Spatial Models, Cognitive Metrics And Majority Voting Equilibria

Longstanding results demonstrate that, if policy choices are defined in spaces with more than one dimension, a majority rule equilibrium fails to exist for a very general class of smooth preference profiles. However we show here that if agents perceive political similarity and difference in “city block” terms, then the dimension-by-dimension median can be a majority rule equilibrium even in spaces with an arbitrarily large number of dimensions; we provide necessary and sufficient conditions for the existence of such an equilibrium. This result is important because city block preferences accord more closely with empirical research on human perception than do many smooth preference profiles. The implication is that, if the already extensive empirical research findings on human perceptions of similarity and difference extend also to perceptions of political similarity and difference, then the possibility of equilibrium under majority rule re-emerges, with implications for both non-cooperative and cooperative models of political