A theory of coalition formation in committees

Abstract

Let G = ( N, W) be a strong weighted majority game and let A be a set of alternatives. Denote by L the set of linear orders on A. A social choice function F: L N → A is a representation of G if the simple game G ∗( F) associated with F equals G. A coalition S is determining in G if it satisfies the following condition. Let F be a representation of G and let R N ϵ L N . Then, if a simple majority of the members of S consider an alternative x to be their best choice, then S can ‘enforce’ x to be a Nash equilibrium payoff in the resulting non-cooperative voting game g( F, R N ). In this paper we generalize the above notion of a determining coalition to committees (i.e., proper and monotonic simple games), and give a complete characterization of the set of determining coalitions of a committee. Furthermore, we discuss our notion of a determining coalition in the light of some real-life data on formation of coalitions in town councils in Israel.