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Bargaining Sets of Voting Games

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  • Bezalel Peleg

    ()

  • Peter Sudholter

    ()

Abstract

Let A be a finite set of m � 3 alternatives, let N be a finite set of n � 3 players and let R n be a profile of linear preference orderings on A of the players. Throughout most of the paper the considered voting system is the majority rule. Let u N be a profile of utility functions for R N. Using a -effectiveness we define the NTU game V uN 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. Moreover, 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. Moreover, we prove the following startling result: 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. We also compute the NTU games which are derived from choice by plurality voting and approval voting, and we analyze some interesting examples.

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Paper provided by The Center for the Study of Rationality, Hebrew University, Jerusalem in its series Discussion Paper Series with number dp376.

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Length: 22 pages
Date of creation: Dec 2004
Date of revision:
Handle: RePEc:huj:dispap:dp376

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Keywords: NTU game; bargaining set; majority rule; plurality voting; approval voting;

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  1. 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.
  2. Mas-Colell, Andreu, 1989. "An equivalence theorem for a bargaining set," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 129-139, April.
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Cited by:
  1. Adam Idzik & Gyula O.H. Katona & Rajiv Vohra, 1999. "Civil Conflict: Ended Or Never Ending?," Working Papers 99-33, Brown University, Department of Economics.
  2. Lloyd S. Shapley, 1992. "Kernels of Replicated Market Games," UCLA Economics Working Papers 654, UCLA Department of Economics.

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