Bargaining Sets of Voting Games
Let A be a finite set of m ³ 3 alternatives, let N be a finite set of n ³ 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 u N 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. 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 ³ 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 ³ 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.
|Date of creation:||Dec 2004|
|Date of revision:|
|Contact details of provider:|| Postal: Feldman Building - Givat Ram - 91904 Jerusalem|
Web page: http://www.ratio.huji.ac.il/
More information through EDIRC
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Gaertner,Wulf, 2001.
"Domain Conditions in Social Choice Theory,"
Cambridge University Press, number 9780521791021, November.
- 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.
- 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.
- Mas-Colell, Andreu, 1989. "An equivalence theorem for a bargaining set," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 129-139, April.
When requesting a correction, please mention this item's handle: RePEc:huj:dispap:dp376. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Tomer Siedner)
If references are entirely missing, you can add them using this form.