A Theory of Voting Equilibria

A voting equilibrium arises when the voters in an electorate, acting in accordance with both their preferences for the candidates and their perceptions of the relative chances of various pairs of candidates being in contention for victory, generate an election result that justifies their perceptions. Voting equilibria always exist, and the set of equilibria can vary substantially with the choice of voting system. We compare equilibria under the plurality rule, approval voting, and the Borda system. We consider a candidate-positioning game and find that the plurality rule imposes little restriction on the position of the winning candidate in three-candidate races, while approval voting leads to a winner positioned at the median of the voter distribution. We contrast campaign activities intended to influence voter preferences with activities meant to influence only perceptions of candidate viability.