Priority Classes and Weighted Constrained Equal Awards Rules for the Claims Problem

We revisit the "claims problem" (O'Neill, 1982), where a group of individuals have claims on a resource but there is not enough of it to honor all of the claims. We characterize the rules satisfying three well-known invariance axioms: consistency, composition up, and claims truncation invariance. They are priority-augmented versions of the standard weighted constrained equal awards rules, also known as weighted gains methods (Moulin, 2000): individuals are sorted into priority classes; the resource is distributed among the individuals in the first priority class using a weighted constrained equal awards rule; if some of the resource is left over, then it is distributed among the individuals in the second priority class, again using a weighted constrained equal awards rule; the distribution carries on in this way until the resource is exhausted. Our characterization extends to a generalized version of the claims problem where there are multiple divisible and indivisible resources and individuals have claims on each of these.