Robust Political Equilibria in Plurality and Runoff Voting Games

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.