On the Dimension of the Set of Yolk Centers

Abstract

The yolk describes likely outcomes in the spatial model of voting. Martin, Nganmeni, and Tovey conjectured that given an odd number of ideal points in Rk the dimension of the set of yolk centers is at most k−2. We prove this conjecture and show the result is tight. We also show that k−1 is tight for an even number voters. Moreover, our results provide some insight into whether uniqueness is a general condition for the yolk solution concept.