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 preferences, which govern their behavior when their vote cannot affect the election outcome. Specifically, we study two models that have been recently considered in the literature: lazy voters, who prefer to abstain when they are not pivotal, and truth-biased voters, who prefer to vote truthfully when they are not pivotal. We extend prior work by investigating the behavior of both lazy and truth-biased voters under different tie-breaking rules (lexicographic rule, random voter rule, random candidate 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 impact of 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 computational problems. Our results extend to settings where some of the voters may be non-strategic. 
Edith Elkind and Evangelos Markakis and Svetlana Obraztsova and Piotr   Skowron
cs.GT