Poisson Games, Strategic Candidacy, and Duverger's Law

Abstract

Duvergers law predicts a long-run two-candidate stable outcome under a plurality voting system. The waste vote argument explains the law by emphasizing strategic voters' tendency to abandon candidates commonly perceived to have the least support. However, the argument does not apply to cases where two or more candidates have the same least expected equilibrium vote share, so there is no unique candidate to abandon and a three-candidate equilibrium outcome is possible. We show that the incentive of candidates to strategically withdraw from elections in order to avoid extreme outcomes eliminates such non-Duvergerian equilibria. We model the election situation as a two-stage game where candidates first make strategic entry decisions, followed by plurality voting, which is modeled as a Poisson game a la Myerson (2000). In this framework with strategic voting, strategic candidacy, and uncertainty about voter preferences, Duverger's law is obtained except when there exists a Condorcet winner.

Keywords: Duverger's law, plurality voting, Poisson game, strategic voting, strategic candidacy, risk aversion, Condorcet winner

JEL Classification: D72