Bargaining Sets of Voting Games

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Bargaining Sets of Voting Games

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Bezalel Peleg ()
Peter Sudholter ()

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Bezalel Peleg

Abstract

Let A be a finite set of m ³ 3 alternatives, let N be a finite set of n ³ 3 players and let Rⁿ 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.

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Paper provided by Center for Rationality and Interactive Decision Theory, Hebrew University, Jerusalem in its series Discussion Paper Series with number dp376.

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

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Find related papers by JEL classification:
C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations

This paper has been announced in the following NEP Reports:

NEP-ALL-2004-12-20 (All new papers)
NEP-DCM-2004-12-20 (Discrete Choice Models)
NEP-DCM-2004-12-22 (Discrete Choice Models)
NEP-GTH-2004-12-20 (Game Theory)
NEP-MIC-2004-12-20 (Microeconomics)
NEP-POL-2004-12-20 (Positive Political Economics)

References listed on IDEAS
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Mas-Colell, Andreu, 1989. "An equivalence theorem for a bargaining set," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 129-139, April. [Downloadable!] (restricted)
Bezalel Peleg & Peter Sudholter, 2004. "On the Non-Emptiness of the Mas-Colell Bargaining Set," Discussion Paper Series dp360, Center for Rationality and Interactive Decision Theory, Hebrew University, Jerusalem. [Downloadable!]
Other versions:
- 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. [Downloadable!] (restricted)

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