Strategy-Proofness of Voting Rules Under Voter Beliefs

Abstract

We use the notion of ordinal Bayesian incentive compatibility (OBIC) to study vote manipulation in the setting where voters possess probabilistic beliefs on how others will vote. We consider the general family of positively correlated beliefs where the manipulator believes that her top-ranked candidate is more likely to win against other candidates (top skewed) and her bottom-ranked candidate is more likely to lose against other candidates (bottom skewed). Under such beliefs that satisfy both the top skewed and bottom skewed conditions, our results present plurality as the only positional scoring rule that is OBIC. Compared to related work on OBIC characterizations, the conditions of top skewed and bottom skewed that we provide are weak sufficient conditions that describe a large family of realistic voter beliefs. To illustrate this, we show that the classical Mallows model produces posterior beliefs that are both top skewed and bottom skewed.