The Core In Fuzzy Spatial Models

Predictions concerning voting outcomes in crisp spatial models rely heavily on the existence of a core, in the absence of which political players choosing among a set of alternatives by majority rule will not be able to arrive at a stable choice. No matter which option they might initially choose, most voting rules will permit another option to defeat the previously chosen one. Such problems particularly plague majority rule spatial models at dimensionalities greater than one. In a series of recent papers, we have argued that fuzzy spatial models offer a partial solution to this problem. In this paper, we explore the existence of a fuzzy core. Our major conclusion is that a fuzzy core is more likely in two or more dimensions as the number of players increases.