Bargaining sets of majority voting games

Let A be a finite set of in alternatives, let N be a finite set of n players, and let R-N be a profile of linear orders on A of the players. Let u(N) be a profile of utility functions for R-N. We define the nontransferable utility (NTU) game V-uN that corresponds to simple majority voting, and investigate its Aumann-Davis-Maschler and Mas-Colell bargaining sets. The first bargaining set is nonempty for in <= 3, and it may be empty for in >= 4. However, 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 in <= 5, and it may be empty for in >= 6. Furthermore, it may be empty even if we insist that n be odd, provided that in is sufficiently large. Nevertheless, we show that the Mas-Colell bargaining set of any simple majority voting game derived from the k-fold replication of R-N is nonempty, provided that k >= n + 2.