This is the pre-peer-reviewed version of the following article: Centripetal and Centrifugal Incentives under Different Electoral Systems Ernesto Calvo Timothy Hellwig Forthcoming in the American Journal of Political Science Abstract In a seminal article, Cox (1990) suggested that electoral systems with larger district magnitudes provide incentives for parties to advocate more extreme policy positions. In this article we put this proposition to the test. Informed by recent advances in spatial models of party competition, we introduce a design that embeds the effect of electoral rules in the utility function of voters. We then estimate the equilibrium location of parties as the weight voters attach to the expected distribution of seats and votes changes. Our model predicts that electoral rules affect large and small parties in different ways. We find centripetal effects only for parties that are favorably biased by electoral rules. By contrast, smaller parties see their vote share decline and are pushed toward more extreme equilibrium positions. Evidence from thirteen parliamentary democracies supports model predictions. Along with testing the incentives provided by electoral rules, results carry implications for the strategies of vote-maximizing parties and for the role of small parties in multiparty competition.11. Introduction1 Should parties change their policy goals under different electoral rules? Since Downs (1957) first proposed a model of centripetal incentives for a two-party system under plurality rule, scholars have worked to extend equilibrium models of voting to multiparty settings. Gary Cox’s (1990) study marks the beginning of contemporary research on the topic and, in many ways, remains the most detailed exposition of the spatial incentives provided by electoral institutions. Considering an almost exhaustive set of factors determining electoral rules—including district magnitude, aggregation formula, and ballot structure—Cox made predictions linking electoral laws to parties’ position-taking incentives expressed in terms of the dispersion of parties in policy space. Centripetal incentives (or “central clustering”) are said to prevail when the number of votes per voter is high but partial abstention is prohibited and when district magnitude is low. Centrifugal incentives (“ideological dispersion”) are encouraged by the inverse: few votes per voter, allowance of partial abstention, and high district magnitudes. Subsequent research on connections between electoral laws, party systems, and party positions has built on Cox’s insights both formally (e.g., Lin et al. 1999; McGann 2002; Merrill and Adams 2007) and empirically (e.g., Dow 2001; Ezrow 2005; 2008). 1 Both authors contributed equally to the paper. Earlier versions of this article were presented at the European Union Center for Excellence at Texas A&M University, July 2008, and at the 2009 Meeting of the Midwest Political Science Association. We thank Jim Adams, Gary Cox, Lawrence Ezrow, Garrett Glasgow, Jim Granato, Anna Mikulska, Maria Victoria Murillo, Jeff Milyo, Harvey Palmer, Iñaki Sagarzazu, and Guy Whitten for helpful comments. Supplementary information for this article, including data, code, and additional analyses, are available at www.gvpt.umd.edu/calvo or http://mypage.iu.edu/~thellwig.2 In this paper we advance this body of research by proposing a unified model which combines the insights of Cox and others on the mechanical properties of electoral rules with recent work on spatial models of party competition. Our model brings together, into a single utility function, the importance voters accord to their ideological proximity to parties and the weight they attach to parties being favorably or adversely affected by electoral rules. We show that the weight voters assign to mechanically-induced differences in parties’ expected seat shares leads to clear predictions about the expected equilibrium location of parties.2 More importantly, these predictions show that the centripetal and centrifugal effects of electoral rules affect large and small parties in very different ways. The gains from our approach are both theoretical and substantive. Theoretically, our model offers a more explicit set of micro-foundations for how electoral rules are incorporated in voter utility and, in turn, in the policies vote-maximizing parties propose in competitive elections. The utility model is flexible enough to account for heterogeneity in the effect of electoral rules on party strategies across and within different contexts. This flexibility has empirical payoffs: Consistent with what Downs and then Cox suggested, we find that the electoral system affects party equilibrium positions in unidimensional policy space. However, we show that the effect of electoral rules is contingent on party size. As in previous studies (e.g., Dow 2001), we find centripetal incentives for large parties that are favorably biased by electoral rules. But unlike previous work, we demonstrate centrifugal incentives for smaller parties that are penalized by electoral rules. Rules that reward large parties, lead not only to increases in vote shares but also to more moderate ideological positions. By 2 By (Nash) equilibrium we mean a set of party positions from which vote-maximizing parties have no incentive to deviate.3contrast, rules that penalize smaller parties push their policy preferences toward more extreme equilibrium locations. In other words, non-proportional rules “crowd out” smaller parties, who vacate the center of the policy space while winning parties moderate their policy stances. Because the utility function we adopt penalizes parties who win fewer seats than their vote share (Maurice Duverger’s well known psychological effect), our model converges with prior research, generating predictions in which plurality-like rules reduce the effective number of electoral parties (Duverger 1954; Amorim Neto and Cox 1997; Ordeshook and Shvetzova 1994). Our predictions for the equilibrium location of parties, however, lead to very different conclusions. We next present a model of voter utility and demonstrate how information about electoral rules updates this expected utility over K parties competing in the election. We then, in section 3, introduce the data to test our model empirically. Section 4 reports results for how electoral rules affect party equilibrium positions and electoral success. The