A proportional approach to claims problems with a guaranteed minimum

In distribution problems, and specifically in bankruptcy issues, the Proportional (P ) and the Egalitarian (EA) divisions are two of the most popular ways to resolve the conflict. Nonetheless, when using the egalitarian division, agents may receive more than her claim. We propose a compromise between the proportional and the egalitarian solutions by considering the restriction that no one receives more than her claim. We show that the most egalitarian compromise fulfilling this restriction ensures a minimum amount to each agent, and it can be interpreted as a process that works in two steps as follows: first, all agents receive an equal share up to the smallest claim (egalitarian distribution), and then the remaining estate (if any) is allocated proportionally to the remaining claims (proportional solution). Finally, we obtain that the recursive application of this process finishes at the Constrained Equal Awards solution (CEA).