Lorenz and lexicographic maximal allocations for bankruptcy problems

Abstract

This paper investigates the use of egalitarian criteria to select allocations in bankruptcy problems. In our work, we characterize the sets of Lorenz maximal elements for these problems. We show that the allocation selected by the Proportional Rule is the only allocation that belongs to all these Lorenz maximal sets. We prove that the Talmud Rule selects the lexicographic maximal element within a certain set. We introduce and analyze a new sharing rule for bankruptcy problems that shares strong similarities with the Talmud Rule.

J. Arin acknowledges financial support from Project 9/UPV00031.321-15352/2003 of the University of the Basque Country, Projects SEJ-2006-05455 and ECO2009-11213 of the Ministry of Education and Science of Spain and Project GIC07/146-IT-377-07 of the Basque Goverment. Likewise, J. Benito acknowledges financial support from Projects SEJ-2006-11510 and ECO2009-12836 of the Ministry of Education and Science of Spain.