Fuzzy Black's Median Voter Theorem: Examining the Structure of Fuzzy Rules and Strict Preference

Under certain aggregation rules, particular subsets of the voting population fully characterize the social preference relation, and the preferences of the remaining voters become irrelevant. In the traditional literature, these types of rules, i.e. voting and simple rules, have received considerable attention because they produce non-empty social maximal sets under single-peaked preference profiles but are particularly poorly behaved in multi-dimensional space. However, the effects of fuzzy preference relations on these types of rules is largely unexplored. This paper extends the analysis of voting and simple rules in the fuzzy framework. In doing so, we contribute to this literature by relaxing previous assumptions about strict preference and by illustrating that Black's Median Voter Theorem does not hold under all conceptualizations of the fuzzy maximal set.