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Bargaining Sets of Majority Voting Games

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  • Ron Holzman
  • Bezalel Peleg
  • Peter Sudholter

Abstract

Let A be a finite set of m alternatives, let N be a finite set of n players and let R N be a profile of linear preference orderings on A of the players. Let u N be a profile of utility functions for R N . We define the NTU game V u N that corresponds to simple majority voting, and investigate its Aumann-Davis-Maschler and Mas-Colell bargaining sets. The first bargaining set is nonempty for m £ 3 and it may be empty for m ³ 4. However, in a simple probabilistic model, for fixed m, the probability that the Aumann-Davis-Maschler bargaining set is nonempty tends to one if n tends to infinity. The Mas-Colell bargaining set is nonempty for m £ 5 and it may be empty for m ³ 6. Furthermore, it may be empty even if we insist that n be odd, provided that m is sufficiently large. Nevertheless, we show that the Mas-Colell bargaining set of any simple majority voting game derived from the k-th replication of R N is nonempty, provided that k ³ n + 2.
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Suggested Citation

  • Ron Holzman & Bezalel Peleg & Peter Sudholter, 2005. "Bargaining Sets of Majority Voting Games," Levine's Bibliography 122247000000000935, UCLA Department of Economics.
    • Handle: RePEc:cla:levrem:122247000000000935
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    References listed on IDEAS

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    1. Mas-Colell, Andreu, 1989. "An equivalence theorem for a bargaining set," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 129-139, April.
    2. Gaertner,Wulf, 2006. "Domain Conditions in Social Choice Theory," Cambridge Books, Cambridge University Press, number 9780521028745, January.
    3. Peleg, Bezalel & Sudholter, Peter, 2005. "On the non-emptiness of the Mas-Colell bargaining set," Journal of Mathematical Economics, Elsevier, vol. 41(8), pages 1060-1068, December.
    4. Vohra, Rajiv, 1991. "An existence theorem for a bargaining set," Journal of Mathematical Economics, Elsevier, vol. 20(1), pages 19-34.
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    Cited by:

    1. Roland Pongou & Lawrence Diffo Lambo & Bertrand Tchantcho, 2008. "Cooperation, stability and social welfare under majority rule," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 35(3), pages 555-574, June.

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    More about this item

    JEL classification:

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

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