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.
Black, Duncan
(1948) `On the Rationale of Group Decision-Making', Journal of Political Economy56: 23-34.
2.
Cox, Gary
(1987) `The Uncovered Set and the Core', American Journal of Political Science31: 408-422.
3.
Dahl, Robert A.
(1956) A Preface to Democratic Theory. Chicago: University of Chicago Press.
4.
Davis, Otto
, Morris H. DeGroot and Melvin Hinich (1972) `Social Preference Orderings and Majority Rule', Econometrica40: 147-157.
5.
Enelow, James M.
and Melvin J. Hinich (1983) `On Plott's Pairwise Symmetry Condition for Majority Rule Equilibrium', Public Choice40: 317-321.
6.
Feld, Scott L.
and Bernard Grofman (1987) `Necessary and Sufficient Conditions for a Majority Winner in n-Dimensional Spatial Voting Games: An Intuitive Approach', American Journal of Political Science31: 709-728.
7.
Feld, Scott L.
, Bernard Grofman and Nicholas R. Miller (1988) `Centripetal Forces in Spatial Voting: On the Size of the Yolk', Public Choice59: 37-50.
8.
Feld, Scott L.Bernard Grofman
and Nicholas R. Miller (1989) `Limits on Agenda Control in Spatial Voting Games', Mathematical and Computer Modelling12: 405-416.
9.
Ferejohn, John A.
, Richard D. McKelvey and Edward W. Packel (1984) `Limiting Distributions for Continuous State Markov Voting Models', Social Choice and Welfare1: 45-67.
10.
Hoyer, Robert W.
and Lawrence S. Mayer (1974) `Comparing Strategies in a Spatial Model of Electoral Competition', American Journal of Political Science18: 501-523.
11.
McKelvey, Richard D.
(1976) `Intransitivities in Multidimensional Voting Models and Some Implications for Agenda Control', Journal of Economic Theory12: 472-482.
12.
McKelvey, Richard D.
(1979) `General Conditions for Global Intransitivities in Formal Voting Models', Econometrica47: 1085-1112.
13.
McKelvey, Richard D.
(1986) `Covering, Dominance and Institution Free Properties of Social Choice', American Journal of Political Science30: 283-314.
14.
Miller, Nicholas R.
(1980) `A New Solution Set for Tournaments and Majority Voting', American Journal of Political Science24: 68-96.
15.
Plott, Charles R.
(1967) `A Notion of Equilibrium and Its Possibility under Majority Rule', American Economic Review57: 787-806.
16.
Schofield, Norman
(1982) `Instability and Development in the Political Economy', in Peter C. Ordeshook and Kenneth A. Shepsle (eds), Political Equilibrium. Boston: Kluwer-Nijhoff.
