On the Extent of Strategic Voting

On the Extent of Strategic Voting Abstract Social scientists have long speculated about individuals’ tendencies to manipulate elections by misrepresenting their preferences. The fact that preference orderings are generally unobserved, however, has made it very dicult to document strategic behavior empirically. Exploiting the incentive structure of Germany’s voting system to solve the fundamental identification problem, this paper estimates the extent of strategic voting in large, real-world elections. Evidence from reduced form as well as structural methods indicates that almost one third of voters abandons their most preferred candidate if she is not in contention for victory. As predicted by theory, tactical behavior has a non-trivial impact on individual races. Yet, as one aggregates across districts, these set each other, resulting in ects on the overall distribution of seats. distortions considerably 1 partially more modest 1. Introduction Democracy is rooted in the conviction that collective choices should be based on the preferences of all members of society. To provide citizens with an opportunity to participate in the decision making process, almost all democratic states rely on elections. Yet, as a mechanism for eliciting and aggregating preferences, elections are known to be flawed (Arrow 1951). Among other shortcomings, practically every reasonable voting system fails to be strategy-proof (Gibbard 1973; Satterthwaite 1975). As a result, strategic voters may be able to manipulate the outcome of an election by misrepresenting their true preferences. Although social scientists have long speculated about individuals’ proclivities to cast tactical ballots (e.g., Black 1948; Downs 1957; Duverger 1954; Farquharson 1969; Sen 1970), and despite a plethora of anecdotal evidence, it has proven extremely dicult to document strategic behavior empirically. The key problem is that voters’ tastes are generally unobserved. Without imposing further assumptions it is, therefore, impossible to know whether ballots accurately reflect the underlying preference orderings and to what extent tactical voting distorts electoral outcomes. In fact, Degan and Merlo (2009) prove that any crosssection of votes can be rationalized by some utility function, without resorting to strategic behavior. While there are many ways in which agents could be strategic, this paper focuses on testing one of the central predictions of rational choice voting theory. According to the theory, strategic voters choose someone other than their most preferred candidate whenever the latter is believed to have no chance of winning (see, e.g., Myerson and Weber 1993). Conversely, agents who always vote for their favorite contestant–regardless of whether she is in contention for victory–are said to be sincere.1 In order to resolve the fundamental identification problem the present paper exploits the structure of parliamentary elections in Germany. Under the German system individuals have two votes. Both are submitted simultaneously, but are associated with very dierent incentives. The list vote is cast for a party and counted on the national level. Up to a first-order approximation, list votes determine the distribution of seats in the Bundestag. Since mandates are awarded on a proportional basis (conditional on clearing a 5%-threshold), it is in practically every voter’s best interest to reveal his true “preferences” by choosing the party he wishes to gain the marginal seat.2 1 Naturally, issues of tactical voting do not arise in elections with only two candidates. In such cases even strategic voters simply select their favorite contestant. 2 Note well, individuals’ preferences over which party wins the marginal seat in parliament need not coincide with their deep ideological convictions. Nevertheless, it is useful to think of preferences in this narrowly defined way, as it conditions on expectations about post-election coalition formation, the influence of campaign activities, etc. 2 By contrast, the candidate vote is counted in a first-past-the-post system on the district level. Whoever wins the plurality of votes in a given district is automatically elected to parliament. Votes cast for any other contestant are “lost.” Although the candidate vote is primarily used to determine the identity of local representatives, by securing a disproportionate share of districts parties may actually increase their seat totals (see Section 4 for details). Hence, when it comes to choosing among dierent candidates, voters have a clear incentive to behave tactically. As in all elections under plurality rule, they should never vote for their favorite party’s nominee if she is known to be “out of the race.” Figure 1 demonstrates how observing the same individuals under both electoral regimes facilitates identification. For the sake of illustration, suppose that candidates are perfect representatives of their parties and that it is known a priori who has a realistic chance of winning. First, entertain the possibility that all voters cast sincere ballots. As shown in the panels on the left, if this were indeed the case, there would be a one-to-one correspondence between list and candidate votes–irrespective of whether the particular candidate is a contender. Next, assume that all voters behave tactically. In such a world only candidates who are believed to be in contention for victory should receive any votes. Thus, for non-contenders the curve representing the relationship between list and candidate votes ought to be perfectly flat.3 Lastly, consider the case in which there are both sincere and strategic types. As before, sincere agents vote for their preferred candidate, but no tactical type chooses a non-contender. Consequently, the line relating non-contenders’ share of the candidate vote to their parties’ list votes must have a slope between zero and one. It is this slope, denoted by , that identifies the fraction of voters who are sincere. Of course, not all candidates are perfect representatives of their parties–despite the fact that party platforms are much more salient in Germany than in the U.S. (see, e.g., Korte 2010a). For instance, some candidates are more charismatic, better qualified, or have a higher media profile than others. Supporters of rival parties might, therefore, be “drawn in” by a candidate’s personal appeal. Conditional on being out of the race, however, theory predicts that even high valence contestants will be deserted by tactical voters. Hence, after carefully controlling for candidate quality, the partial correlation between non-contenders’ list and candidate votes continues to measure the fraction of agents who stick with their preferred contestant.4 3 Strictly speaking, the shape of the curve for contenders is indeterminate. While it has to lie weakly above the origin and must end at (100%, 100%), the slope at intermediate points will generally depend on the correlation of preferences. If, however, tastes are approximately uncorrelated within precincts, then one would expect an almost one-to-one relationship between list and candidate votes. 4 Of course, there exist more elaborate models in which voters are reluctant to abandon high valence candidates. Empirically, however, there is no evidence that this is the case. If anything, there is a small 3 To account for heterogeneity across candidates this paper uses previously unavailable precinct level data from the 2005 and 2009 federal elections. In Germany, precincts are the smallest administrative units at which votes are counted, and each precinct is fully contained within one electoral district. Since races take place at the district level, these data allow for  in Figure 1 to be estimated from within-candidate variation only, thereby conditioning on the characteristics of candidates and their competitors. Figure 2 provides an empirical example from the 2009 election in District 207. Each panel plots a candidate’s own vote share against her party’s share of the list vote in the same precinct. In contrast to the contestants in the top row, those in the bottom two rows were widely believed to have no chance of winning. As one would expect if list votes were a good proxy for individuals’ preferences, after allowing for candidate specific intercepts there is an almost one-to-one relationship between list and candidate votes for contenders. Noncontenders, however, are deserted by a significant number of supporters–although by no means all. An important remaining obstacle is that it is generally unknown which candidates are considered to be “in the race.” Fortunately, the raw data are highly suggestive of focal equilibria in which voters coordinate on the most popular parties’ nominees. Given this type of play it is possible to estimate who is a serious contender by drawing from the literature on structural breaks in time series data (e.g., Andrews 1993; Bai 1997; Hansen 2000). Reassuringly, the main findings are qualitatively and quantitatively robust to more than twenty alternative ways of classifying contestants. The results in this paper show that about 30% of voters abandon their most preferred candidate if she is believed to have no chance of winning. Two key pieces of evidence indicate that defection is, in fact, driven by strategic considerations: First, not only do individuals who abandon their favorite contestant substitute toward the nominee of a potential coalition partner, but desertion rates themselves are much higher among voters faced with at least one palatable alternative than among those who can only choose among two evils. Second, estimates of strategic voting are substantially larger for elections perceived as “critical” than for ordinary ones. Alternative explanations, such as agents receiving utility from supporting the eventual winner of the election, are rejected by the data. Although these findings may be interesting in and of themselves, they are ultimately insucient to assess the impact of strategic voting on electoral outcomes. In order to address the question of whether manipulability of electoral systems has important real-world consequences, this paper also estimates a structural model of preferences and voting decisions. negative correlation between the measured quality of a contestant and the fraction of voters who abandon her. 4 Again, list votes provide a crucial source of identifying variation. Reduced form and structural methods yield very similar results with respect to the share of strategic voters, but the latter are also useful in constructing counterfactual election results. Beyond illustrating the importance of the voting scheme (i.e. plurality rule as opposed to proportional representation), the counterfactual experiments show that tactical behavior has a non-trivial impact on individual races. Compared to the current equilibrium, about one in ten districts would change hands if all voters were to cast sincere ballots. However, as one aggregates across districts, these distortions partially oset each other, resulting in only modest eects on the overall distribution of seats. The results in this paper speak directly to large theoretical literatures on tactical voting (e.g., Austen-Smith and Banks 1988; Carroll 2011; Cox 1994; Feddersen and Pesendorfer 1996; Myatt 2007, 2012; Myerson 2002; Myerson and Weber 1993) and strategyproofness in social choice (see Barberà 2011 for a recent review of the latter). On a purely descriptive level, the empirical evidence indicates that the fundamental assumption in rational choice studies of voting holds for some, but not all, individuals. The evidence also suggests that is important to distinguish the impact of strategic voting on individual races from its eect on aggregate seat totals. Moreover, the findings presented below may aid in the formulation of political economy models. Often, these models require an assumption regarding the voting behavior of agents; and the conclusion may depend critically on whether voters are taken to be tactical or sincere (compare, for instance, Besley and Coate 1997 with Osborne and Slivinski 1996). The remainder of the paper proceeds as follows. The next section provides a brief review of the existing empirical literature. Section 3 introduces a formal model of sincere and strategic voting. Section 4 outlines the crucial features of Germany’s electoral system, and Section 5 describes the data. The main results appear in Section 6. Section 7 estimates a structural model of voting decisions and presents several counterfactual experiments to analyze the impact of strategic behavior. The last section concludes.5 2. Previous Literature There exists a large empirical literature on strategic voting and turnout. While laboratory experiments provide generally convincing evidence of tactical behavior (e.g., Duy and Tavits 2008; Eckel and Holt 1989; Forsythe et al. 1993, 1996), real-world results tend to be mixed. 5 There are four appendices. Appendix A contains a formal proof omitted from the body of the paper. Appendix B explains the algorithm for calculating each party’s number of seats in the Bundestag. Appendix C provides precise definitions of all variables used throughout the analysis, and Appendix D elaborates on the numerical methods in the papers’ structural part. 5 Coate et al. (2008), for instance, reject the pivotal voter model based on the finding that it is unable to replicate winning margins in Texas liquor referenda. Reed (1990) and Cox (1994), however, argue that the distribution of votes in Japan’s multimember districts conforms roughly to the predictions of rational choice theory. More recently, Fujiwara (2011) uses a sharp regression discontinuity in Brazilian mayoral elections to show that third-place candidates are more likely to be deserted in races under simple plurality rule than in runo elections. The most comprehensive study to date is Cox (1997). His findings are suggestive of strategic behavior in a number of electoral systems, but indicate a lack thereof in others. Even less is known about the extent of tactical voting. Two notable exceptions are Spenkuch (2012) as well as Kawai and Watanabe (2012). Spenkuch (2012) exploits a highly unusual by-election in Germany, which allowed a party to gain one seat by receiving fewer votes, to put a 12% lower bound on the share of tactical agents. Kawai and Watanabe (2012) estimate a fully structural model of voting decisions in Japan’s general election, concluding that between 63% and 85% of voters are strategic. Their counterfactual experiments suggest that tactical voting had a significant impact on the distribution of seats.6 Recall, the fundamental diculty in inferring strategic behavior from naturally occurring variation is that voters’ preferences are not observed. Thus, any conclusions must either be based on indirect tests (as in Coate et al. 2008; Cox 1997; Fujiwara 2011; Spenkuch 2012), or preferences need to be estimated in order to compare them to actual vote counts (as in Kawai and Watanabe 2012). A separate strand of the literature tries to circumvent this problem by using survey data on voting decisions and political orientations (see, e.g., Abramson et al. 1992; Blais et al. 2001; Niemi et al. 1993; or, for Germany, Gschwend 2007; Pappi and Thurner 2002). Estimates in this tradition typically range from 3% to 17%. Wright (1990, 1992), however, points to important survey biases and raises serious doubts about conclusions based on self-reported votes. Alvarez and Nagler (2000) even show that, depending on the survey design, estimates of strategic voting dier by as much as a factor of seven.7 Most closely related to the present paper is work on ticket-splitting in mixed-electoral systems (for the case of Germany see Barnes et al. 1962; Fisher 1973; Gschwend 2001; Jesse 6 Given that the estimates in Kawai and Watanabe (2012) pertain to Japan’s general elections, whereas this paper studies strategic voting in Germany, the findings are not directly comparable. At least for the case of Germany, the raw data itself rule out strategic voting in excess of 50% (cf. Table 1 and the accompanying discussion). 7 Notwithstanding survey biases, Kawai and Watanabe (2012) as well as Alvarez et al. (2006) point out that some of this literature estimates misaligned voting (i.e. the share of voters who actually voted for someone other than their most preferred candidate) instead of strategic voting (i.e. the fraction of voters who would do so if their preferred candidate was believed to be not in contention for victory). Not surprisingly, both papers argue that the latter number is significantly larger than the former. For comparison, this paper estimates the extent of misaligned voting to be about 5.8%. 6 1988). This literature realizes that voters may cast split ballots for strategic reasons, but it ignores the possibility that contenders dier in their personal appeal, thereby confounding tactical behavior with candidate specific preferences (see the discussion in Klingeman and Wessels 2001). Moreover, even if one accepts the mere presence of ticket splitting as evidence of tactical behavior, naı̈vely estimating the number of split tickets (often from survey data) may over- or understate its true extent. 3. A Model of Sincere and Strategic Voting In order to fix ideas and frame the empirical work to follow, this section introduces a simple model of voting under plurality rule. Instead of considering the complete decision problem associated with list and candidate votes in Germany, it is more useful to focus on the race for a direct mandate in one electoral district, i.e. on a single subgame. The model is a straightforward extension of Myerson and Weber (1993) with the addition of sincere voters, stochastic turnout, and endogenous pivot probabilities.8 3.1. Basic Building Blocks Let the set of candidates be denoted by K = {1, 2, . . . , k}. Members of the electorate (simultaneously) cast single nontransferable votes, and the contestant with the highest vote total is declared the winner of the election. Ties are broken by the flip of a fair coin. Voters are either sincere or tactical,  2 {s, t}. Sincere voters always choose their most preferred candidate, whereas tactical agents act based on personal preferences as well as their beliefs about the actions of other players in the game. The share of agents who are sincere is given by  2 [0, 1]. Each voter has strict preferences over candidates summarized by a vector u = (u1 , . . . , uk ) in some finite set U  Rk , where ui is the expected utility from candidate i winning the district. f (u) denotes the fraction of individuals with a particular preference profile. That is, f is a probability distribution over U . A voter’s type is defined as the tuple (u, ) 2 I  U  {s, t}. For simplicity, u and  are assumed to be independent random variables. Agents know their own type, but are uncertain about the number of other players in the game. This captures the idea that real world elections are characterized by substantial uncertainty about turnout, and that voters are typically not aware of everybody else’s identity. Following Myerson (1998, 2000), assume that the total number of voters is a random variable drawn from a Poisson distribution with mean n < 1.9 n, f , as well as  are common knowledge. 8 See Kawai and Watanabe (2012) for a similar model with a fixed set of voters and a simple ordering restriction on beliefs about pivot probabilities. 9 The Poisson assumption is made for convenience. None of the empirical results depend on it. 7 As mentioned above, strategic agents maximize expected utility taking the behavior of others into account. More specifically, tactical voters choose candidate k only if doing so maximizes (1) u (k, e |u, t) = 1 X e (k, k 0 ) [uk  uk0 ] , 2 k0 2K\{k} where e = (e (k, k 0 ))k,k0 2K denotes players’ common beliefs about the probability of casting a pivotal vote.10 By contrast, sincere players always select their most preferred contestant. They maximize the utility function: u (k, e |u, s) = uk . 3.2. Equilibrium Let  (k|u, ) denote voters’ strategies. That is,  : I !  (K) specifies the probability that a type (u, ) voter casts a ballot for candidate k. In equilibrium it must be the case that, for all (u, ) 2 I, u (k, e |u, ) .  (k|u, ) > 0 only if k 2 arg max 0 k 2K Given , realized vote totals, v = (v (k))k2K , are random variables with means, µ = (µ (k))k2K , equal to (2) µ (k) = n X u2U [ (k|u, s) + (1  )  (k|u, t)] f (u) . From the Poisson assumption it follows that the elements of v are independently distributed (see Myerson 1998 for a proof), which allows the probability of casting the pivotal vote to be expressed in a transparent way. More specifically, not knowing the exact number of players in the game, the ex ante probability of candidate k being tied for first or one vote behind k 0 is given by  (k, k 0 ) = 1 X  =1 10 2 4 ( =  |µ (k)) X +1  0 = !0 ( =  0 |µ (k 0 )) @ Y X 1 k00 2K\{k,k0 }  00 =0 13 ( =  00 |µ (k 00 ))A5 , To see that (1) results from expected utility maximization note that an individual’s vote aects his payo only if it changes the outcome of the election, i.e. if two candidates are either tied for first or one vote apart. If candidate k and k 0 are tied, then voting for the former results in an expected utility gain of uk  12 (uk + uk0 ). If k is one vote behind k 0 , then choosing k changes payos by 12 (uk + uk0 )  uk0 , which is the same as the previous expression. Summing over all candidate pairs and weighting by  e gives (1). 8 where ( =  |µ (k)) denotes the probability of a Poisson random variable  with parameter µ (k) being equal to  .11 Definition: Given the Poisson game  (K, I, n, f, ), a voting equilibrium consists of a strategy function  satisfying, for all (u, ) 2 I, (i) (ii)  (k|u, )  0 8k 2 K, P k2K  (k|u, ) = 1, and (iii)  (k|u, ) > 0 only if k 2 arg maxk0 2K u (k 0 , e |u, ); as well as a set of beliefs such that (iv) e (k, k 0 ) =  (k, k 0 ) Proposition 1: 8k, k 0 2 K. The set of voting equilibria is always non-empty. Proof: See Appendix A. To get a sense of what equilibrium play looks like note that strategic voters’ utility function is homogenous in e . Hence, tactical voting decisions are determined by the relative–not absolute–size of perceived pivot probabilities. From the magnitude theorem in Myerson (2000) it follows that some pivot probabilities are going to be much larger than others; although for large electorates all elements of  will be very close to zero. That is, as n ! 1 most pivot probabilities become infinitesimal relative to, at most, a few remaining ones. Intuitively, this is because homogeneity of the utility function implies that e (k, k 0 ) can be rewritten as the probability of k and k 0 running neck-and-neck ahead of all other contestants, conditional on the election being tied in the first place. Such a tie, however, is substantially more likely to involve the two front-runners than an underdog. Hence, almost all of the probability mass must be concentrated in one or two candidate pairs. Put dierently, in large elections only a subset of candidates will be “in the race,” and strategic voters behave as if choosing only among those who are believed to be serious contenders. Since tactical agents become more inclined to select a particular candidate as they form favorable beliefs about her being in contention for victory–say, because her standing in pre-election polls improves, or due to campaign activities that manipulate voters’ perception of candidate viability–the model above exhibits the potential for bandwagon eects and self-fulfilling prophecies (Simon 1954). This property can result in multiple equilibria, and any candidate that is not a Condorcet loser may be the sole likely winner under plurality rule (cf. Myerson and Weber 1993). Thus, without further refinement the model makes no 11 As is typical in the literature on strategic voting, the probability of three-way ties is assumed to be negligible. 9 prediction on the set of candidates who will be “in the race,” i.e. on which of the many possible equilibria is being played. In reality, however, one may suspect that tactical voters play focal equilibria, especially in cases in which the share of sincere agents is large. When many voters simply select their most preferred candidate, then tastes alone will lead to substantial dierences in vote shares, thereby “pre-determining” who is a serious contender. A number of potential equilibria may even be ruled out completely. Consequently, strategic agents would only want to choose among the most popular contestants. As argued in Section 6.1 the data do, indeed, suggest focal equilibria of this type. Lastly, note how equation (2) gives rise to the estimation strategy outlined in the introduction. Since tactical voters would never support a candidate who is “out of the race” it must be the case that  (k|u, t) = 0 for all non-contenders.  (k|u, s), however, equals either 0 or 1, depending on whether type (u, s) agents prefer k over every other contestant. Given these strategies, the expression for non-contenders’ expected vote shares simplifies to µ (k) /n =  X e u2{u2U |uk >uk0 8k0 } f (ue) . Thus, if one accepts the assumption that list votes are a not only a measure of voters’ preferences over parties, but also a (potentially noisy) proxy for the fraction of individuals who P favor the respective nominees, i.e. for eu f (ue), then  can be identified from the candidatelist vote gradient among non-contenders. Of course, for this assumption to be reasonable it is important to properly account for systematic dierences in candidates’ idiosyncratic appeal. 3.3. A Note on Turnout Before proceeding to the empirical application, it is important to discuss one of the model’s limitations. Instead of considering the decision to go to the polls explicitly, turnout is assumed to be stochastic. Although it is natural to think of n as the (expected) number of agents for whom the cost of voting are smaller than the benefits, this assumption does entail a loss of generality. In particular, in the formulation above it is not the case that turnout varies with the probability of being pivotal. One may rationalize this modeling choice by appealing to the “paradox of voting” (Downs 1957; Riker and Ordeshook 1968). To generate high turnout in light of small pivot probabilities agents have to derive a psychic benefit from going to the polls.12 If the net utility gain is suciently large, then tactical considerations matter very little for turnout, but may nevertheless determine for whom strategic agents vote. That is, the utility from fulfilling 12 For an alternative approach relying on aggregate uncertainty see Myatt (2012). 10 their ‘civic duty’ might bring voters to the polls, but conditional on voting there is little that keeps them from behaving tactically. Naturally, there exist alternative models in which strategic considerations do not determine voting decisions, or only if they are suciently important. For instance, agents might derive utility from voting for the “right candidate,” and this utility may easily outweigh the expected gain from influencing the outcome of the election. Thus, whether individuals vote strategically is ultimately an empirical question. 4. Germany’s Electoral System In order to shed light on the extent of strategic voting the present paper exploits the structure of parliamentary elections in Germany. Elections to the Bundestag are held according to a mixed member system with approximately proportional representation. Except for minor modifications, the same system has been in place since 1953 (see Bawn 1993 for an account of its inception).13 As mentioned in the introduction, each voter casts two dierent votes. The first vote, or candidate vote (Erststimme), is used to elect a constituency representative in each of 299 single-member districts. The second vote, or list vote (Zweitstimme) is cast for a party and counted on the national level. Figure 3 depicts a sample ballot. The column on the right enumerates all electable parties in a particular state together with the first few individuals on the respective party’s list. The column on the left contains the names of all candidates running for district representative. Contestants always appear directly next to the party that nominated them, and both the candidate’s last name as well as the respective party acronym are printed in bold font. The close connection between candidates and parties reflects the fact that most contestants simply campaign on their own party’s platform.14 District representatives are determined in a first-past-the-post system. That is, whichever contestant achieves the plurality of candidate votes in a given district is automatically awarded a seat in the legislature. Winners are said to hold direct mandates, and votes cast for any other candidate are discarded. Figure 4 shows the party aliation of all district winners in the 2005 and 2009 elections. Although the CDU/CSU secured the majority of direct mandates in both years, there remains ample geographic variation, as well as some variation over time. Of the five major parties only the FDP did not win any districts–despite gaining a non-trivial fraction of votes. To still achieve approximately proportional representation of all parties clearing a 5%13 14 In describing the German electoral system this section borrows from Korte (2010b) and Spenkuch (2012). Since the introduction of the two-ballot system in 1953 no independent candidate has ever won a district. 11 threshold, the German electoral system also awards list mandates. First, all list votes are aggregated up to the national level and a total of 598 preliminary seats are distributed to parties on a proportional basis. Each party’s allotment is then broken down to the state level, and compared to its number of direct mandates in the same state. Whichever number is greater determines how many seats the party will actually receive in that state. More formally, let dp,s denote the number of districts that party p won in state s, and let lp,s be how many mandates it would have received in the same state under proportional representation. Then, the final number of seats that p retains in s equals np,s = max {dp,s , lp,s } , P and its total in the Bundestag is given by np = s np,s (see Appendix B for a more detailed description of the algorithm used to allocate seats). If dp,s < lp,s , then in addition to the district winners the first lp,s  dp,s candidates on p’s list are elected as well. Otherwise, only holders of direct mandates receive a seat. Parties are said to win overhang mandates (Überhangmandate) whenever dp,s > lp,s . In such cases the total number of seats in the Bundestag increases beyond 598. Note, however, the number of mandates awarded under proportional representation, i.e. P P P P p s lp,s , exceeds the number of districts, p s dp,s , by a factor of two. Thus, situations in which dp,s > lp,s are a fairly rare. Instead, the list vote determines the overall distribution of seats–at least up to a first-order approximation.15 Critical for the purposes of this paper are the incentives associated with each vote. First, consider the list vote. Due to the fact that seat totals are approximately proportional to parties’ vote shares (and given that it is nearly impossible to predict rounding), most agents can be expected to choose their “preferred” party, defined as the one they would like to win the marginal seat in parliament. In fact, it is easy to see that voting for one’s preferred party is a strictly dominant strategy whenever E [dp,s ] < E [l p,s ]. Only if one anticipates that dp,s > l p,s may it not be optimal to do so. However, most voters cannot reasonably assign a high probability to this case. Historically, it occurred for less than 10% of state-party combinations; and FDP, Greens, as well as The Left have never won any overhang mandates. The vast majority of agents has, therefore, an ex ante incentive to cast “truthful” list votes.16 When it comes to the candidate vote, however, agents should behave tactically–as in 15 Theoretically, overhang mandates may lead to departures from proportionality of up to one third of all seats. In the current equilibrium deviations are much smaller. For instance, relative to its share of the list vote, the CDU/CSU received an additional 7 mandates in 2005, whereas the SPD secured 9 extra seats. 16 The results in this paper are qualitatively and quantitatively robust to focusing on state-party combinantions for which dp,s  l p,s . 12 all elections under plurality rule. If their preferred candidate is believed to be a contender, then voting for her is a dominant strategy. After all, there is a small (but strictly positive) probability that doing so will lead to an extra seat in the Bundestag, and even in cases in which one’s preferred party is unlikely to win an additional mandate, supporting the party’s nominee can prevent a rival faction from increasing its seat total. If, however, a candidate is known to be “out of the race,” then one can always do better by voting for somebody else. Substituting toward a contestant who actually has a chance of winning could benefit a coalition partner, or it might spoil a particularly disliked party’s victory. Even if individuals took the aggregate distribution of seats as fixed, by casting tactical ballots they may elect “better” local representatives. Although expected payos may not be very large, as long as strategic agents are not completely indierent to who carries their district, they should never waste their vote on a candidate who is “out of the race.”17 Table 1 shows the relative frequency of dierent list and candidate vote combinations in the 2009 federal election.18 First and foremost, the evidence indicates that some, but not all voters desert non-contenders. Although candidates of FDP, Greens, and other minor parties are rarely in contention for victory, they are abandoned by only about half of their followers. At the same time, the numbers show that about 46% of all FDP supporters voted for a candidate of the CDU–its coalition partner–whereas 33% of Green Party adherents chose an SPD nominee. It therefore appears that voters who do desert non-contenders substitute toward close political allies. By itself, however, Table 1 is insucient to determine the extent of strategic voting. For instance, some FDP supporters might have chosen CDU candidates not because of tactical considerations, but because they are better qualified or more charismatic. Also, not all CDU and SPD adherents voted for their own party’s nominee. In fact, almost one third of those who deviate end up picking a political rival. While it is possible that these voters chose among the lesser of two evils in districts in which the CDU or the SPD candidate happened to be “out of the race,” it is equally plausible that their voting decisions were based on candidate idiosyncrasies. Simply computing the share of “ticket splitters” among supporters of FDP, Greens, and other minor parties would put the share of strategic voters at slightly above 50%. Compared to the 30% estimate based on the identification strategy outlined above, this naı̈ve approach overstates the extent of strategic voting substantially. 17 At first, the German system may seem very complicated. Yet, the results of Spenkuch (2012) show that voters are keenly aware of the incentives at work. 18 Table 1 is based on a 3.9% random sample of actual votes. German electoral law requires the Federal Returning Ocer to publish descriptive statistics on vote combinations, as well as voting behavior by age and gender (see Bundeswahlleiter 2010). Unfortunately, the micro-data are not publicly accessible. 13 5. Data Sources and Descriptive Statistics In order to estimate the share of strategic voters, it is useful to focus on the 2005 and 2009 federal elections. In these years all of the five major parties were widely expected to clear the 5%-threshold.19 Since voters could be virtually certain that their preferred party would be represented in parliament, list votes should reflect party preferences more accurately in 2005 and 2009 than in other years. In contrast to prior work on ticket splitting in Germany, the analysis in this paper relies on ocial election results by polling precinct (Wahlbezirk). These data have been obtained from the Federal Returning Ocer and were until recently not publicly available. In Germany, precincts are the smallest administrative units at which votes are counted. Each precinct is fully contained within an electoral district and associated with one polling station where a returning ocer oversees the election. By law, no precinct can contain more than 2,500 eligible voters. As of 2009 there were 299 electoral districts and almost 89,000 precincts. Dierentiating between East and West Germany as well as election year, Table 2A displays summary statistics for all precinct level variables used throughout the analysis. Compared to the U.S., turnout is fairly high. Averaging across 2005 and 2009, almost 75% of the electorate went to the polls. Together with a mean size of 821 eligible voters, this means that precincts handle about 615 votes on average. As is well known, CDU, SPD, FDP, and the Green Party fare substantially better in West Germany than in the East. The opposite is true for The Left–the successor of the East German communist party. Moreover, CDU and SPD receive more candidate than list votes. Since nominees of these two parties are serious contenders in most districts, this “surplus” of candidate votes may be indicative of tactical behavior (cf. Cox 1997). At the same time, CDU and SPD might simply field “better” contestants. In fact, the descriptive statistics in Table 2B demonstrate that candidates dier along important dimensions.20 For instance, only 19% of CDU candidates are female, compared to 35% of Social Democrats and 34% of Green Party nominees. Moreover, relative to their FDP, Left, or Green Party counterparts, contestants of CDU and SPD are about four times more likely to be a current member of parliament, and more than forty times as likely to be an incumbent. Therefore, any argument linking dierences in the distribution of list and candidate votes to strategic behavior must be based on an econometric strategy that carefully controls for candidates’ idiosyncratic appeal. 19 For instance, more than 90% of adults sampled in the 2009 pre-election survey of the German Longitudinal Election Study (GLES) expected the FDP and Green Party to receive more than five percent of the list vote. 20 The information in Table 2B has been compiled from ocial publications by the Federal Returning Ocer (Bundeswahlleiter 2005c, 2009b). 14 6. Estimating the Extent of Strategic Voting 6.1. Econometric Approach Following the argument in the introduction, the fraction of sincere voters can be identified from the partial correlation between non-contenders’ share of the candidate vote and their parties’ share of the list vote, after accounting for candidate quality. Hence, with ideal data it would be possible to estimate the parameter of interest, , from (3) C L L vk,r,d,t = k,t + vk,r,d,t  1 [k 2 / Ct (d)] + vk,r,d,t  1 [k 2 Ct (d)] + k,r,d,t , C where vk,r,d,t denotes contestant k’s share of the candidate vote in precinct r during election L year t, and vk,r,d,t is her party’s share of the list vote in the same precinct. Ct (d) stands for the set of candidates who are believed to be contenders in district d, and k,t marks a year specific candidate fixed eect. N.B.: As races take place at the level of the electoral district, precinct level data allow for identification using only within-candidate variation, thereby conditioning on candidate quality, beliefs about tie probabilities, etc. There does remain one obstacle. Since Ct (d) is unobserved, it is not clear which candidates were considered to be “in the race.” If agents had perfect foresight then only contestants who ended up finishing first or second would have been a priori serious contenders. In reality, however, voters are likely to have noisy priors and may believe more than just two candidates to be in contention for the direct mandate (Cox 1994 shows that this can be an equilibrium).21 Fortunately, the raw data suggest an intuitively appealing heuristic for classifying contenders. To see this consider Table 3, which contains a cross-tabulation of candidates’ own rank (based on the candidate vote) against the ranking of their party among voters in the same district (based on the list vote). Out of the 598 contestants whose party placed first, only 41 did not win a direct mandate and a mere 2 finished third or lower. In contrast, none of the candidates who ran for a party ranked fourth or worse came in first, and only 3 finished second. Overall, the correlation between list and candidate vote based rank is .93. The evidence is, therefore, consistent with voters playing focal equilibria in which they coordinate on the most popular parties’ nominees. This impression is further strengthened by the regression results in Table 4. The estimated specifications are analogous to (3), but allow for the slope to vary by preference, i.e. list vote, based rank. As should be the case if list votes were not only a measure of individuals’ preferences over parties but also a good proxy for voters’ assessment of the respective nominees, 21 Unfortunately, pre-election surveys in Germany are too small to derive reliable estimates of voters’ expectations. For instance, in only 50 electoral districts did the German Longitudinal Election Study (GLES)–the best available data source–survey more than 15 adults prior to the 2009 elections. 15 the R2 of these specifications is extraordinarily high. Moreover, there is a near one-to-one correspondence between list and candidate votes for the first two contestants. For for those ranked third and below, however, the candidate-list vote gradient is significantly smaller, suggesting that voters desert (only) candidates of “unpopular” parties.22 Based on the results in Tables 3 and 4, it seems reasonable to assume that contestants backed by one of a district’s two favored parties are serious contenders, whereas candidates of parties ranked fourth and below should be considered “out of the race.” The only ambiguity arises with respect to those in third place. In practice, almost 10% of third ranked contestants finish first or second. Hence, one would want to classify some (but not all) of them as serious competitors, especially in cases in which only a few percentage points separate their own party from the one in second place. Drawing from the literature on structural breaks in time series data (e.g., Bai 1997; Hansen 2000) it is possible to estimate a cuto value, , separating candidates into contenders and non-contenders.23 More specifically, a candidate is said to be a contender if and only if her party trails a district’s second most popular one by less than  percentage points. With this simple heuristic in hand, the estimating equation becomes (4) h C L = k,t + vk,r,d,t  1 v L,2 vk,r,d,t d,t nd i h L  v Lk,d,t >  + vk,r,d,t  1 v L,2 d,t nd i  v Lk,d,t   + k,r,d,t . Here, v Lk,d,t denotes the list vote share of candidate k’s party in district d, and v L,2 nd is that of d,t the second most popular party in the same district. All other symbols are as defined above. If (4) is correctly specified, then searching for the value of  that maximizes the R2 yields a super-consistent estimate of the true break point (Hansen 2000). Moreover, under the null hypothesis that such a point exists, estimates of the model’s other parameters are normally distributed and standard errors need not be adjusted for sampling variability in the location of the break (see, e.g., Bai 1997).24 Although intuitively appealing, there is no guarantee that this method classifies all candidates correctly. For this reason Section 6.3 performs a series of robustness checks, demonstrating that the main findings are qualitatively and quantitatively robust to employing more than twenty alternative definitions. 22 One can reject the null hypothesis of equal slopes at the 1%-level. Card et al. (2008) use the same approach in combination with regression discontinuity methods to test for “tipping points” in the dynamics of neighborhoods’ racial composition. 24 Complications arise under the null of no break. In this case,  will have a non-standard distribution, and conventional hypothesis tests will have incorrect size. One way to correct for this problem would be to follow Card et al. (2008) and split the data into a sample used to estimate the location of the change point, and another one for further analyses. Given the evidence in Tables 3 and 4, the possibility of no break, i.e. that all contenders suer from equal desertion rates, seems unlikely in the present context. Moreover, the robustness checks in Table 8 indicate that the results are qualitatively and quantitatively robust to misspecification of the change point. 23 16