The Nash solution to bargaining problems is shown to induce a collective choice rule generating fully rational choice functions. This property is not shared by other solutions, including the Kalai-Smorodinsky, Gauthier, utilitarian, and egalitarian solution. An axiom of bargaining problems, Invariance under Affine Transformations of Utility, turns out to be crucially important for constructing a collective choice rule based on a bargaining solution. The Nash collective choice rule, however, violates the condition of Independence of Irrelevant Alternatives.