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The Geometry of Majority Rule

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  • Nicholas R. Miller
  • Bernard Grofman
  • Scott L. Feld

Abstract

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.

Suggested Citation

  • Nicholas R. Miller & Bernard Grofman & Scott L. Feld, 1989. "The Geometry of Majority Rule," Journal of Theoretical Politics, , vol. 1(4), pages 379-406, October.
    • Handle: RePEc:sae:jothpo:v:1:y:1989:i:4:p:379-406
    DOI: 10.1177/0951692889001004001
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    References listed on IDEAS

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    1. James Enelow & Melvin Hinisch, 1983. "On Plott's pairwise symmetry condition for majority rule equilibrium," Public Choice, Springer, vol. 40(3), pages 317-321, January.
    2. McKelvey, Richard D, 1979. "General Conditions for Global Intransitivities in Formal Voting Models," Econometrica, Econometric Society, vol. 47(5), pages 1085-1112, September.
    3. Scott Feld & Bernard Grofman & Nicholas Miller, 1988. "Centripetal forces in spatial voting: On the size of the Yolk," Public Choice, Springer, vol. 59(1), pages 37-50, October.
    4. McKelvey, Richard D., 1976. "Intransitivities in multidimensional voting models and some implications for agenda control," Journal of Economic Theory, Elsevier, vol. 12(3), pages 472-482, June.
    5. Davis, Otto A & DeGroot, Morris H & Hinich, Melvin J, 1972. "Social Preference Orderings and Majority Rule," Econometrica, Econometric Society, vol. 40(1), pages 147-157, January.
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    Cited by:

    1. Nicholas R. Miller, 2015. "The spatial model of social choice and voting," Chapters, in: Jac C. Heckelman & Nicholas R. Miller (ed.), Handbook of Social Choice and Voting, chapter 10, pages 163-181, Edward Elgar Publishing.
    2. Michel Le Breton & Karine Van Der Straeten, 2017. "Alliances Électorales et Gouvernementales : La Contribution de la Théorie des Jeux Coopératifs à la Science Politique," Revue d'économie politique, Dalloz, vol. 127(4), pages 637-736.
    3. Bernard GROFMAN & Joseph GODFREY, 2014. "Aspiration Models of Committee Decision Making," Economics Working Paper from Condorcet Center for political Economy at CREM-CNRS 2014-04-ccr, Condorcet Center for political Economy.
    4. Michel Regenwetter & James Adams & Bernard Grofman, 2002. "On the (Sample) Condorcet Efficiency of Majority Rule: An alternative view of majority cycles and social homogeneity," Theory and Decision, Springer, vol. 53(2), pages 153-186, September.

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    Keywords

    majority rule; spatial voting models;

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