Equilibria of Plurality Voting with Abstentions

TL;DR

This paper models plurality voting with abstentions as a strategic game, analyzing Nash equilibria in simultaneous and sequential voting scenarios, revealing computational complexity and complex equilibrium behaviors.

Contribution

It introduces a game-theoretic framework for plurality voting with abstentions, characterizes equilibrium existence, and analyzes differences between simultaneous and sequential voting.

Findings

Pure Nash equilibria exist under certain preference profiles.

Checking equilibrium conditions is computationally hard.

Sequential voting equilibria can be counterintuitive with multiple candidates.

Abstract

In the traditional voting manipulation literature, it is assumed that a group of manipulators jointly misrepresent their preferences to get a certain candidate elected, while the remaining voters are truthful. In this paper, we depart from this assumption, and consider the setting where all voters are strategic. In this case, the election can be viewed as a game, and the election outcomes correspond to Nash equilibria of this game. We use this framework to analyze two variants of Plurality voting, namely, simultaneous voting, where all voters submit their ballots at the same time, and sequential voting, where the voters express their preferences one by one. For simultaneous voting, we characterize the preference profiles that admit a pure Nash equilibrium, but show that it is computationally hard to check if a given profile fits our criterion. For sequential voting, we provide a complete analysis of the setting with two candidates, and show that for three or more candidates the equilibria of sequential voting may behave in a counterintuitive manner.