The Geometry of Majority Rule

We present some basic results concerning the spatial theory of voting in such a way that the theorems and their proofs should be accessible to a broad audience of political scientists. We do this by making the presentation essentially geometrical. We present the following results in particular: Plott's `pairwise symmetry' condition for an unbeaten point; McKelvey's `global cycling' theorem; Ferejohn, McKelvey and Packel's cardioid construction for establishing bounds on a `win set'; and McKelvey's circular bound on the `uncovered set' of points.