AN ANALOG OF THE MEDIAN VOTER THEOREM FOR APPROVAL VOTING
Kyle Duke1, Francis Su2.
1James Madison University, Virginia Beach, VA, 2Harvey Mudd College, Claremont, CA.
The median voter theorem is a well-known result in social choice theory for majority-rule elections. We develop an analog 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 defined median voter by considering the left and right end points of each voter's approval set. 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 investigate variants of this result.