Cooperation,stability and social welfare under majority rule

We resolve collective irrationality in the stability set, a solution concept for voting games proposed by Rubinstein (J Econ Theory 23:150–159, 1980) to resolve the well-known paradox of voting in the core. A lack of cooperation within winning coalitions prevents their members from eliminating an alternative globally less preferred to another one when they observe the rational behavior defining the stability set. Allowing for the possibility of accompanying a coalitional vote with a binding solidarity agreement is a natural response to this cooperation failure. This leads to a new standard of behavior and a new solution concept called stability set with binding solidarity agreement or S _c -stability set. It is shown that the S _c -stability set and a newly defined version of the Mas-Colell bargaining set for simple games are not comparable with respect to set inclusion. The S _c -stability set includes the core, is included in the stability set and contains only Pareto-optimal alternatives. When individual preferences are complete linear orders, the S _c -stability set is always non-empty.