"Back to Black : The Median Voter Revisited"

Abstract :
Pure strategy Nash equilibria involving two candidates almost never exist in spatial majority voting games when the number of positional dimensions is at least two. In such cases, the majority core is empty. Assume that each candidate only knows every voter’s ideal point in the policy space but not their indifference surfaces. For any proper spatial voting game, we identify the set of imprudent positions in the space. If a candidate adopts an imprudent position, then there exists a position for their opponent that will defeat them with probability one. The prudent core is the set of positions that are not imprudent in this sense. We show that a prudent core always exists. Assuming simple majority voting and an odd number of voters, the prudent core is the dimension-by-dimension median and equals the majority core whenever the latter is non-empty. Some foundations for prudent behavior are given.