Individual monotonicity and the leximin solution

Most axiomatic treatments of bargaining do not give a substantive role to individually irrational points. We show in this paper that it can matter greatly whether axioms and solutions are formulated with respect to the entire feasible set or with respect to only the individually rational portion. In particular, a principle of individual monotonicity becomes much more powerful when all feasible points are considered. We characterize the n-person Leximin solution as the only solution that satisfies Pareto efficiency, symmetry, individual monotonicity, and independence of individually irrational points.