The Half-Win Set and the Geometry of Spatial Voting Games: Research Note.

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 emply a useful new geometric constructio, 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. Copyright 1991 by Kluwer Academic Publishers