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.