Valence politics and equilibrium in spatial election models

Spatial models of two-party or two-candidate competition almost never have pure-strategy Nash equilibria when the issue space has more than one dimens ion. This paper shows that the introduction of valence issues can create co nditions where equilibria exist, even in a multidimensional setting. We der ive sufficient conditions for the existence of equilibria, and characterize the spatial locations of two competing parties or candidates when such equ ilibria exist. The party with the advantage on the valence dimension will g enerally take a moderate position on the positional issues. We consider the implications of these results for public perceptions of the parties, incum bency advantages, and realigning elections.