper is that there is a moderate amount ofstrategicdesertionof third parties in a dual ballot system when a second round is not likely to be held. This desertion is more pronounced when a second round is less likely to happen and when a race is closer. These findings are robust to controls for various demographic characteristics of the electorate. Since overall strategic desertion appears to be moderate in magnitude, one mightconcludethatthedual-ballot system moderates strategic voting, consistent with Duverger s hypothesis. 2 Existing literature 2.1 Theoretical literature The issue of strategic voting and the analysis of the properties of various electoral rules and systems has a large theoretical literature. Duverger (1967) emphasizes the empirical regularity that a single ballot system is conducive to a two-party system, whereas a dual ballot system makes it possible for more than two candidates to have a positive number of supporters in equilibrium. Palfrey (1989) provides a formal mathematical discussion of the empirical regularity observed by Duverger. Under some regularity assumptions about the distribution of voter preferences, in the limit a potential third party will have zero votes. Myerson and Weber (1993) and Myerson (2002) compare the effect of different voting rules on the equilibrium outcomes of a candidate positioning game and conclude that plurality voting is not very restrictive with regards to the position of thewinnerrelativetothedistributionof voter preferences, which one might see as a problematic feature. Cox (1994) provides a theoretical extension of Duverger s Law to multimember districts: the multimember analogue of the idea that only the top two candidates have a positive number of votes is that in an M-seat district, M+1 candidates have nonzero support. Martinelli (2002) analyzes the information aggregation advantages of runoff elections: if the third party candidate is popular, runoff elections lead to higher expected payoffs. In particular, the first round of the elections can serve as a mechanism to learn about the preference distribution of the electorate. 4

Amorerecentstrandoftheliteratureonstrategicvotingandrunoffelectionscontestssomeofthe propositions from the preceding work. Myatt (2007) argues that because of the large amount of coordination required, strategic voting has a limited role. Furthermore, he shows that, under a qualified majority rule, controlling for the distance of the third party strategic voting incentives are decreasing in the marginality of the election - a counterintuitive result. Bouton (2012) characterizes the equilibria of runoff election systems, and argues that some difficulties may emerge in these systems as well. In particular, contrary to Duverger s Law, third candidates are deserted if one endogenizes the outcome of the second round and sincere voting equilibria might not exist. Bouton and Gratton (2012) show that even in a dual ballot system there are always incentives to desert the third party candidate and that the at most one equilibrium where more than two candidates receive votes requires some non-sincere voting. 2.2 Experimental literature Rietz (2008) surveys the early experimental literature on strategic coordination in three-way elections. He concludes that when the Condorcet loser problem arises (that is, in the case where a candidate that is not preferred by the majority and would lose in two-way electionsfacingeitheroftheothertwo could win), experimental subjects recognize the need for coordination. Whether this coordination can actually happen depends on the availability of signals. Bassi (2008) compares the behavior of subjects under different voting rules. She finds that under plurality voting, subjects are relatively sophisticated but not necessarily insincere, while in more complicated settings they are less sincere and less sophisticated. In addition, Duvergerian outcomes emerge as subjects become more experienced. Meffert and Gschwend (2007, 2008) investigate plurality and coalition voting games in the laboratory. They find relative sophistication and coordination succes and the use ofheuristicstosimplifydecisionmaking. Similarly, der Straeten et al. (2010) find that strategic voting operates in relatively simple setups in the laboratory (such as one-round elections), but in more complicated settings (such as two-round) elections subjects use simplifying heuristics. 5

2.3 Empirical literature The empirical literature on strategic voting can be divided into three categories: some papers use individual-level surveys to understand expectations and choices, another part of the literature relies on quasi-experiments, and finally, some recent papers estimate structuralmodelsfromaggregatedatasets. Blais et al. (2001) use survey evidence from Canada on voters expectationsaboutelectionoutcomes and their votes to argue that about 3% of voters cast strategic votes. DuchandPalmer(2002)report amuchhigheramount(13.6%)ofstrategicswitchingusinganational survey of Hungarian citizens. They argue that strategic voting is present in repsonse to wasted vote situations. Abramson et al. (2010) argue through cross-country comparison and data on voters intentions that strategic desertion is present not only in plurality but also in proportional systems. The idea is that voters use heuristics, rather than calculations, and with the potential influence of differentpartiesinmind,theydesertsmall parties in PR voting as well. Fujiwara (2011) uses the discontinuous assignment of singleanddualballotvotinginbraziltoar- gue that under single ballot voting there is strategic desertion. Based on a population cutoff, some municipalities are randomly assigned a single ballot system and some a double ballot system. The key observation is that the vote share of smaller parties is significantly smaller under the single ballot system, close to the point of discontiunity. Spenkuch (2012a) uses the death of a candidate and a flaw in the German electoral system to demonstrate that voters canbeconvincedtostrategicallydesert their most preferred party. Kiss (2012) uses Hungarian election data and argues that the correlation between the observed plausibility of the third party candidate from the first round and the desertion of the third party candidates in the second round is indication of strategic voting. The weakness of this paper is that it can only deal with the 1990 to 1998 elections because in the later elections, in the vast majority of cases there were only two candidates in the second round. In turn, the number of candidates with a positive support in the second round already tells us something about strategic sophistication. 6

Degan and Merlo (2009) depart from the decision theoretic and gametheoreticapproachusedin most of the literature and provide a theoretical discussion of the circumstances under which sincere voting can be falsified. Their method is based on an application of separation results to the ideological space. Building on this, Merlo and de Paula (2010) provide a nonparametric identification and estimation strategy for the distribution of ideological preferences from aggregate data. Kawai and Watanabe (2012) take a structural approach to the problem of estimating strategic voting: under certain distributional and other assumptions, the extent of strategic voting is partially identified from aggregate data. Independently from this paper, Spenkuch (2012b) follows a similar approach. Using German data, proportional votes are used as a reflection of underlying preferences and the deviation of proportion of plurality votes cast for candidates who are perceived to be non-contenders is interpreted as strategic voting. While the approach taken here is similar, there are several notable differences in both the electoral setting and the findings. German elections have a single round and there are more than two parties that are able to secure single-member district seats in that round. In other words, in the Hungarian elections it is always clear who the contenders are, in the German elections it is less clear. Also, the presence of strategic desertion of non-contendersismuchlarger(almostonethird) thanin the Hungarian data used for this paper. This is most likely because in the Hungarian case strategic considerations are moderated by the dual-ballot system and the compensation seats. I also find that the closeness has a significant and positive impact on desertion. The literature on mixed electoral systems is smaller, but some work is related to this present paper. Benoit (2001) analyzes both election and survey data from the first three elections (1990, 1994, 1998) to conclude that split voting is small and not widespread in Hungarian elections, although it grows over time. It also provides a summary of the different kinds of strategic considerations specific to the Hungarian case. My paper uses data from different elections and imposes more structure in the sense that the incentives of the supporters of specific parties will be considered. Karp et al. (2002) 7

study data from the New Zealand elections and argue that ticket-splitting patterns are consistent with voters deserting candidates not perceived to be viable. Gschwend (2007) uses survey data from German elections to provide evidence on different types of strategic voting. The weakness of this and other survey studies is the small sample size and that there might well be a large gap between actual votes and survey responses. The main strength and novel element of my paper relative to most of the empirical literature is that I am using a setting where the same voters are observed in two different strategic settings to measure strategic voting, rather than different voters in different settings. Relative to the literature in political science that uses survey data, I am using much larger datasets of true voting decision, rather than reported preferences and beliefs. Furthermore, by linking electoral and demographic data, I am able to control for a variety of observable characteristics of the electorate. Compared to the literature that also exploits mixed elections, my use of the second round asaproxyforcompetitiveness, aswell as the datasets used are new elements. 3 The Hungarian political context 3.1 Elections Since 1990, the Hungarian general elections have been held in amixed, dual-ballotsystem. Thereare 386 seats in the Parliament: 176 are allocated to the winners of the SMD races, 152 to party lists in aproportionalmannerand58for compensation (forvotesthat were received by losing candidates). Korosenyi (1998) and Korosenyi et al. (2007) give detailed descriptions of the electoral system and the various rules. Schiemann (2001) analyzes the origins of the system as a result of bargaining between the opposition and the ruling communists during the 1989 negoations. In the SMD races, a second round is held if no candidate gets an absolute majority in the first round; the top three candidates and candidates with at least 15% of the vote qualify for the second round. 8

3.2 Parties In this paper, I use data from the general elections of 2002 and 2006,astheyhadthesamefour parliamentary parties participate, and are broadly similar. These four parties are 1. the Hungarian Socialist Party (MSZP), 2. the Alliance of Free Democrats (SZDSZ), 3. the Hungarian Democratic Forum (MDF), 4. Fidesz. Ideologically, the MSZP and the SZDSZ are left-wing, with the SZDSZbeingmoreliberalonsocial issues, while the MDF and Fidesz are right-wing, conservative. A simplified ideological ordering of the four parties from left to right would be MSZP, SZDSZ, MDF, Fidesz. On the European level, MSZP s representatives sit in the Progressive Alliance of Socialists and Democrats group in the European Parliament, while in this period the SZDSZ s representatives were sitting in the Alliance of Liberals and Democrats for Europe group, and both the MDF s and Fidesz s representatives were in the European People s Party group. Notably, these pairings describe the typical coalitions of these parties: the SZDSZ and the MSZP governed in coalition for ten years (1994-1998, 2002-2008) and the MDF and Fidesz governed in coalition for four years (1998-2002). Also, in most cases, whenever more than one party from the same side qualifies for the second round, one of them drops out and endorses the other: there were only 25 three-candidate races in the second round of the elections in 2006. In several cases, parties from the same side field joint candidates, and in 2002 Fidesz and MDF ran on a joint list with all candidates joint. To further substantiate the idea that the electorate perceives these parties in pairs (MSZP-SZDSZ and Fidesz-MDF), I report data from a nationally representative survey on the perception of the parties and their ideologies in Tables 1 to 3 1. 1 Sources: Voter symphaties and perceived ideologies: TÁRKI Joint Research Center TDATA-G34: DKMKA Hungarian Election Study 2003 master file (N=3016). data sheet. Version: 2011-03-18; Self-reported ideologies: TÁRKI Joint Research Center TDATA-H46: The political attitudes and the method of the campaign of the candidates and the elected politician after the 2010 parliamentary elections in Hungary. data sheet. Version: 2011-04-18. 9

Table 1: Correlation of party sympathies (survey of voters, N=3016) MSZP SZDSZ MDF Fidesz MSZP 1 SZDSZ 0.6771 1 MDF 0.1088 0.3924 1 Fidesz -0.3117-0.0527 0.5136 1 Table 2: Perceived ideologies (1=Left 10=Right) (survey of voters) Variable Mean Std. Dev. N MSZP perceived ideology 2.733 1.849 1125 SZDSZ perceived ideology 4.132 1.961 1125 MDF perceived ideology 7.020 1.957 1124 Fidesz perceived ideology 8.288 1.834 1125 Table 3: Self-reported ideologies (survey of candidates andrepresentatives) Variable Mean Std. Dev. N MSZP self-reported ideology 1.529412 1.06495 51 Fidesz self-reported ideology 7.419753 1.810008 162 10

4 Data 4.1 Election data There are 176 single-member districts and 10910 precincts, so on average each single-member district has 62 precincts. Precincts are only units of observations. Being assigned to a precinct in Hungary means that a voter is assigned to a voting location, but precincts are not related to any political or social institutions. Data from Hungarian general elections areavailableattheprecinctlevel. Table 4reportssummarystatisticsforvariablesonparticipation. Table 5 reports summary statistics on the results of the four significant, parliamentary parties discussed in the previous section. The main trends of the elections are visible in Table 5. The two large parties, MSZP and Fidesz are very close to each other and to 50%. Indeed, if one adds the voteshares of the two parties on each side in the first round, the sum is barely under 50%. That is, if the supporters of the small parties decided to support the large parties on their own sides, the elections would be decided in the first round between two parties (a Duvergerian outcome). There are several reasons why they might decide not to make this switch in the first round in general. As mentioned before, theirfavoritepartiesreceiveseatsfrom the compensation list and expressive voting can play a role too. However, in a large number of cases (37% of all SMDs) a second round is not held. 11

Table 4: Summary statistics: Precincts Variable Mean Std. Dev. N Nofregisteredvotersbeforethe1stroundin2006 732.393 276.282 10910 Nofvotersaddedtoregisteronelectiondayin1strndin2006 4.363 7.001 10910 Nofvotersintheregistersatembassiesin1strndin2006 0.744 9.503 10910 Nofeligiblevotersin1stroundin2006 737.5 278.322 10910 Nofcitizenswhoweredeniedtheballotin1stroundin2006 0.839 2.138 10910 Nofballotsreceivedfromembassiesin1stroundin2006 0.612 8.042 10910 Nwhoturnedoutin1stroundin2006 500.234 208.423 10910 NofballotsintheboxinSMDin1stroundin2006 500.007 208.283 10910 NofmissingballotsinSMDin1stroundin2006-0.227 0.832 10910 NofinvalidvotesinSMDin1stroundin2006 4.711 4.001 10910 NofvalidvotesinSMDin1stroundin2006 495.296 207.159 10910 Nofregisteredvoterspriorto2ndroundin2006 742.103 269.682 6775 Nofvotersaddedtoregisteronelectiondayin2ndroundin2006 3.736 5.003 6775 Nofvotersintheregistersatembassiesin2ndrndin2006 0.877 11.282 6775 Nofeligiblevotersin2ndroundin2006 746.716 271.545 6775 Nofcitizenswhoweredeniedtheballotin2ndroundin2006 0.408 1.294 6775 Nofballotsreceivedfromembassiesin2ndroundin2006 0.63 8.487 6775 Nwhoturnedoutin2ndroundin2006 480.774 191.823 6775 Nofballotsintheboxin2ndroundin2006 480.7 191.776 6775 Nofmissingballotsin2ndroundin2006-0.074 0.42 6775 Nofinvalidvotesin2ndroundin2006 2.508 2.15 6775 Nofvalidvotesin2ndroundin2006 478.192 191.207 6775 Nofballotsintheboxin1stroundlistvotingin2006 500.032 208.294 10910 Nofmissingballotsin1stroundlistvotingin2006-0.202 0.795 10910 Nofinvalidvotesin1stroundlistvotingin2006 4.336 3.86 10910 Nofvalidvotesin1stroundlistvotingin2006 495.697 207.355 10910 Table 5: Summary statistics: Results 2006 Variable Mean Std. Dev. N MSZP PR 0.429 0.109 9064 MSZP SMD 0.424 0.119 9064 MSZP Second Round 0.492 0.141 5706 Fidesz PR 0.433 0.117 9064 Fidesz SMD 0.435 0.12 9064 Fidesz Second Round 0.484 0.108 5706 SZDSZ PR 0.057 0.041 9064 SZDSZ SMD 0.059 0.053 9064 SZDSZ Second Round 0.012 0.083 5706 MDF PR 0.049 0.021 9064 MDF SMD 0.049 0.037 9064 MDF Second Round 0.006 0.015 5706

4.2 Demographic data Demographic data used for this paper were collected during the 2001 census. This is the most recent census for which data is available, and I am using data at the lowest level of aggregation at which data can be accessed. This is the level of counting areas. Counting areas in Hungary have on average 200 individuals, so their average size is between the average sizes of US census blocks and block groups. I present summary statistics for all available demographic variables in Tables 13 to 18 in Appendix A. 4.3 Other data In order to quantitatively substantiate the ideological positions of parties, in Section 3.2, I discussed survey results on correlations between preferences for different parties. In addition, I will make use of asurveyofcandidatesandmembersofparliamentontheirpolitical opinions and campaign strategies. This will help us better understand the ideological leaning of parties, as well as present evidence on the plausibility of a possible competing hypothesis concerning differential campaign strategies. To establish the alignment of MPs and candidates with their parties, I rely on roll call voting data from the Hungarian Parliament. Each four year term has approximately 8000 votes and for each of these, the vote of each member is recorded. Therefore this data can be usedtoempiricallyasseswhether individual politicians are indeed closely aligned with their parties as I have claimed. 4.4 A note on levels of analysis Each counting area falls within a precinct. Therefore, for the purposes of this paper, the data available at the counting area level is collapsed to the precinct level. Althoughvotingdataisaggregatedatthe precinct level, voting outcomes apply to the single-member district. Therefore, in some of the analyses variables are included at the SMD level. Throughout this paper, I refer to SMD races and SMD level variables, which are two different things: an SMD race, isaracebetweenpartiesfortheseatina particular single-member district and an SMD level variable, isavariabletakenatthesmdlevel.for example, one can talk about the proportional (PR) result of a party at the SMD level. Throughout the paper, analyses are carried out at the precinct level to minimize the potential for ecological problems. 13

5 Strategic incentives: A simple model Consider electoral competition between three parties in one-dimensional space. Suppose there are three parties with fixed ideologies/positions/policies: two large ones, L 1 and L 2 and a small one S. By this, we mean that there is some exogeneous information (e.g., surverys) on the approximate level of support for each party. This information suggests that only L 1 and L 2 can win the election. Voters can be divided into three categories based on their preference rankings: those with L 1 S L 2,those with S L 1 L 2 and those whose most preferred alternative is L 2.Thatis,wecouldsaythatL 1 and S are on the same side: one side is composed of the voters who prefer L 2 over the other parties, and the other side is composed of voters who prefer L 1 and S over L 2. Voters are characterized by their own position, x i and the utility e i they derive from voting for their most preferred party (expressive voting). The key object is e i,asiwilldiscussbelow.ithassomepopulationdistributionwithcdff. The important question is what votes supporters of S cast. Do they vote expressively, in the sense of Fiorina (1976), for S or they vote strategically for L 1? If they have a quadratic loss function, they derive the following utilities, where u i (E V ) denotes the utility voter i derives from having E elected when she voted for V : u i (L 1 S) = (S L 1 ) 2 + e i u i (L 1 L 1 ) = (S L 1 ) 2 u i (L 2 S) = (S L 2 ) 2 + e i u i (L 2 L 1 ) = (S L 2 ) 2. In a game theoretic model, we would be interested in an equilibrium strategy. Here however, we will posit that voters have beliefs over the probability of each party winning depending on their vote. Essentially, voters believe that their vote matters. Suppose that the following beliefs characterize 14

voters, where Pr(E V ) denotes the belief that party E will be elected if she votes V : Pr(L 1 S) = π Pr(L 1 L 1 ) = ρ Pr(L 2 S) = 1 π Pr(L 2 L 1 ) = 1 ρ, where ρ>π. From these, we can calculate the expected utility for a supporter of S to vote from voting for L 1 and from voting for S: E [u i voting for S] = π (S L 1 ) 2 (1 π)(s L 2 ) 2 + e i E [u i voting for L 1 ] = ρ (S L 1 ) 2 (1 ρ)(s L 2 ) 2. Thus she will vote for L 1,whenever E [u i voting for L 1 ] >E[u i voting for S]. Characterizing the set of voters in terms of their e i,utilityderivedfromexpressivevoting,i will vote for L 1,whenever t (π ρ)(s L 1 ) 2 +(ρ π)(s L 2 ) 2 >e i. As e i has some population distribution F,thefollowingcomparativestaticshold: 1. The bigger difference there is in the perceived probability ofl 1 winning depending on which party a voter chooses, the more supporters of S vote for L 1 : t (ρ π) =(S L 2) 2 (S L 1 ) 2 > 0. 2. The bigger the distance between the platforms of L 1 and S, thefewersupportersofs vote for 15

L 1 : t (S L 1 ) 2 = π ρ<0. 3. The bigger the distance between the platforms of L 2 and S, themoresupportersofs vote for L 1 : t (S L 2 ) 2 = ρ π>0. 6 Empirical strategy and results My empirical strategy consists of several parts. First I define a measure of desertion of small parties as the difference between their PR and SMD votes. This measure represents a lower bound on people who vote for different parties with their two votes, as movement from pary X to party Y is cancelled by movement from party Y to party X. The key identifying assumption is that voters cast their proportional votes sincerely, while they might cast their SMD votes either sincerely or strategically. Using this measure, I establish that desertion of small parties (defined as the difference between their SMD and PR votes) occurs when a second round is not held. Second, I examine whether the likelihood of a second round being held influences the level of desertion. Sincethepresenceofasecondroundis obviously endogenous to desertion (if desertion occurs in the first round, then there is a mechanically lower chance of a second round being held), I propose three measures of this likelihood that do not depend on first-round desertion: (1) the PR votes of the major parties, (2) the presence of a second round in the previous election, (3) the PR votes of the major parties in the previous election. Second, Iexaminetheeffectoftheclosenessoftheelectionandthestrengths of various parties (own-side and opposing) on the level of desertion. To avoid endogeneity in the case of closeness, I use the closeness of the second round as a proxy. Third, I demonstrate the robustness of results to the introduction of controls. 16

6.1 Desertion of small parties The simplest way to establish the desertion of small parties is to compare the PR and SMD votes of these parties in the first round, as it is done in Tables 6-8. Table 6: Summary statistics: Results of small parties 2006 Variable Mean Std. Dev. MDF PR 0.049 0.021 MDF SMD 0.049 0.037 SZDSZ PR 0.057 0.041 SZDSZ SMD 0.059 0.053 N 9064 Table 7: Summary statistics: Results of small parties 2006 - Second round held Variable Mean Std. Dev. MDF PR 0.049 0.021 MDF SMD 0.051 0.039 SZDSZ PR 0.061 0.045 SZDSZ SMD 0.066 0.059 N 5706 Table 8: Summary statistics: Results of small parties 2006 - Second round not held Variable Mean Std. Dev. MDF PR 0.049 0.021 MDF SMD 0.047 0.033 SZDSZ PR 0.051 0.031 SZDSZ SMD 0.047 0.036 N 3358 17

On average, both small parties, SZDSZ and MDF lose some (about 8%and4%)oftheirsupportin the SMD races compared to the PR race in the cases when a second round is not held. In fact, when asecondroundisheld,theyhavemoresmdvotesthanprvotes. Whether a second round is held obviously depends on desertion and addition of voters. To explain simply: it would be erroneous to claim that SZDSZ has more votes for SMD candidates than in PR when a second round is held because asecondroundisheld;infactitisjustaslikelythatasecondroundisheldbecauseszdszhas relatively high support, and therefore the major parties cannot have an absolute majority in the first round. That is, the findings in Tables 6-8 do not in themselves show that voters desert these small parties because they anticipate that the election will be called in the first round. If the small party supporters vote for one of the large parties in the first round, thenasecondroundislesslikely,asthis in effect means a two-party race, which will end in the first round. Therefore, so far I am not making aclaimaboutcausality. Inordertodoso,Ifirstwritethecontents of Tables 6-8 as a regression equation. Define a variable called desertion as desertion= (SZDSZ PR SZDSZ SMD) +(MDF PR-MDF SMD). This variable then measures the difference in the PR and SMD vote shares of small parties, or in other words, the proportion of people who desert them. The equation desertion i = α + βsecond round 2006 i + ε i (1) where second round is an indicator for a second round being held can then be estimated using OLS. Results with robust standard errors are provided in Table 9. As discussed before, the results from the OLS estimation of Equation (1) are not meant to have a causal interpretation. Table 9 simply shows that there is less desertion when a second round occurs, and the estimation of a regression equation is meant to facilitate comparison with the estimates that follow for which I claim causality. First, I modify Equation (1) to include the presence of a second 18

round in the preceding election: desertion i = α + βsecond round 2002 i + ε i. (2) An estimation of Equation (2) with OLS (results provided in Table 9) show a similar pattern as Equation (1). Second, rather than considering the binary variable second round, Iuseusevariableswhichmeasure how close the election is to having a second round: votesharesofthelargeparties. SincetheSMD voteshares of the large parties depend mechanically on the SMD voteshares of the small parties, I use their PR voteshares and also, in another equation, their PR voteshares from the preceding elections. Define variables called strong as strong 2006 =max{pr Fidesz 2006, PR MSZP 2006}, strong 2002 =max{pr Fidesz 2002, PR MSZP 2002}. IestimatethefollowingequationsusingOLSanddisplaytheresults in Table 9: desertion i = α + βstrong 2006 i + ε i, (3) desertion i = α + βstrong 2002 i + ε i. (4) The results show that the stronger the large parties are, and therefore the less likely it is that a second round will be held, the more voters desert small parties. 19

Table 9: Desertion of small parties and the presence/likelihood of a second round (1) (2) (3) (4) desertion desertion desertion desertion Second round held in SMD in 2006-0.00898 (-12.78) Second round held in SMD in 2002-0.00891 (-11.45) Result of the stronger of the two large parties 2006 0.0206 (2.43) Result of the stronger of the two large parties 2002 0.0215 (2.91) Constant 0.00370 0.00448-0.0120-0.0123 (7.59) (7.01) (-2.86) (-3.37) Observations 9064 9064 9064 9064 t statistics in parentheses p<0.05, p<0.01, p<0.001 In Tables 10 and 11 I show that these results are robust to the inclusion of aggregate demographic controls, such as average age and the mean level of urbanization. In the appendix, I also include tables where the coefficients are estimated with the inclusion of the full set of demographic controls. The results so far suggest that candidates of the smaller parties are deserted by voters, and the level of desertion depends on whether a second round is present or likely to be present. If a second round is held, there is less desertion, and a similar pattern is observed when looking at the likelihood of a second round. The intuitive interpretation is that if a second round is held, there is no (or less) reason to desert small parties in the first round. Quantitavely, if a second round is present in either of the two elections,desertionisdecreasedoneeigth to one quarter of a standard deviation. Taking the likelihood (strengthofthestrongerlargeparty) variable, we have that changing the strength of the stronger of the two parties from its lowest level of 37% to 62% (that is, changing the likelihood of a second round from almost certain to very unlikely) is associated with an increase in desertion by 0.5 to 1.5%. 20

Table 10: Desertion of small parties and the presence/likelihood of a second round - aggregate demographic controls (1) (2) (3) (4) (5) (6) desertion desertion desertion desertion desertion desertion Second round 2006-0.00898-0.00864-0.00681 (-12.78) (-11.89) (-8.85) Second round 2002-0.00891-0.00736-0.00468 (-11.45) (-8.70) (-5.42) (mean) urban 0.000636-0.00699 0.000756-0.00715 (0.26) (-2.93) (0.31) (-2.97) (mean) project -0.000405-0.00573-0.0000584-0.00571 (-0.16) (-2.25) (-0.02) (-2.22) (mean) residential -0.000691-0.0180-0.00122-0.0183 (-0.10) (-2.75) (-0.18) (-2.80) (mean) suburban -0.00348-0.00664-0.00360-0.00694 (-1.50) (-2.90) (-1.55) (-3.02) (mean) rural 0.00550 0.000142 0.00483-0.000366 (2.57) (0.06) (2.23) (-0.16) (mean) age 0.000133 0.000140 0.000141 0.000139 (0.83) (0.85) (0.88) (0.85) (mean) ltm -0.000211-0.0000471-0.000175-0.0000266 (-2.44) (-0.50) (-1.99) (-0.28) (mean) gs 0.0000679 0.00000489 0.0000660 0.00000726 (1.66) (0.12) (1.61) (0.17) (mean) vs -0.000222-0.000119-0.000233-0.000132 (-4.15) (-2.04) (-4.33) (-2.27) (mean) hs 0.0000936 0.0000573 0.0000952 0.0000603 (1.81) (1.10) (1.85) (1.16) (mean) coll 0.000383 0.000329 0.000367 0.000319 (6.05) (5.46) (5.84) (5.32) (mean) unemployed -0.0166 0.00951-0.0111 0.00843 (-1.10) (0.62) (-0.73) (0.55) (mean) retired -0.00765-0.00695-0.00799-0.00750 (-0.87) (-0.78) (-0.91) (-0.84) r_prop 0.0308 0.0123 0.0309 0.0108 (3.31) (1.23) (3.30) (1.08) Constant 0.00370-0.00427 0.00764 0.00448-0.00451 0.00721 (7.59) (-0.67) (1.12) (7.01) (-0.71) (1.06) County fixed effects No No Yes No No Yes Observations 9064 8583 8583 9064 8583 8583 t statistics in parentheses p<0.05, p<0.01, p<0.001

Table 11: Desertion of small parties and the presence/likelihood of a second round - aggregate demographic controls (1) (2) (3) (4) (5) (6) desertion desertion desertion desertion desertion desertion Strong 2006 0.0206 0.0592 0.0454 (2.43) (6.68) (4.75) Strong 2002 0.0215 0.0480 0.0304 (2.91) (6.38) (3.50) (mean) urban 0.00107-0.00741 0.000939-0.00730 (0.43) (-3.08) (0.38) (-3.03) (mean) project 0.000644-0.00543 0.000827-0.00521 (0.25) (-2.11) (0.32) (-2.02) (mean) residential 0.00164-0.0178 0.00161-0.0175 (0.24) (-2.71) (0.24) (-2.65) (mean) suburban -0.00347-0.00695-0.00344-0.00683 (-1.48) (-3.02) (-1.47) (-2.97) (mean) rural 0.00497-0.000344 0.00490-0.000295 (2.30) (-0.15) (2.25) (-0.13) (mean) age 0.000154 0.000150 0.000159 0.000148 (0.95) (0.92) (0.99) (0.90) (mean) ltm -0.000216-0.0000435-0.000198-0.0000384 (-2.52) (-0.46) (-2.29) (-0.41) (mean) gs 0.0000772 0.0000111 0.0000708 0.00000780 (1.86) (0.26) (1.72) (0.18) (mean) vs -0.000248-0.000140-0.000247-0.000137 (-4.56) (-2.39) (-4.56) (-2.34) (mean) hs 0.0000879 0.0000620 0.0000958 0.0000617 (1.69) (1.19) (1.85) (1.19) (mean) coll 0.000403 0.000335 0.000391 0.000326 (6.27) (5.56) (6.10) (5.39) (mean) unemployed -0.0209 0.00752-0.0150 0.00793 (-1.37) (0.49) (-1.00) (0.52) (mean) retired -0.00902-0.00768-0.00833-0.00739 (-1.02) (-0.86) (-0.94) (-0.83) r_prop 0.0286 0.0112 0.0302 0.0109 (3.08) (1.13) (3.25) (1.10) Constant -0.0120-0.0387-0.0181-0.0123-0.0336-0.0106 (-2.86) (-5.18) (-2.12) (-3.37) (-4.65) (-1.30) County fixed effects No No Yes No No Yes Observations 9064 8583 8583 9064 8583 8583 t statistics in parentheses p<0.05, p<0.01, p<0.001

6.2 Marginality of the race Having established that small parties are indeed deserted by voterswhenasecondroundisnotheld and the level of desertion increases as the perceived likelihood of a second round declines, I now turn to the effect of the analysis of the (perceived) marginality/closeness of the race. One can define a distance variable as distance = MSZP -Fidesz and estimate the equation desertion i = α + βdistance i + ε i. (5) The strategy used here is to use second round voteshares as they are a relatively clean proxy for expected closeness. The idea is that if there is a second round, which in practice has two contenders, voting is free of strategic incentives, and voters will vote for their most preferred party. As only the two major parties take part in these races, this is a proxy for how close they are. The weakness of this method is that the same-year version of this variable can only beusedwhentherewasindeedasecond round, and even the version that uses the previous election does not apply to all SMDs. Nevertheless, IestimateEquation(5)withthesecondroundcloseness(in2002 and 2006) as a proxy for expected closeness and report results in Table 12. The results, namely that the smaller the distance is between the major parties, the more desertion happens are consistent with a hypothesis of strategic desertion. Quantitatively, changing the distance between the large parties from the smallest (effectively 0) to thelargest(around35%)isassociated with a 1.5 to 2 per cent decrease in desertion. 23

Table 12: Desertion of small parties and closeness (1) (2) (3) (4) (5) (6) desertion desertion desertion desertion desertion desertion distance -0.0467-0.0484-0.0631 distance -0.0443-0.0524-0.171 (-6.82) (-7.53) (-24.41) (-9.45) (-9.86) (-10.42) (mean) urban -0.0000973-0.000542 0.00669 0.0000575 (-0.03) (-0.17) (2.28) (0.02) (mean) project -0.00395-0.00616 0.000732-0.00507 (-1.02) (-1.74) (0.24) (-1.64) (mean) residential -0.000510-0.0150 0.00333-0.0152 (-0.05) (-1.50) (0.37) (-1.73) (mean) suburban -0.00538-0.000400-0.00420-0.00603 (-1.60) (-0.13) (-1.54) (-2.23) (mean) rural 0.00456 0.00519 0.00300-0.00143 (1.43) (1.69) (1.14) (-0.52) (mean) age 0.000293-0.0000442 0.0000272-0.0000291 (1.29) (-0.19) (0.13) (-0.14) (mean) ltm -0.000278-0.0000840-0.0000396-0.0000209 (-2.36) (-0.72) (-0.44) (-0.22) (mean) gs 0.000153-0.0000487 0.000104 0.0000154 (2.69) (-0.88) (2.12) (0.32) (mean) vs -0.000182-0.0000142-0.000209-0.0000192 (-2.54) (-0.19) (-3.23) (-0.29) (mean) hs -0.00000743-0.0000641 0.00000190-0.0000693 (-0.11) (-0.96) (0.03) (-1.18) (mean) coll 0.000523 0.000230 0.000402 0.000322 (6.30) (3.01) (5.38) (4.60) (mean) unemployed -0.0158 0.0276-0.00177 0.0282 (-0.78) (1.43) (-0.11) (1.64) (mean) retired -0.00845 0.00716-0.000697 0.00812 (-0.68) (0.59) (-0.06) (0.71) r_prop 0.0330 0.00657 0.0176 0.00634 (2.74) (0.55) (1.89) (0.67) Constant -0.000727-0.0155 0.0383 0.00211-0.00345 0.0171 (-0.93) (-1.74) (4.09) (3.03) (-0.44) (2.04) County fixed effects No No Yes No No Yes Observations 5706 5369 5369 6540 6131 6131 t statistics in parentheses p<0.05, p<0.01, p<0.001

7 Discussion: Assumptions and competing hypotheses For the difference between PR and SMD votes to measure strategic voting, I had to make several assumptions. If these assumptions do not hold up, there are competing hypotheses that could explain the observed pattern of voteshares. In this section, I will discuss some of these hypotheses and their plausibility. In general, these hypotheses seem weak because they do not explain the systematic patterns observed. That is, for the competing hypotheses to explain the observed patterns, they would have to have systematic trends, such as small party candidates being weaker overall than big party candidates. Recall that the key assumption was that proportional votes are uncontaminated by strategic concerns. This might not be an entirely true as due to the possiblity that asmallpartywillnotqualifyforthe Parliament, voters might also consider not voting for their proportional list. Relaxing the assumption to say that we only need to assume that proportional voting does not have any strategic incentives that are not also present for SMD voting is sufficient for the results to hold up in the sense that we would be observing a strategic component of the vote. Besides describing the relationships between parties, it is alsoimportanttoexploretheinternaldynamics of parties. One of the primary concerns about the identification strategy used in this paper is the possible differences between individual candidates and their parties. In fact, in the Hungarian political context (unlike for example in the United States) this concern turns out to be not very important. The reason for this is the close alignment of candidates andrepresentativesofpartieswiththe central party line. This is supported by both anecdotal evidence and an analysis of data from votes in the Parliament. On the anecdotal side, typically all candidates of a party campaign with the same basic posters, and the party leaders (who are usually the candidates for prime minister) appear along with them on these posters. Another piece of anecdotal evidence is that before the 2010 elections, Viktor Orbán, chairman of Fidesz and the current prime minister met with each one of his parties 176 candidates at his house to vet them before the elections. Also interestingly, at each vote in the Parliament (they are done through an electronic system) party leaders shout out their party s vote. One can look at voteshares in parliamentary votes to see that indeed MPs vote in party blocks. 25

Unfortunately name-by-name roll-call data is not available atthemoment. However,onecanshowa distribution of the number of yea votes for each term, 1998-2002, 2002-2006, and 2006-2010. For each term, by far the most common voteshares are around the number of MPs in the governing coalition. They are always slightly below those, because MPs are frequently not present. This suggests that MPs indeed follow party lines when voting, meaning that we shouldbelessconcernedaboutthepossible differences between individual candidates and their parties. When a voter votes for a candidate fielded by a party it is a safe bet that if the candidate is elected, she will vote together with her fellow MPs from her party. 2 2 When asked about whether a representative should vote according to the party line or her own preferences when the two conflict, 66% of representatives and candidates say that they should vote according to the party line. TÁRKI Joint Research Center TDATA-H46: The political attitudes and the method of the campaign of the candidates and the elected politician after the 2010 parliamentary elections in Hungary. data sheet. Version: 2011-04-18. 26

Another potential competing hypothesis is that parties might have differing campaign strategies and they might also differ by race. For example, desertion might be higher in close races because of more campaign activity. This hypothesis is hard to asses because of data limitations on campaigning. However, it is hard to see what trends in campaign strategies could be causing the observed differences between PR and SMD votes. 27

Finally, theoretically turnout might differ between different races, depending for example on expected closeness. As far as it can be seen from the data, these differences do not have substantial impacts. 8 Conclusion In this paper present some evidence there is a moderate amount ofticket-splittingamongsmall-party supporters when a second round is not likely to happen in Hungary s dual-ballot system. Small party supporters are more likely to desert their party when a second roundislesslikelyandwhentheelection is closer, consistent with strategic voting. The overall small magnitude of desertion is consistent with Duverger s hypothesis about the effect of a dual-ballot election, especially in light of the fact that in the second round, parties and voters do end up coordinating suchthatonlytwopartiesreceive votes. One caveat about the findings of this paper is that we should be careful with generalizing them to other contexts. In particular, the results are obtained using the specific characteristics and institutional set-up of Hungarian general elections, and it isunclearwhethervotersoperatesimilarly in other countries, particularly ones with more mature democracies. Second, even within Hungary, the results are obtained under a specific arrangement of the four parties, so as this arrangement changes (as it has: after 2010 elections, there SZDSZ and MDF were not in the Parliament anymore and there were two other parties instead; in 2010 Fidesz had 67% of the seats), the findings might not hold up. 28

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