Equivariant retracts and a topological social choice model

Abstract

In this paper we use the equivariant theory of retracts to give some results about the topological social choice theory. One of them is an equivariant version of the Chichilnisky-Heal Impossibility Theorem when a compact group acts on the preferences space. We also improve one result about the preservation of equivariant ANR's by symmetric powers, which is related to a geometrical characterization of the impossibility of social choice rules on the circumference due to Candeal and Indurain.