The half-win set and the geometry of spatial voting games

Abstract

In the spatial context, when preferences can be characterized by circular indifference curves, we show that we can derive all the information about the majority preference relationship in a space from the win-set of any single point. Furthermore, the size of win sets increases for points along any ray outward from a central point in the space, the point that is the center of the yolk. To prove these results we employ a useful new geometric construction, the half-win set. The implication of these results is that embedding choice in a continuous n-dimensional space imposes great constraints on the nature of the majority-preference relationship.