Bargaining Sets of Majority Voting Games

Ron Holzman (), Bezalel Peleg () and Peter Sudholter ()

Discussion Paper Series from Center for Rationality and Interactive Decision Theory, Hebrew University, Jerusalem

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.

Keywords: NTU game; voting game; majority rule; bargaining set (search for similar items in EconPapers)
JEL-codes: C71 D71 (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-cdm, nep-gth and nep-mic
Date: 2005-11
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Published in Mathematics of Operations Research, 2007, vol. 32, pp. 857-872.

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Working Paper: Bargaining Sets of Majority Voting Games (2005)
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