Let A be a finite set of m alternatives, let N be a finite set of n players and let R<sup>N</sup> be a profile of linear preference orderings on A of the players. Let u<sup>N</sup> be a profile of utility functions for R<sup>N</sup>. We define the NTU game V<sub>u<sup>N</sup></sub> that corresponds to simple majority voting, and investigate its Aumann-Davis-Maschler and Mas-Colell bargaining sets. The first bargaining set is nonempty for m <FONT FACE="Symbol">£</FONT> 3 and it may be empty for m <FONT FACE="Symbol">³</FONT> 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 m <FONT FACE="Symbol">£</FONT> 5 and it may be empty for m <FONT FACE="Symbol">³</FONT> 6. Furthermore, it may be empty even if we insist that n be odd, provided that m is sufficiently large. Nevertheless, we show that the Mas-Colell bargaining set of any simple majority voting game derived from the k-th replication of R<sup>N</sup> is nonempty, provided that k <FONT FACE="Symbol">³</FONT> n + 2.
