How much can you claim?

In a “claims problem” (O'Neill, 1982), a group of individuals have claims on a resource but there is not enough of it to honor all of the claims. A widely studied property of distribution rules, “claims truncation invariance”, advances the existence of a maximal reasonable claim: the endowment of the resource. We examine the implications of imposing any maximal claim, no matter how large. Our conclusions establish the centrality of the “constrained equal awards rule” and its asymmetric generalizations in the class of asymmetric rationing rules (Moulin, 2000).