Sustainability, exemption, and the constrained equal awards rule: a note

We consider the problem of distributing the liquidation value of a bankrupt firm among its creditors. Herrero and Villar [TOP 10 (2002) 261; Mathematical Social Sciences 42 (2001) 307] show that (i) the constrained equal awards rule is the only rule satisfying sustainability and composition down, and that (ii) it is the only rule satisfying exemption, composition down, and bilateral consistency. This note has three results. First, we give a direct and elementary proof of (i). Second, we connect (i) and (ii) by means of the Elevator Lemma, which is introduced by Thomson [Mimeo, University of Rochester, 2000]. Third, by exploiting the Elevator Lemma, we show that the constrained equal awards rule is the only rule satisfying exemption, composition down, and converse consistency. Thus, (ii) can be obtained as a corollary of our new characterization of the rule. D 2003 Elsevier B.V. All rights reserved.