Candidate Stability and Nonbinary Social Choice

A voting procedure is candidate stable if no candidate would prefer to withdraw from an election when all of the other potential candidates enter. Dutta, Jackson, and Le Breton have recently established a number of theorems showing that candidate stability is incompatible with some other desirable properties of voting procedures. This article shows that Grether and Plott's nonbinary generalization of Arrow's Theorem can be used to provide a simple proof of Dutta, Jackson, and Le Breton's impossibility theorem for the case in which the voters and potential candidates have no one in common.