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1 This article was downloaded by: [University of Konstanz] On: 6 May 2009 Access details: Access Details: [subscription number ] Publisher Routledge Informa Ltd Registered in England and Wales Registered Number: Registered office: Mortimer House, Mortimer Street, London W1T 3JH, UK West European Politics Publication details, including instructions for authors and subscription information: Strategic Voting under Proportional Representation: Threshold Insurance in German Elections Susumu Shikano; Michael Herrmann; Paul W. Thurner Online Publication Date: 01 May 2009 To cite this Article Shikano, Susumu, Herrmann, Michael and Thurner, Paul W.(2009)'Strategic Voting under Proportional Representation: Threshold Insurance in German Elections',West European Politics,32:3, To link to this Article: DOI: / URL: PLEASE SCROLL DOWN FOR ARTICLE Full terms and conditions of use: This article may be used for research, teaching and private study purposes. Any substantial or systematic reproduction, re-distribution, re-selling, loan or sub-licensing, systematic supply or distribution in any form to anyone is expressly forbidden. The publisher does not give any warranty express or implied or make any representation that the contents will be complete or accurate or up to date. The accuracy of any instructions, formulae and drug doses should be independently verified with primary sources. The publisher shall not be liable for any loss, actions, claims, proceedings, demand or costs or damages whatsoever or howsoever caused arising directly or indirectly in connection with or arising out of the use of this material.

2 West European Politics, Vol. 32, No. 3, , May 2009 Strategic Voting under Proportional Representation: Threshold Insurance in German Elections SUSUMU SHIKANO, MICHAEL HERRMANN and PAUL W. THURNER Does proportional representation imply incentives for strategic voting? This article investigates whether adherents of the major German parties voted against their preference in order to increase the chance of a majority coalition between their favourite party and the preelectorally declared junior coalition partner. Focusing exclusively on the PR vote, the authors test whether strategic voting is guided by expectations with regard to the coalition formation stage. To that end they use a two-step estimation procedure to simultaneously predict (in-)complete party preferences and sincere and strategic voting in a random utility framework. Their results show that voters preferences, rather than mapping directly into party choice, are affected by their expectations on small parties re-entry chances. Voting under proportional representation (PR) is often viewed as genuinely sincere, that is, voters are assumed to simply vote for whichever party or candidate they most prefer. While scholars of voting behaviour have repeatedly focused on the possibility of insincere or so-called strategic voting in majority systems, such behaviour has largely been dismissed in the context of PR systems. Strategic voting theory posits that voters cast their vote in order to maximise their influence on government formation. In contrast to sincere voting, this may or may not involve voting for the most preferred alternative, depending on the electoral situation faced by the individual voter. Given the situation of simple plurality elections, for example, a voter who expects her preferred candidate to come in third place might decide to cast a strategic vote for the relatively more preferred among the candidates or parties in order to avoid the victory of a worse alternative (Fisher 2004). Similar incentives for strategic voting have been shown to exist under various other election schemes, such as approval voting Correspondence Address: Susumu.Shikano@uni-konstanz.de; miherrma@rumms.uni-mannheim.de; paul.thurner@gsi.uni-muenchen.de ISSN Print/ Online ª 2009 Taylor & Francis DOI: /

3 Strategic Voting in German Elections 635 (Hoffman 1982), multimember elections (Cox 1984), or runoff elections (Niou 2001). Only recently, however, scholars have begun to recognise the possibility of incentives for strategic voting in PR systems (van Holsteyn and Irwin 2003; Blais et al. 2006; Bargsted and Kedar 2009; Meffert and Gschwend 2008). Assessing these incentives is of great importance as PR is one of the most commonly applied election systems worldwide. If voters change their PR vote according to their perception of the likely outcome of the election, then polls, campaigns and coalition announcements may have profound influences on voters short-term behaviour. In this article we add to the recent literature on strategic voting under PR by presenting evidence for sophisticated vote switching. We analyse the 1994 German federal election because of the existence of a unique data set for testing our hypotheses. Specifically, we show that supporters of major parties often opted for their preferred party s designated junior coalition partner to increase the chance of a majority coalition led by their preferred party. The next section gives an idea about the meaning of strategic voting under PR in general as well as in the German context more specifically. We will highlight some of the difficulties in empirically detecting a strategic PR vote. In section two, we propose a modelling approach to infer strategic PR voting from survey data. In section three, we apply the model to data from the 1994 German federal election. Results are given in section four. We conclude with a discussion of the virtues of our approach. Conceptualising Strategic PR Voting Voting can be considered as a choice from a discrete set of parties or candidates. Strategic voting as opposed to sincere voting arises when the optimal choice does not correspond to the first-ranked party of a complete preference ordering: Sincere voting requires each voter to vote according to its preferences in any pairwise comparison of alternatives. An actor casts a sophisticated vote when it votes against its preferences in a pairwise comparison (Morrow 1994: 134, see also Ordeshook 1986: 258 ff.). Strategic voters seek to maximise their expected utility from the outcome of the election. Strategy implies that, in addition to their preferences, individual voters form expectations or probability beliefs about the likely outcome of the election and includes these in their decisions (see Cox 1984: 726). Strategic voting is therefore the result of the total calculus of voting given preferences and beliefs on the probabilities of the relevant states of a specific electoral situation (see McKelvey and Ordeshook 1972; Black 1978; Cain 1978; Cox 1997; Fey 1997). Accordingly, the party that yields the highest expected utility is chosen and this may not always be the party that is most preferred in terms of preferences where expectations are not taken into account. In simple plurality elections, voter expectations are driven by the question of candidates (non-)viability in winning the election because plurality rule

4 636 S. Shikano et al. renders all votes for hopeless candidates essentially wasted. By contrast, in the context of PR elections, voter expectations and strategic voting do not rest so much on the conversion of votes into seats than on the anticipation of post-election coalition building. Coalition governments usually are the norm in systems employing proportional seat allocation rules. While in some elections and countries it is hard to tell, beforehand, which coalitions are likely to form, most of the time it is nevertheless clear that certain constellations emerge as more likely than others prior to election day. Now, if voters perceive certain coalitions as more likely to form than others then this might create an incentive to vote for a party, other than the most preferred one. There is an emerging literature emphasising the possibility for strategic voting under PR (see Van Holsteyn and Irwin 2003; Blais et al. 2006, Bargsted and Kedar 2009; Bowler et al. 2008; Duch 2008; Marsh 2008; Meffert and Gschwend 2008). Bargsted and Kedar (2009), for example, suggest that centre-right voters expecting a centre-left coalition government choose to defect from their preferred centre-right party and instead vote for the most rightist of parties in the prospective coalition in an attempt to balance out the government. 1 They find evidence for this type of coalition balancing with respect to the three major parties in the 2006 Israeli Knesset election. Blais et al. (2006) in their analysis of the 2003 Knesset election found that almost 10 per cent of voters defected from their first preference due to coalition considerations. Coalition preferences turned out to be a strong predictor of vote choice, even controlling for other factors such as party evaluation or ideology. Van Holsteyn and Irwin (2003) examine coalition expectations in the 2002 Dutch parliamentary election. They demonstrate that even in systems with very many parties and various options for coalition building, voters still hold fairly clear expectations about which coalitions are likely to form. They also show that, given different hypothetical coalition scenarios, some voters alter their vote to endorse parties that are more likely to participate in the preferred coalition government. Taken together, these studies suggest the possibility that voters might cast their PR vote for a party other than their most preferred one. In the next section we shall address the idea of a strategic PR vote in the context of German Bundestag elections. Our focus will be on a particular form of voting, namely on the deviation from a first party preference in order to increase the probability that a voter s most preferred party actually is part of the government. Strategic PR Voting in German Elections The German electoral system is commonly designated as a mixed electoral system (Massicotte and Blais 1999; Shugart and Wattenberg 2001). It combines PR with plurality rule in single-member districts, giving two votes to each voter: the first vote (Erststimme) is cast for a constituency candidate,

5 Strategic Voting in German Elections 637 the second vote (Zweitstimme) for a list of party representatives from a given state. PR votes, aggregated at the national level, determine the total number of seats to which a party is entitled. The district vote has only very little impact on the allocation of party seats, as district winners do not receive extra seats but fill the seats allocated to their party according to the PR vote. 2 Like many other PR systems, Germany employs a threshold of representation that bars parties obtaining less than 5 per cent of second votes nationwide from entering into parliament. 3 It is common for German parties to declare informal pre-electoral coalitions (Golder 2005), whereby usually the smaller parliamentary parties Free Democratic Party (FDP) and Greens commit themselves in advance to one of the larger parties, i.e. FDP to Christian Democratic Union (CDU) and the Greens to Social Democratic Party of Germany (SPD). Thus voters know beforehand which coalitions are likely to form (provided those coalitions are majority coalitions). The tendency of small parties to form pre-electoral coalitions with either one of the large parties creates an incentive for supporters of CDU and SPD to defect from their first preference, if they are unsure whether their party s coalition partner will overcome the 5 per cent threshold. If its coalition partner fails to enter parliament while the other party s coalition partner succeeds, the opposing coalition would assume government. If neither of the two small parties enters parliament, both large parties would most likely form a grand coalition. Thus, by casting a vote for a small party, supporters of major parties employ a coalition insurance strategy (see Pappi and Thurner 2002; Gschwend 2007), i.e. they insure against a 5 per cent loss of the coalition lead by their most preferred party. We are not the first to mention the possibility of a strategic PR vote in the German elections. In fact, the idea is widely known among scholars and observers of German electoral politics and has also been invoked in prior work on voter behaviour in Germany (e.g. Roberts 1988; Schoen 1999; Thurner and Pappi 1999, Blais et al. 2001; Gschwend 2007). Only a few studies have thus far attempted to provide evidence for this kind of behaviour. Most notably, Pappi and Thurner (2002) found that coalition preferences induce certain types of split-ticket voting. Gschwend (2007) extends these findings, demonstrating for the first time that voter expectations regarding small-party entry into parliament have a significant impact on voters propensity to split their vote. Departing from these studies we intend to infer strategic PR voting without reference to split-ticket voting. For identifying a strategic PR vote, previous studies chose to rely on the event of a split vote between a major and a minor party, i.e. voters who cast their district vote for a candidate of a larger party, say CDU, and the PR vote for its smaller coalition partner, say FDP, were assumed to be strategically motivated. More precisely, the voters were assumed to cast their district vote for their sincere first preference and the PR vote strategically for their preferred party s junior coalition partner. This, however, is not the only conclusion one could draw: the same pattern

6 638 S. Shikano et al. of ticket splitting could also result from strategic voting on the district level, i.e. by supporters of the candidates of small parties who intend to avoid wasting their district vote. The latter kind of strategic voting can be found among significant parts of German voters (Herrmann and Pappi 2008). Accordingly, the district vote for a large party might well be strategic and the PR vote for a small party sincere. Thus we cannot decide, prima facie, which kind of strategic voting is being observed in a split ticket. This is in line with Cox s (1997: 82) argument that casting a list vote for the FDP and a candidate vote for, say, the Christian Democratic Union (CDU) is not unambiguous evidence of ordinary strategic voting, however. It may be that the voter truly prefers the CDU, casts a sincere vote for the CDU candidate, but casts her list vote strategically for the FDP, because the FDP is both in alliance with the CDU and in danger of falling below the 5% national threshold (in which case the FDP would get no seats and the CDU might not be able to form a government)... So how is one to tell whether some component of the discrepancy between the FDP s candidate and list votes is due to ordinary strategic voting, intended to avoid wasting the constituency vote? The ambiguity inherent in measures of split voting and described by Cox makes previous results somewhat less convincing. Ticket splitting is neither a necessary nor a sufficient condition for the identification of a strategic PR vote. In order to overcome these problems, we propose a solution that statistically infers cardinal utility from voters stated preference orderings and their determinants. This inferred cardinal utility enables us to account for the moderating impact of strategy-relevant expectations at the same time taking account of the inherent uncertainty of utility. Modelling Strategic Voting under PR: A New Approach In the following, we shall focus exclusively on the PR vote thus avoiding the pitfalls of split-vote measures. Given the conventional definition of a strategic vote as a decision deviating from first preference, a straightforward way to investigate strategic voting is to model the actual vote decision by reference to the voters preference orderings of alternatives. We thus propose a two-step estimation framework in which voter preference formation is modelled together with the subsequent vote decision. In this set-up the vote choice is explained on the basis of a multiplicative expected utility model in which party utility is endogenously derived from sincere preference orders. Observed (in-)complete preference orders and the stated choice are assumed to be the outcome of a single underlying utility function where expectations on coalition formation are the relevant motives of the deviation from first preference. Figure 1 depicts the two-step estimation process.

7 Strategic Voting in German Elections 639 FIGURE 1 A TWO-STAGE ANALYSIS OF STRATEGIC AND SINCERE VOTING In the first step, party utility is modelled as a function of voters retrospective evaluation of government activity and their issue-based prospective evaluation of party positions. Applying the so-called rank ordered logit model, we estimate voter utility for each party on the basis of the observed party rankings. In a second step those estimates are used in combination with variables on voters expectations in order to model their actual voting decision which comes closest to usually employed expected utility framework. The estimation of voter utility from other explanatory variables allows us to construct a cardinal measure for voter utility that can be combined with measures of voter expectations to account for the potential moderating impact of expectations on the final voting decision. Thus, our framework is fully consistent with the concept of expected utility, which posits a multiplicative relationship between party preference and voter beliefs. Furthermore we are able to simultaneously explain sincere and strategic voting within one and the same model. The innovative part of our two-step framework consists in using for the first time rank ordered logit (ROL) analysis for modelling strategic voting. Whereas ROL analysis, in essence, results from a straightforward expansion of the multinomial logit model for multiple responses (rankings), ROL has almost never been applied in electoral research. 4 Since it is central to our theoretical argument and the following empirical analysis, we give a short introduction. More detailed presentations can be found in Chapman and Staelin (1982), Allison and Christakis (1994), or Skrondal and Rabe- Hesketh (2003). The Statistical Model Multinomial logit and conditional logit are now accepted tools for the modelling of voters confronted with multiple choices, e.g. the choice of a party from a given set of parties (see Thurner 2000). Rank ordered logit, on

8 640 S. Shikano et al. the other hand, can be used to model voters (in-)complete rankings of all parties in a given choice set. This is accomplished by treating the assignment of each rank as a choice process itself, thus decomposing rank orderings into sequences of choices, where at each stage the alternative with the highest utility is picked from the choice set and ranked according to some ordinal numbering scheme. Consider the following random utility model: U ij ¼ V ij þ e ij with V ij ¼ x ij b þ z i g j ð1þ where U ij is the utility of party j to voter i, which is decomposed into a deterministic component V ij and a stochastic error term e ij. The deterministic component V ij is modelled as a function of characteristics of party j relative to voter i, x ij, with corresponding parameter vector b, and characteristics of voter i, z i, with respective, alternative specific, parameter vector g j. Accordingly, b and g j can be interpreted as importance weights in voter i s utility function. Utility maximisation implies that i votes for the party j if it yields a higher utility than any other party k in his choice set S. Since utility is assumed to be subject to unobservable random error, we do not know which party actually yields the highest utility, so we can only make a probabilistic statement about whether i votes for party j, i.e. the probability that j yields the highest utility of all parties in the choice set S PrðjjSÞ ¼Pr½U j max k2s ðu k ÞŠ; 8k 6¼ j. For some specified error distribution, this probability can be expressed as a multinomial logit (see McFadden 1974; Ben-Akiva and Lerman 1985; Train 1986). Thus multinomial logit is an expression for the probability that party j is most preferred, i.e. that j yields the highest utility of all parties in S. In electoral research, voters stated party choice is usually taken as the observational equivalent to their first preference and modelled with multinomial logit. On the other hand, multinomial logit can also be used to model observed voter preferences. For instance, assume that voter i s choice set S consists of four parties S ¼ {a, b, c, d} and that her preferences are given by the relation c a b d. As a consequence, the probability of observing party c on first rank can be expressed by multinomial logit. To obtain probability statements for the remaining party ranking, simply note that the second most preferred party a yields the highest utility among the remaining parties (excluding c). Hence the probability of observing a on second rank can again be expressed with multinomial logit, this time, for the set of parties a, b and d. Likewise the probability of observing party b in third rank can be expressed with a multinomial logit model for a set of parties b and d. The probability of the entire preference ordering is given by the product of those multinomial logit probabilities: 5 Prðc a b dþ ¼ ev c P j2se V j e V a e P V b P j¼fa;b;dge V j j¼fb;dge V j ð2þ

9 Strategic Voting in German Elections 641 This model is also called exploded logit (Chapman and Staelin 1982), as the ranking of the four parties is exploded into a sequence of three separate logit models. There is also a behavioural interpretation of equation (2): assume rank orderings as being generated by a process in which a voter first chooses her most preferred party from all available parties. From the remaining parties she again chooses his most preferred one, and so on, until there is only one party left in the choice set. Thus, an observed preference ordering can be understood as being generated by a repeated selection process in which an individual sequentially picks the best alternative from an ever shrinking choice set. Likewise, the probability of any given rank ordering can be expressed as a product of multinomial logit probabilities. Let S denote voter i s choice set containing J parties j ¼ 1, 2,..., J, and let r ¼ 1, 2,..., R denote the preference ranks i assigns to the parties in S. Then, for any preference ordering O, the rank ordered logit model is given by: PrðO j SÞ ¼ YR 1 exp V jr ½Š P J l¼r exp V ð3þ j½lš r¼1 (Beggs et al. 1981; Chapman and Staelin 1982; Hausman and Ruud 1987; Allison and Christakis 1994; Skrondal and Rabe-Hesketh 2003, Train 2003). Mathematically, multinomial logit can be considered a special case of rank ordered logit: when only one alternative is ranked first and all other alternatives remain unranked (3) reduces to a multinomial logit model. 6 Estimation of the rank ordered logit model is carried out by maximum likelihood estimation. The likelihood function is obtained by taking the product of (3) over all observed preference orderings. Interpretation of results (i.e. logit coefficients, odds ratios, predicted probabilities) is identical to multinomial logit, with the exception that the outcome to be explained is not the probability of choosing party j, but the probability that party j is most preferred (or ranked first). 7 So far we have assumed that each voters preferences are complete and strictly transitive, i.e. that every party in S is assigned a unique rank. However, rank ordered logit analysis is not restricted to this type of preference ordering. Allison and Christakis (1994) discuss these issues in detail and propose some modifications of the model to incorporate ties in preference rankings as well as incomplete rankings. 8 Rank ordered logit and multinomial logit are not different behavioural models but are based on the same random utility framework. Both models aim at estimating an underlying utility function that accounts either for the voting decision or for voter preference. Thus, it is possible to use rank ordered logit in order to estimate a utility ^V ij of each party for individual voters that accounts for voters sincere party preferences, conditional on such variables as retrospective evaluation of government performance or party policy distances, and then reuse those estimates of cardinal utility for a subsequent multinomial logit analysis of strategic voting behaviour, by

10 642 S. Shikano et al. further conditioning on voters expectations about parties electoral success. This approach differs significantly from previous applications in which party preferences are treated as exogenous and are directly used as proxy for utility. Instead, the approach above allows us to incorporate other theoretically relevant variables, thus combining sincere and strategic voting in one empirical model of voter behaviour. In the following we will apply this framework to explain strategic list voting in German federal elections. Testing for Strategic PR Voting in the 1994 German Federal Election Hypotheses Strategic PR voting mainly implies that supporters of a major party cast their party list vote for the prospective junior coalition partner in order to help it overcome the 5 per cent threshold, a phenomenon that is also known as Leihstimme (lend vote) (Pappi and Thurner 2002). The 1994 Bundestag election provides an appropriate context to test for this kind of behaviour. In the previous period, the governing coalition was formed by the CDU and FDP. Both parties asserted beforehand their willingness to keep up with the coalition for another election period. An alternative pre-electoral coalition was declared by SPD and Greens, respectively. The former communist Party of Democratic Socialism (PDS), however, a party, which obtained about as many seats as the FDP or Greens, was excluded from pre-electoral coalition formation. One may argue that this is not applicable to East German voters since the PDS had supported the formation of a minority coalition of the SPD and Greens in an East German federal state (Saxony-Anhalt) a couple of months prior to the 1994 election. This is, however, the unique exception at that time and not comparable with the other federal states where the FDP and the Greens have been established coalition partners of the CDU and SPD, respectively. Hence, the PDS was not considered a real option for strategic voting by large party supporters seeking to ensure a majority coalition. Taking these arguments together, we expect the FDP and Greens to be more likely to attract strategic votes if voters are unsure about their entry into parliament. We do not expect this effect for the PDS, as it was not part of any pre-electoral coalition. Restated in terms of our two-stage modelling framework, we expect that, in the second stage, the (expected) utility of strategically voting for the FDP or Greens should be higher for voters who are not certain about the respective party s entry into parliament than for other voters. Data and Measurement Voter preference can be measured in various ways: For example, one could ask respondents directly about their most preferred party, their second most

11 Strategic Voting in German Elections 643 preferred party, etc. Such questions are rarely asked in election surveys. Essentially the same information is contained in reactions to party feeling thermometers. Therefore, researchers often construct party rankings from feeling thermometer scores or treat thermometer scores as cardinal measures of party/candidate utility. In general this approach is acceptable in the absence of other measures of voter preference. However, we will rely on a more thorough measurement of preferences asking survey participants for a pairwise comparison of all combinations of parties (see Pappi and Eckstein 1998). The main advantage of this approach, compared with thermometer-based measurements, is that it allows for intransitivity in voter preferences. 9 While transitive preferences are a necessary assumption underlying all strategic voting research, the extent to which this assumption actually holds remains an empirical question. In the usual feeling thermometer-based approach, transitivity of preferences is forced by the response format, which makes it impossible to discern transitive from intransitive preferences. To avoid artificial rankings by voters with intransitive preferences, we use paired comparison data which allow for identifying patterns of intransitivity or random response. Furthermore we expect paired comparisons to elicit sincere party preferences in a much more valid way than thermometer rankings. Research on strategic voting is essentially concerned with the deviation of the voting decision from party preference. Therefore it is crucial that preference measures are exogenous to the voting decision, i.e. that respondents who are unsure about their first preference do not anchor their response to their voting decision. Direct questions about party rankings, such as feeling thermometers, should bias responses more easily towards the voting intention and thus introduce a higher level of endogeneity than paired comparisons. 10 Accordingly, we will use survey data from the 1994 German federal election that contain paired comparisons of all combinations of following parties: 11 CDU (Christian Democrats), 12 SPD (Social Democrats), FDP (Liberals), the Greens and PDS (Socialists). The following question wording was used: In the following, I will provide you several times with the names of two parties and I would like to ask you to say which of the parties you prefer if you have to decide only between the two. CDU or SPD CDU or FDP... The Greens or PDS. Respondents either named the party they preferred or stated their indifference towards the two parties ( I can t decide ). Comparisons were sought for five parties; accordingly respondents stated their preference for 10 pairs of parties (5 6 4/2). Rank orderings were constructed for all respondents whose preference judgements were transitive and complete (cf. Pappi and Eckstein 1998). The percentage of those respondents was

12 644 S. Shikano et al. remarkably high in West Germany with 79.5 per cent and somewhat lower in East Germany with 72.1 per cent. From this group of respondents we had to further subtract those that did not provide information on their voting decision. 13 Also not considered in the analysis are respondents who are completely indifferent between all five parties, which leaves us with a final sample of 1013 West German and 234 East German respondents. Results To get an impression of the distribution of stated preferences and stated choices in the data consider Table 1 which gives relative frequencies of stated preferences and stated party choice for PR votes in the East and West German sample, respectively. As a reference, we also include vote shares for the district vote, although in this article we are mainly concerned with the PR vote. Actually, there is a clear regularity between preference and choice: parties shares of first preferences are, except for the PDS in East Germany, always between that of PR and district votes. The two large parties CDU and SPD receive more votes for their district candidates than would be expected from their share of first preferences. Conversely, small parties receive more PR votes than their shares of first preference indicate. Hence there are deviations of voters stated choices from their stated party preferences. Furthermore, we can observe differences between East and West German voters with respect to their preferences for CDU and PDS. Specifically in the East German sample, voters preferences for CDU and PDS show a bimodal pattern, with each party scoring high on first and last preference but much lower on intermediate preference ranks. In the West German sample preferences for CDU and PDS are distributed rather unimodally, with CDU being mostly in first rank and PDS predominantly in fifth. This suggests a stronger polarisation of the East German electorate with respect TABLE 1 FREQUENCIES OF STATED CHOICE AND STATED PREFERENCE (%) List Vote District Vote 1st 2nd Preference 3rd 4th 5th West (n ¼ 1013) CDU/CSU SPD FDP Greens PDS East (n ¼ 234) CDU SPD FDP Greens PDS

13 Strategic Voting in German Elections 645 to a left right ideological dimension, where the CDU takes a conservative right-most and the PDS a left-most position. The relationship between vote choice and party preference is further clarified by looking at their bivariate distribution, which is given in Table 2. The row marginals of the individual tables give the number of respondents who cast their list/district vote for their first, second, third, etc. preference, respectively. About per cent of all voters deviated from their first TABLE 2 JOINT DISTRIBUTION OF VOTE CHOICE AND PREFERENCE West Germany PR Vote 1st 2nd 3rd 4th 5th Total CDU/CSU SPD FDP Greens PDS Total Deviation from first preference: 17.6%. District Vote 1st 2nd 3rd 4th 5th Total CDU/CSU SPD FDP Greens PDS Total Deviation from first preference: 13.2%. East Germany PR Vote 1st 2nd 3rd 4th 5th Total CDU SPD FDP Greens PDS Total Deviation from first preference: 21.4%. District Vote 1st 2nd 3rd 4th 5th Total CDU SPD FDP Greens PDS Total Deviation from first preference: 12%.

14 646 S. Shikano et al. preference when they cast their vote, which suggests a substantial amount of strategic voting. Most of those who deviate from their first preference cast their vote for their second most preferred party or party district candidate. Therefore, we need to take at least voters second preference into consideration to model their vote choice. Interestingly, the PR vote shows a higher degree of deviation from the first preference than the district vote. 14 Thus, the district vote corresponds more closely to voters preferences over party lists than the PR vote. This finding should be counter-intuitive for those assuming that the PR vote more closely reflects voter preferences than the district vote. It is not so surprising, however, if one expects strategic voting on the PR ballot as well. If strategic voting occurs on both ballots, then there is nothing that would prevent defection rates from being higher on the PR vote than on the district vote. In particular, preferences could be distributed in favour of larger parties but some of the larger parties adherents could vote for small parties for strategic reasons. Thus, a substantive amount of small party voters, for example FDP voters, might actually prefer the larger potential coalition partner but cast a strategic vote to increase the chances for a particular coalition to form. To test for this kind of strategic voting, we model first voters stated preferences with rank ordered logit in order to obtain individual utility estimates ^V ij for each voter and each party (linear prediction: ^b 0 x). We assume that party preference formation is determined by retrospective as well as prospective considerations. Correspondingly, the independent variables used in the first step are respondents retrospective judgement of government work (1: satisfied; 0: not satisfied) and absolute policy distances between voters and parties on the following three issues: bugging operations, highway speed limit and job-creation programmes. For each issue respondents were asked for their individual positions as well as the position of all parties on a seven point scale. In the second step, PR vote was modelled with conditional logit on the basis of the estimated utility values and voters beliefs about the entry into parliament of the FDP and Greens. 15 For rank ordered logit estimation we used voter preferences with varying lengths. Results are given in the appendix. To account for possible voter heterogeneity, estimations were conducted separately for East and West German respondents. We ran several analyses on the basis of first preference only, first and second preference, first to third preference and for the full rank order of parties. Using first preference only reduces the analysis to a simple multinomial logit model. With the inclusion of later preference ranks the estimation equation is exploded to include those additional selection stages as well. One reason not to rely on voters full rank orderings is that the accuracy of their judgements may decrease with lower preference. For instance, a voter may be certain about her most preferred and second most preferred parties but hold only diffuse preferences among less preferred parties. In particular, a German voter usually casts two votes in an election which may

15 Strategic Voting in German Elections 647 promote the formation of a clear first and second preference, but not necessarily an elaboration of a definite preference ordering for all parties. The fact that, since 1957, federal governments in Germany have been twoparty coalitions may further contribute to this tendency. On the other hand, if strategic PR voting is to mean anything, then it would be at least voting for a second preference party in order to improve the outcome in terms of the coalition that will form. 16 Thus, while we cannot be certain that voters hold clear preferences beyond their stated first and second preference, a minimal requirement for strategic voting is that voters hold a clear preference between their top two choices. Their assignment of lower ranks may, however, involve more randomness which would cause coefficient estimates based on lower ranks to be closer to zero than those based on higher ranks (Chapman and Staelin 1982; Allison and Christakis 1994). An informal way to assess this kind of heteroscedasticity across preference rankings, suggested by Chapman and Staelin, is to plot values of model fit, such as McFadden s R 2, from the individual model estimations and look for sharp decreases between ranking stages. In Figure 2 we plot McFadden s pseudo R 2 for different depths of preference in order to know up to which rank we should take preference into consideration. As can be seen, pseudo R 2 declines constantly with longer preference rankings, which suggests that the assignment of later ranks is less well captured by our model than the assignment of earlier ranks. Furthermore, model estimations for the West German sample show a larger decline of pseudo R 2 between the second and third ranking stage. This suggests terminating the analysis of preference after second rank. Accordingly, in the first step, we rely only on ranks one to three, i.e. on the first two ranking stages. 17 In using estimation results from rank ordered logit in the second step, we have to note that the estimated utility should not be regarded as a point estimate but as an estimated distribution. Simply taking the estimated values as measures for voter utility in the second step would assume that we knew these values with certainty. This would be no problem if we were only interested in obtaining parameter estimates. Generally, such estimates would be unbiased, however their standard errors would be too small. Because there is estimation error and hence uncertainty in our estimates from the first step, we need to ensure that some of this uncertainty is carried over into the second step analysis to avoid artificially deflated standard errors. Therefore, we drew 1000 coefficient vectors from a normal distribution with mean vector ^b and variance covariance matrix equal to the variance covariance matrix of the estimated coefficients. For each set of coefficients (i.e. each coefficient vector) we computed predicted voter utilities for each party and used these values in order to model the vote choice with multinomial logit. Hence the vote choice estimation is repeated 1000 times, each time with different predicted values for party utility and each time yielding different coefficient values and associated standard errors. Results

16 648 S. Shikano et al. FIGURE 2 McFADDEN S PSEUDO R 2 FOR DIFFERENT DEPTH OF PREFERENCE from those 1000 estimations are then combined according to Rubin s rules to yield the quantities of interest, i.e. coefficients and their respective standard errors. According to Rubin (1987), the unbiased parameter estimate from a series of multiply imputed datasets is simply the mean of the individual parameter estimates. 18 The unbiased variance of the parameter estimate is the mean of the individual parameter variances within each dataset plus the variance of the parameter estimates between datasets, with an adjustment for the number of imputations, s 2 ¼ 1 X M k s2 k þ 1 þ 1 M 1 M 1 X ^b k k b 2 ð4þ (cf. Allison 2001; King et al. 2001), where M denotes the number of replications k, s the standard error of a given coefficient estimate ^b, and b the mean coefficient estimate across all M datasets. Table 3 summarises the estimation results for West German voters. Model 1 measures utility generically for every party assuming the impact

17 Strategic Voting in German Elections 649 TABLE 3 RESULTS FROM REPEATED a ESTIMATION OF MULTINOMIAL LOGIT DEPEN- DENT VARIABLE: VOTE INTENTION FOR PARTY LIST WEST GERMAN SAMPLE (N ¼ 1313) Model 1 Model 2 Model 3 Coef. SE Coef. SE Coef. SE Constant b SPD FDP Greens PDS Utility CDU SPD FDP Greens PDS Interaction with uncertainty FDP Greens PDS a Number of replications: b Reference category: CDU. (coefficient) of party utility on party choice to be constant across parties. The coefficient is significant (p 5.05), which suggests that our estimates of voters party preferences predict the vote intention well. Model 2 allows the effect of utility on party choice to vary across alternatives, by estimating separate alternative-specific coefficients of voter utility for each party. Comparing coefficients with each other, the value for the FDP stands out as relatively low. This suggests that the vote for the FDP is motivated less by sincere party preference than the vote for the other parties. In contrast, the vote for the Greens seems to be more strongly driven by sincere preferences. In order to test whether this lower coefficient for the FDP can be balanced off by accounting for strategic voting based on the expectation that the FDP enters parliament, we add interaction terms between utility and the entry expectation for the FDP as well as for the other two small parties, Greens and PDS. Respondents were asked: How likely do you assess the entry of FDP/Greens/PDS into the Bundestag to be?, with answers on a five point scale ranging from very unlikely to very likely. Answers falling in the middle category were taken as an indication of uncertainty. The expectation variable is thus coded 1 if respondents are uncertain about the entry of the respective party and 0 otherwise. In accordance with the Leihstimmen (lendvote) hypothesis we expect a positive coefficient for this interaction term for FDP and Greens, respectively (see section two above), while we do not expect a significant interaction for PDS as they were not part of any preelectoral coalition.

18 650 S. Shikano et al. The estimation result of Model 3 confirms our hypotheses with regard to the FDP and the PDS vote, but not with regardtothegreenvote.voterswhoare uncertain about the FDP s entry into parliament are more likely as compared with other voters to cast their PR vote for this party, as indicated by the significant (p ) interaction coefficient for the FDP. 19 The interaction coefficient for the PDS does not reach statistical significance, which is as expected, since the PDS was not part of a pre-electoral coalition and hence should not attract strategic PR votes. Our expectations are not confirmed, however, for the Green vote, as indicated by the insignificant interaction term. This might be due to the fact that in 1994, the Greens formed for the first time a pre-electoral coalition with the SPD at the federal level. So far, they had traditionally been in opposition to the established party system. Therefore, the Greens may not yet have been considered as a mature partner for SPD in a coalition government. Conversely, the FDP, at that time, had been in office with the CDU for three election periods, making it a credible option for strategic list voting. 20 Discussion This study aimed at providing evidence for strategic list voting in German Bundestag elections by applying an innovative modelling framework. Previous research often inferred the extent of strategic list voting from split-ticket voting, i.e. voting for a district candidate of a major party and for a small party list. Such reasoning, however, runs the risk of confounding strategic voting on the party list ballot with strategic voting on the district ballot two entirely different notions of strategic voting that are both present in mixed electoral systems. The framework presented in this paper departs from previous studies by considering the party PR vote alone. Furthermore, we allowed for the incorporation of (in-)complete preference orders and vote choice within the same discrete choice model. Our analysis shows that this approach works well in predicting strategic list voting in German federal elections. In particular, it can be shown that German voters adjust their voting behaviour with regard to the future governmental alternatives as presented to them by informal pre-electoral coalitions of CDU together with FDP. Uncertainty about the FDP s entry into parliament the junior partner of the CDU in a prospective coalition government made voters more likely to vote for the FDP than voters who were certain about the FDP s entry into parliament. Due to the peculiar data requirements of our theoretical argument, our analysis had to be restricted to one particular election. However, the mechanism of strategic list voting which we propose, should apply to most of the German Bundestag elections, before and after In the election of 1994 the Green party, for the first time, announced a pre-electoral commitment towards the SPD. Before, the only small party forming any pre-electoral coalition was the FDP. This might explain why we found evidence of strategic voting for the FDP but not for the Green party. We would expect, though, that strategic voting for the Green party has

19 Strategic Voting in German Elections 651 increased since that time. In particular, after the 1998 election, the Green party for the first time assumed government together with the SPD. We would conjecture that the success of this coalition increased the amount of strategic voting among supporters of the SPD who previously might have been doubtful about the feasibility of such an alliance. While the focus of our paper was on strategic PR voting the modelling approach we have taken is not restricted to that particular form of strategic voting. It might also inform research on other forms of sophisticated voting. To see how, note that studies of strategic voting often assume voter behaviour to be guided by some sort of expected utility model, yet they differ in the extent to which they actually apply this model to empirical data. 21 Some studies deviate from the expected utility model by treating party preferences and voter expectations as independent determinants of the voting decision (cf. Alvarez and Nagler 2000; Alvarez et al. 2006; Blais et al. 2005). Thus, voter expectations of party/candidate success are additively combined with determinants of party utility, such as class, age, parties policy stands, etc. While the use of appropriate statistical methods like (multinomial) logit allows for obtaining a cardinal measure of expected utility based on the ordinal measure of the determinants, it clearly deviates from the theoretical model which supposes the multiplicative interaction of utility and expectation. However, in order to multiply utility by expectation, one needs a cardinal measure of utility. Other approaches interpret party preference as measured by so-called feeling thermometer scores as a cardinal measure of utility (Cain 1978; Ordeshook and Zeng 1997), or construct it from proxy variables such as party identification (Gschwend 2007; Karp et al. 2002). In doing so, one imposes the strong assumption of cardinal utility measurement which requires that thermometer scores are comparable between individuals (such that, for example, a value of two means the same thing for every voter). In addition, measurement is also assumed to be free of error as party identification and feeling thermometers are treated as direct measures of utility. The framework we have presented does not suffer from these problems and most closely resembles the form of an expected utility model. We would, therefore, suggest it as a research design for studying strategic voting under other electoral rules as well, such as first-past-the-post as in Britain and Canada, or other mixed electoral rules as, for example, in New Zealand or Italy. Acknowledgements We thank Alexander Herzog and two anonymous reviewers for helpful comments. Notes 1. According to the authors the same logic holds, of course, for the case of moderate-left voters expecting a centre-right government.