Multidimensional electoral competition between differentiated candidates

It is known that multidimensional Downsian competition fails to admit an equilibrium in pure strategies unless very stringent conditions on the distribution of voters’ bliss points are imposed (Plott 1967). This paper revisits this problem considering that the two vote share maximizing candidates are differentiated. That is, candidates strategically decide positions only in some of the n dimensions while in the rest their positions are assumed to be fixed. These fixed dimensions may be viewed as candidates’ immutable characteristics (race, religion, culture, etc.). We find that if candidates are sufficiently differentiated - if in the fixed dimensions their positions are sufficiently different - then a unique Nash equilibrium in pure strategies is guaranteed to exist for any distribution of voters’ bliss points. Perhaps more importantly, we show that this is true even if there exists a unique fixed dimension and candidates instrumentally decide their positions in all other n-1 dimensions.