A bargaining situation is described by a set of alternative which are feasible to n individuals when they do cooperate, and an alternative which comes about when they do not cooperate. The paper addresses the question of which cooperative outcome will be chosen. A Nash-type approach is used to prove that, under plausible axioms describing the underlying bargaining process, the individuals must be doing interpersonal comparison of utility. The model and the solution overcome some difficulties recently described by Nydegger and Owen.