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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 uN 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 � 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 � 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 � n + 2.

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Bibliographic Info

Paper provided by UCLA Department of Economics in its series Levine's Bibliography with number 122247000000000935.

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Date of creation: 31 Dec 2005
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Handle: RePEc:cla:levrem:122247000000000935

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  1. Gaertner,Wulf, 2006. "Domain Conditions in Social Choice Theory," Cambridge Books, Cambridge University Press, number 9780521028745, October.
  2. Mas-Colell, Andreu, 1989. "An equivalence theorem for a bargaining set," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 129-139, April.
  3. Bezalel Peleg & Peter Sudholter, 2004. "On the Non-Emptiness of the Mas-Colell Bargaining Set," Discussion Paper Series dp360, The Center for the Study of Rationality, Hebrew University, Jerusalem.
  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, vol. 35(3), pages 555-574, June.

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