Spatial models, cognitive metrics, and majority rule equilibria

Long-standing results demonstrate that, if policy choices are defined in spaces with more than one dimension, majority-rule equilibrium fails to exist for a general class of smooth preference profiles. This article shows 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 and it provides necessary and sufficient conditions for the existence of such an equilibrium. This is important because city block preferences accord more closely with empirical research on human perception than do many smooth preferences. It implies that, if 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.