Robust Political Equilibria Under Plurality and Runoff Rule

Abstract

A central problem for the game theoretic analysis of voting is that voting games have very many Nash equilibria. In this paper, we consider a new refinement concept for voting games that combines two ideas that appear reasonable for voting games: First, trembling hand perfection (voters sometimes make mistakes when casting their vote) and second, coordination of voters with similar interests. We apply this refinement to an analysis of multicandidate elections under plurality rule and runoff rule. For plurality rule, we show that our refinement implies Duverger's law: In all equilibria, (at most) two candidates receive a positive number of votes. For the case of 3 candidates, we can completely characterize the set of equilibria. Often, there exists a unique equilibrium satisfying our refinement; surprisingly, this is even true, if there is no Condorcet winner. We also consider the equilibria under a runoff rule and analyze when plurality rule and runoff rule yield different outcomes.