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Centripetal and Centrifugal Incentives under Different Electoral Systems


  • Ernesto Calvo is Associate Professor of Government and Politics, University of Maryland, 3144F Tydings Hall, College Park, MD 20742 ( Timothy Hellwig is Assistant Professor of Political Science, Indiana University, Woodburn Hall 210, Bloomington, IN 47405 (

  • Both authors contributed equally to the article. 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, Anna Mikulska, Jeff Milyo, Harvey Palmer, Iñaki Sagarzazu, and Guy Whitten for helpful comments. Supplementary information for this article, including data, code, and additional analyses, is available at

  • By (Nash) equilibrium we mean a set of party positions from which vote-maximizing parties have no incentive to deviate.


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 13 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.