It seems that decisions in many voting bodies might be described by a two-stage game in which the first stage is a bargaining process and the second is a vote that is often a formality. This does not mean that the voting is irrelevant, but, rather, that it limits the threats that may be made and so influences bargaining power at the first stage. In an idealization of such a two-stage game, majority groups have equal bargaining power, and nonmajority groups have none. This chapter uses a recent extension of bargaining theory that attributes bargaining power to groups as well as individuals and assumes that a minimum winning voting block has bargaining power one and other groups and individuals have bargaining power zero. For TU games, this yields a striking rule for the bargaining solution: the surplus generated by the coalition is either distributed as equal payouts, or distributed among the members with lesser individual rationality constraints, so that their payouts are equal, while others get their individual rationality constraints.
- 1. For a good overview, with some important recent results, see Dasgupta and Maskin, (2008). For a sample of earlier writing with emphasis on cooperative game theory, see Riker (1962). For noncooperative models see Gibbard (1973), Satterthwaite (1975), and Feldman (1979). In earlier discussion, Bowen (1943) should not be neglected. Bowen’s paper also gave rise to a very large critical literature.
- 2. Maskin (1999). This paper was presented in 1977 but not published until twenty years later.
- 3. This is the simple majority game discussed in von Neumann and Morgenstern (1994/2004, at pp. 222-31).