Bargaining Sets of Voting Games

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 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.

Keywords: NTU game; bargaining set; majority rule; plurality voting; approval voting (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-dcm, nep-gth, nep-mic and nep-pol
Date: 2004-12
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