A note on Condorcet consistency and the median voter

Abstract

We discuss to which extent the median voter theorem extends to the domain of single-peaked preferences on median spaces. After observing that on this domain a Condorcet winner need not exist, we show that if a Condorcet winner does exist, then it coincides with the median alternative ('the median voter'). Based on this result, we propose two non-cooperative games that implement the unique strategy-proof social choice rule on this domain. --