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

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