Candidate Stability and Voting Correspondences

We extend the analysis of Dutta et al. (in Econometrica, 69:1013–1038, 2001) on strategic candidacy to multivalued environments. For each agenda and each profile of voters’ preferences over running candidates, a voting correspondence selects set of running candidates. A voting correspondence is candidate stable if no candidate ever has an incentive to withdraw her candidacy when all other potential candidates run for office. In the multivalued framework, candidates’ incentives to withdraw depend on candidates’ preferences over sets. If candidates cannot vote and they compare sets of candidates according to their expected utility conditional on some prior probability assessment, then a voting correspondence satisfies candidate stability and unanimity if and only if it is dictatorial. If the probability assessments are restricted to be uniform, candidates’ preferences over sets are consistent with leximin preferences, or candidates can vote, then possibility results are obtained.