Properties of consistent voting systems

Abstract

We consider exactly and strongly consistent voting functions where the alternative set is the set of real numbers and each person's preference ordering is determined by a utility function ¦x−x^*¦ wherex ^* is his most preferred alternative. We prove that a voting function which is continuous, anonymous, weakly Pareto, and strongly and exactly consistent must coincide with a class of generalized medians studied byMoulin [1978]. Thus, such a function is actually strategyproof. The continuity assumption can be weakened a little, but we give an example of a noncontinuous function which is strongly and exactly consistent, anonymous, and weakly Pareto, but is not strategyproof.