TOPOLOGICAL AGGREGATION OF PREFERENCES - THE CASE OF A CONTINUUM OF AGENTS

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