The topological approach to the aggregation of preferences

(1) A domain of preferences allows for topological aggregation for each number of people if and only if this domain of preferences is contractible. (2) The combination of continuity and the Pareto principle implies the existence of a unique manipulator. (3) Arrow’s theorem can be translated into the previous statement. All of these results are obtained via algebraic topology. This paper introduces some of the tools developed in topology and applies them upon the problem of preference aggregation. This paper is based upon a lecture given at the conference “Mathematical aspects of social choice”, CREM, Université de Caen and CNRS, November 8–10, 2004. I thank the organizers Maurice Salles and Vincent Merlin for their warm hospitality, and the participants for the stimulating discussion. I am indebted to Bart Capéau and Roeland Vervenne for helpful remarks. I thank the referee for combining speed and quality.