Independent social choice correspondences

Abstract

A fixed agenda social choice correspondence Φ on outcome set X maps each profile of individual preferences into a nonempty subset of X. If Φ satisfies an analogue of Arrow's independence of irrelevant alternatives condition, then either the range of Φ contains exactly two alternatives, or else there is at most one individual whose preferences have any bearing on Φ. This is the case even if Φ is not defined for any proper subset of X.