Empirical analysis of plurality election equilibria

Abstract

Voting is widely used to aggregate the different preferences of agents, even though these agents are often able to manipulate the outcome through strategic voting. Most research on manipulation of voting methods studies (1) limited solution concepts, (2) limited preferences, or (3) scenarios with a few manipulators that have a common goal. In contrast, we study voting in plurality elections through the lens of Nash equilibrium, which allows for the possibility that any number of agents, with arbitrary different goals, could all be manipulators. This is possible thanks to recent advances in (Bayes-)Nash equilibrium computation for large games. Although plurality has numerous pure-strategy Nash equilibria, we demonstrate how a simple equilibrium refinement---assuming that agents only deviate from truthfulness when it will change the outcome---dramatically reduces this set. We also use symmetric Bayes-Nash equilibria to investigate the case where voters are uncertain of each others' preferences. This refinement does not completely eliminate the problem of multiple equilibria. However, it does show that even when agents manipulate, plurality still tends to lead to good outcomes (e.g., Condorcet winners, candidates that would win if voters were truthful, outcomes with high social welfare).