Monotonicity and Candidate Stable Voting Correspondences

Dutta, Jackson and Le Breton (Econometrica, 2001) initiates the study of strategic candidacy. A voting procedure satisfies candidate stability if no candidate has incentives to withdraw her candidacy in order to manipulate the voting outcome in her favor. Dutta et al. (2001) shows that a single valued voting procedure satisfying candidate stability and unanimity must be dictatorial if voters have strict preferences and candidates cannot vote. Eraslan and McLennan (JET, 2004) extends this result to a framework that allows weak preferences and multi-valued voting procedures (voting correspondences). They obtain the existence of a serial dictatorship under a stronger version of candidate stability. We show that voting correspondences satisfying strong candidate stability and unanimity are monotonic, that is, if a winning candidate's position is weakly improved in all voters' preference rankings, then the candidate remains a winner. Monotonicity provides a direct link between the standard dictatorship in Dutta et al. (2001) and the serial dictatorship in Eraslan and McLennan (2004). Using this particular property of voting correspondences, we provide an alternative proof to Eraslan and McLennan's result.