Fuzzy voters, crisp votes

In a binary choice voting scenario, voters may have fuzzy preferences but are required to make crisp choices. In order to compare a crisp voting procedure with more general mechanisms of fuzzy preference aggregation, we first focus on the latter. We present a formulation of strategy-proofness in this setting and study its consequences. On one hand, we achieve an axiomatic recommendation of the median as the aggregation rule for fuzzy preferences. On the other hand, we present conditions under which strategic concerns imply the optimality of a crisp voting procedure and argue that there is a potential gain in the integration of the preference and choice aggregation programs - namely that an underlying fuzzy preference structure may also help inform the selection of a choice aggregation rule.