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The uncovered set and the core: Cox's (1987) result revisited

Author

Listed:
  • Anindya Bhattacharya
  • Victoria Brosi
  • Francesco Ciardiello

Abstract

In this work first it is shown that in contradiction to the well-known claim in Cox (1987) (repeated in a number of subsequent works), the uncovered set in a multidimensional spatial voting situation (under the usual regularity conditions) does not necessarily coincide with the core even when the core is singleton: in particular, the posited coincidence result, while true for an odd number of voters, may cease to be true when the number of voters is even. Then we provide a characterization result for the case with even number of voters: a singleton core is the uncovered set in this case if and only if the unique element in the core is the Condorcet winner.

Suggested Citation

  • Anindya Bhattacharya & Victoria Brosi & Francesco Ciardiello, 2018. "The uncovered set and the core: Cox's (1987) result revisited," Discussion Papers 18/13, Department of Economics, University of York.
    • Handle: RePEc:yor:yorken:18/13
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    References listed on IDEAS

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    1. Elizabeth Maggie Penn, 2009. "A Model of Farsighted Voting," American Journal of Political Science, John Wiley & Sons, vol. 53(1), pages 36-54, January.
    2. Georges Bordes & Michel Le Breton & Maurice Salles, 1992. "Gillies and Miller's Subrelations of a Relation over an Infinite Set of Alternatives: General Results and Applications to Voting Games," Mathematics of Operations Research, INFORMS, vol. 17(3), pages 509-518, August.
    3. Bordes, Georges, 1983. "On the possibility of reasonable consistent majoritarian choice: Some positive results," Journal of Economic Theory, Elsevier, vol. 31(1), pages 122-132, October.
    4. Jac C. Heckelman & Nicholas R. Miller (ed.), 2015. "Handbook of Social Choice and Voting," Books, Edward Elgar Publishing, number 15584.
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    Cited by:

    1. Anindya Bhattacharya & Francesco Ciardiello, 2022. "On spatial majority voting with an even (vis-a-vis odd) number of voters: a note," Papers 2208.06849, arXiv.org.

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    More about this item

    Keywords

    Spatial Voting Games; Uncovered set; Core; Stable Set.;
    All these keywords.

    JEL classification:

    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games

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