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On the Chacteristic Numbers of Voting Games

Author

Listed:
  • Vincent Merlin

    (CREM - Centre de recherche en économie et management - UNICAEN - Université de Caen Normandie - NU - Normandie Université - UR - Université de Rennes - CNRS - Centre National de la Recherche Scientifique)

  • Matthieu Martin

    (THEMA - Théorie économique, modélisation et applications - UCP - Université de Cergy Pontoise - Université Paris-Seine - CNRS - Centre National de la Recherche Scientifique)

Abstract

This paper deals with the non-emptiness of the stability set for any proper voting game. We present an upper bound on the number of alternatives which guarantees the non emptiness of this solution concept. We show that this bound is greater than or equal to the one given by Le Breton and Salles (1990) for quota games.

Suggested Citation

  • Vincent Merlin & Matthieu Martin, 2006. "On the Chacteristic Numbers of Voting Games," Post-Print halshs-00010172, HAL.
    • Handle: RePEc:hal:journl:halshs-00010172
    DOI: 10.1142/S0219198906001156
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-00010172
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    References listed on IDEAS

    as
    1. Le Breton, Michel, 1990. "On some combinatorial problems arising in the theory of voting games," Mathematical Social Sciences, Elsevier, vol. 19(2), pages 179-193, April.
    2. Le Breton, M & Salles, M, 1990. "The Stability Set of Voting Games: Classification and Genericity Results," International Journal of Game Theory, Springer;Game Theory Society, vol. 19(2), pages 111-127.
    3. Greenberg, Joseph, 1979. "Consistent Majority Rules over Compact Sets of Alternatives," Econometrica, Econometric Society, vol. 47(3), pages 627-636, May.
    4. Mathieu Martin, 2000. "A note on the non-emptiness of the stability set," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 17(3), pages 559-565.
    5. Rubinstein, Ariel, 1980. "Stability of decision systems under majority rule," Journal of Economic Theory, Elsevier, vol. 23(2), pages 150-159, October.
    6. Peleg, Bezalel, 1978. "Consistent Voting Systems," Econometrica, Econometric Society, vol. 46(1), pages 153-161, January.
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    Cited by:

    1. Kumabe, Masahiro & Mihara, H. Reiju, 2011. "Preference aggregation theory without acyclicity: The core without majority dissatisfaction," Games and Economic Behavior, Elsevier, vol. 72(1), pages 187-201, May.

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    More about this item

    Keywords

    voting game; core; stability set;
    All these keywords.

    JEL classification:

    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • D7 - Microeconomics - - Analysis of Collective Decision-Making

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