Candidate Stability and Probabilistic Voting Procedures

Resumen

We extend the study by Dutta, Jackson and Le Breton (Econometrica, 2001) of the strategic incentives of the candidates to withdraw their candidacy to probabilistic environments. A probabilistic voting procedure is a rule that for each set of candidates at stake and each profile of voters� preferences selects a lottery on the set of candidates. It is exit stable if a candidate never benefits by leaving the fray unilaterally. It is candidate stable at a given agenda if no running candidate has incentives to quit. We assume that the candidates are Expected Utility maximizers and show that any exit stable and unanimous probabilistic voting procedure is a probabilistic combination of dictatorial rules. The results for candidate stability depend on the size of the agenda. If there are at least four initial candidates, candidate stability implies the selection to be consistent with a random dictatorship whenever a candidate quits, but this is not the case when all the candidates are at stake. However, when there are only three candidates, sub-additive distributions of the veto power are also admitted.