An Analogue of the Median Voter Theorem for Approval Voting

The Median Voter Theorem is a well-known result in social choice theory for majority-rule elections. We develop an analogue in the context of approval voting. We consider voters to have preference sets that are intervals on a line, called approval sets, and the approval winner is a point on the line that is contained in the most approval sets. We define median voter by considering the left and right end points of each voters approval sets. We consider the case where approval sets are equal length. We show that if the pairwise agreement proportion is at least 3/4, then the median voter interval will contain the approval winner. We also prove that under an alternate geometric condition, the median voter interval will contain the approval winner, and we investigatevariants of this result.

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