SINGLE PEAKED FUZZY PREFERENCES IN ONE-DIMENSIONAL MODELS: DOES BLACK'S MEDIAN VOTER THEOREM HOLD?

Black's Median Voter Theorem is among the more useful mathematical tools available to political scientists for predicting choices of political actors based on their preferences over a finite set of alternatives within an institutional or constitutional setting. If the alternatives can be placed on a single-dimensional continuum such that the preferences of all players descend monotonically from their ideal point, then the outcome will be the alternative at the median position. We demonstrate that the Median Voter Theorem holds for fuzzy preferences. Our approach considers the degree to which players prefer options in binary relations.