Topological Aggregation of Preferences: The Case of a Continuum of Agents

Abstract

This paper studies the topological approach to social choice theory initiated by G. Chichilnisky (1980), extending it to the case of a continuum of agents. The social choice rules are continuous anonymous maps defined on preference spaces which respect unanimity. We establish that a social choice rule exists for a continuum of agents if and only if the space of preferences is contractible, extending an earlier result of Chichilnisky and Heal. We provide also a topological characterization of such rules as generalized means or mathematical expectations of individual preferences.

JEL Classification: D71, D60