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The Geometry of Majority Rule

Bernard Grofman

Scott L. Feld

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.

Key Words: majority rule • spatial voting models

Journal of Theoretical Politics, Vol. 1, No. 4, 379-406 (1989)
DOI: 10.1177/0951692889001004001


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