Nash Equilibrium Strategies in Directional Models of Two-Candidate Spatial Competition.

The standard approach to two-party political competition in a multidimensional issue space models voters as voting for the alternative that is located closest to their own most preferred location. Another approach to understanding voter choice is based on preferred direction of change with respect to some specified neutral point (e.g., an origin or status quo point). For the two-dimensional Matthews directional model (Matthews, 1979), the authors provide geometric conditions in terms of the number of medians through the neutral point for there to be a Condorcet (undominated) direction. In this two-dimensional setting, the set of residual locations for which no Condorcet directions exist is identical to the null dual set (Schofield, 1978) and to the heart (Schofield, 1993). In two dimensions, for most locations of the origin/status quo point, a Condorcet direction exists and points toward the yolk, a geometric construct first identified by McKelvey (1986). The authors also provide some simulation results on the size of the null dual set in two dimensions when the underlying distribution of points is nonsymmetric. Copyright 1999 by Kluwer Academic Publishers