Integrating Proportionality and Egalitarianism in Claims Problems

We study the problem of allocating a finite estate among agents whose total claims exceed the available resources, a standard framework in the theory of claims problems. Two canonical rules embody competing fairness ideals: the Proportional rule allocates in proportion to claims, while the Constrained Equal Awards (CEA) rule equalizes awards as much as possible subject to claim-boundedness. We introduce the P-CEA family of compromise rules, which assigns each agent a fixed baseline award, capped by her claim, and distributes the remaining estate proportionally to residual claims. By varying the baseline parameter, this family generates a continuum of allocation rules that interpolates between the Proportional and CEA benchmarks. We provide an axiomatic characterization based on two threshold-dependent principles: No Advantageous Reallocation, which prevents agents with claims above the threshold from benefiting through coordinated claim redistribution that preserves the threshold condition, and Sustainable Lower Bound, which guarantees each agent at least the minimum of her claim and the threshold. We further develop a dual analysis that reallocates losses instead of awards and characterize the corresponding dual family using the dual versions of our axioms.