The Theory of Fixed Agenda Social Choice Correspondences

The theory of fixed-agenda social choice correspondences studies the properties of correspondences mapping profiles of individual preferences into nonempty subsets of the set of alternatives. Unlike the classical theory, the output of the aggregation exercise is a social choice (or choices) rather than a social ordering of the alternatives. Although this is an intuitive approach to social choice, many of the classical impossibility theorems in the relational framework have counterparts in the correspondence framework. These results depend critically on the way the independence axiom is formulated in this framework. We propose a new independence condition which is logically weaker than Denicolo’s Independence condition, and logically independent of his Weak Independence condition. We call this condition S-independence. Assuming S-independence, we characterize all social choice correspondences satisfying strong Pareto, anonymity and neutrality. We call these correspondences S-correspondences as they are closely related to the S-rules of Bossert and Suzumura. Finally, we provide an argument for S-independence based on a novel approach to rationalizability.

This is one of a series of seminars in the Whitaker Ideas Forum. Ashley will be representing the Group Decision Making Cluster.