Equilibria of Plurality Voting: Lazy and Truth-Biased Voters

We present a systematic study of Plurality elections with strategic voters who,in addition to having preferences over election winners, have secondary prefer-ences, which govern their behavior when their vote cannot affect the election out-come. Specifically, we study two models that have been recently considered in theliterature [6, 17]: lazy voters, who prefer to abstain when they are not pivotal, andtruth-biased voters, who prefer to vote truthfully when they are not pivotal. We ex-tend prior work by investigating the behavior of both lazy and truth-biased votersunder different tie-breaking rules (lexicographic rule, random voter rule, randomcandidate rule). Two of these six combinations of secondary preferences and a tie-breaking rule have been studied in prior work. In order to understand the impactof different secondary preferences and tie-breaking rules on the election outcomes,we study the remaining four combinations. We characterize pure Nash equilibria(PNE) of the resulting strategic games and study the complexity of related compu-tational problems. Our results extend to settings where some of the voters may benon-strategic.