On Committee Decision Making: A Game Theoretical Approach

In this paper, we study the committee decision making process using game theory. By a committee, we mean any group of people who have to pick one option from a given set of alternatives. A well defined voting rule is specified by which the committee arrives at a decision. Each member has a preference relation on the set of all alternatives. A new solution concept called the one-core is introduced and studied. Intuitively, the one-core consists of all maximal (for the proposer) proposals which are undominated assuming that the player who makes the proposal does not cooperate in any effort to dominate the proposal. For games with non-emtpy cores, the one-core proposals are shown to be better than the core. For games with empty cores, the one-core proposals tend to be pessimistic, i.e., they indicate the security level of the players. This is because the stability requirements of the one-core are too strong for such games. A bargaining set modeled along the lines of the Aumann-Maschler bargaining set for characteristic function games is defined for committee games. Because of its relaxed stability requirements, the bargaining set indicates more reasonable proposals than the one-core. The existence of both the one-core and the bargaining set are studied and these concepts are compared with two other well known solution concepts---the core and the Condorcet solution.