Bargaining Sets of Voting Games
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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- 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.
- 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.
- Gaertner,Wulf, 2006.
"Domain Conditions in Social Choice Theory,"
Cambridge University Press, number 9780521028745, October.
- 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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