Bargaining Sets of Majority Voting Games
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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- Gaertner,Wulf, 2006.
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- Bezalel Peleg & Peter Sudholter, 2004. "On the Non-Emptiness of the Mas-Colell Bargaining Set," Discussion Paper Series dp360, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
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