Stability and Coordination in Duverger's Law: A Formal Model of Preelection Polls and Strategic Voting

This paper investigates the dynamics of the “wasted vote” phenomenon and Duverger's Law. I construct a theoretical model in order to consider how preelection polls serve to inform the electorate about the relative chances of the candidates and how that information acts over time to decrease the support of the trailing candidate. The results shed light on how public opinion polls can aggregate information in the electorate and coordinate voters on the viable candidates in the election. Specifically, I show that in a Bayesian game model of strategic voting there exist non-Duvergerian equilibria in which all three candidates receive votes (in the limit). These equilibria require extreme coordination, however, and any variation in beliefs leads voters away from them to one of the Duvergerian equilibria. Thus, non-Duvergerian equilibria are unstable, while two-party equilibria are not. In addition, I describe how preelection polls provide information to voters about the viability of candidates and can thus be used by voters to coordinate on a Duvergerian outcome.

[1]  W. Riker,et al.  The Number of Political Parties: A Reexamination of Duverger's Law , 1976 .

[2]  Darrell M. West,et al.  Polling effects in election campaigns , 1991 .

[3]  M. Duverger.  Political Parties Their Organization and Activity in the Modern State , 1964 .

[4]  G. Cox.  Strategic Voting Equilibria under the Single Nontransferable Vote , 1994, American Political Science Review.

[5]  D. Hill,et al.  The Political Consequences of Electoral Laws , 1969 .

[6]  John H. Aldrich.  Before the Convention: Strategies and Choices in Presidential Nomination Campaigns , 1980 .

[7]  Joseph L. Bernd,et al.  Mathematical applications in political science , 1976 .

[8]  Thomas R. Palfrey,et al.  A mathematical proof of Duverger's Law , 1988 .

[9]  John O. Ledyard,et al.  The pure theory of large two-candidate elections , 1984 .

[10]  Matthew Soberg Shugart,et al.  Seats and Votes: The Effects and Determinants of Electoral Systems , 1989 .

[11]  John H. Aldrich,et al.  Third-Party and Independent Candidates in American Politics: Wallace, Anderson, and Perot , 1995 .

[12]  Thomas A. Rietz,et al.  An experiment on coordination in multi-candidate elections: The importance of polls and election histories , 1993 .

[13]  J. Harsanyi.  Games with Incomplete Information Played by 'Bayesian' Players, Part III. The Basic Probability Distribution of the Game , 1968 .

[14]  John P. Georges,et al.  Optimal sophisticated voting strategies in single ballot elections involving three candidates , 1993 .

[15]  Thomas R. Palfrey,et al.  Laboratory research in political economy , 1991 .

[16]  Henry E. Brady.  Knowledge, Strategy, and Momentum in Presidential Primaries , 1993, Political Analysis.

[17]  P. H. Argersinger.  "A Place on the Ballot": Fusion Politics and Antifusion Laws , 1980 .

[18]  Jerome H. Black,et al.  The Multicandidate Calculus of Voting: Application to Canadian Federal Elections , 1978 .

[19]  Larry M. Bartels.  Presidential Primaries and the Dynamics of Public Choice , 1988 .

[20]  W. Riker,et al.  The Two-party System and Duverger's Law: An Essay on the History of Political Science , 1982, American Political Science Review.

[21]  H. Simon,et al.  American Association for Public Opinion Research Bandwagon and Underdog Effects and the Possibility of Election Predictions , 2009 .

[22]  T. Feddersen,et al.  A Voting Model Implying Duverger's Law and Positive Turnout , 1992 .

[23]  Peter C. Ordeshook,et al.  Models of strategic choice in politics , 1989 .

[24]  A. Downs.  An Economic Theory of Democracy , 1957 .

[25]  Arend Lijphart,et al.  Electoral Systems and Party Systems , 1994 .

[26]  R. Weber,et al.  A Theory of Voting Equilibria , 1993, American Political Science Review.

[27]  Peter C. Ordeshook,et al.  Elections with limited information: A fulfilled expectations model using contemporaneous poll and endorsement data as information sources , 1985 .

[28]  Bernard Grofman,et al.  Electoral Laws and Their Political Consequences , 1986 .

[29]  H. Rosenthal,et al.  Digitized by the Internet Archive in 2011 With^ Funding from Testing Game-theoretic Models of Free Riding: New Evidence on Probability Bias and Learning , 2022 .

[30]  Tom W. Smith.  THE FIRST STRAW? A STUDY OF THE ORIGINS OF ELECTION POLLS , 1990 .

[31]  Stephen Wright,et al.  Plurality and runoff systems and numbers of candidates , 1989 .

[32]  W. Riker,et al.  Liberalism Against Populism: A Confrontation Between the Theory of Democracy and the Theory of Social Choice , 1982 .

[33]  Alex Cukierman,et al.  Asymmetric information and the electoral momentum of public opinion polls , 1991 .