Plurality Voting under Uncertainty

TL;DR

This paper extends a behavioral game-theoretic model of strategic voting under uncertainty in Plurality voting, proving equilibrium existence and convergence in more general settings, and analyzing regret-minimization behavior.

Contribution

It generalizes previous models by considering varied uncertainty levels, simultaneous decisions, and broader best-response notions, establishing equilibrium existence and convergence guarantees.

Findings

Existence of voting equilibrium in the most general case.

Guaranteed convergence of iterative voting processes.

Behavioral differences between regret-minimization and best-response strategies.

Abstract

Understanding the nature of strategic voting is the holy grail of social choice theory, where game-theory, social science and recently computational approaches are all applied in order to model the incentives and behavior of voters. In a recent paper, Meir et al.[EC'14] made another step in this direction, by suggesting a behavioral game-theoretic model for voters under uncertainty. For a specific variation of best-response heuristics, they proved initial existence and convergence results in the Plurality voting system. In this paper, we extend the model in multiple directions, considering voters with different uncertainty levels, simultaneous strategic decisions, and a more permissive notion of best-response. We prove that a voting equilibrium exists even in the most general case. Further, any society voting in an iterative setting is guaranteed to converge. We also analyze an alternative behavior where voters try to minimize their worst-case regret. We show that the two behaviors coincide in the simple setting of Meir et al., but not in the general case.