Integrating Proportionality and Egalitarianism in Claims Problems

2026-05-26

AI Summary

This study addresses the core challenge of reconciling proportional fairness with egalitarian fairness in claims problems where total claims exceed available resources. The authors propose the P-CEA family of rules, which first guarantees each agent a baseline allocation not exceeding their claim and at least a specified threshold, then distributes any remaining endowment proportionally to residual claims. By constructing a continuous compromise mechanism bridging the proportional rule and the constrained equal awards rule, and introducing two threshold-dependent axioms—“no advantageous reallocation” and “sustainable lower bound”—the paper provides a complete axiomatic characterization. Furthermore, it develops a dual analytical framework based on loss redistribution, thereby achieving the first systematic unification of proportionality and egalitarianism in the context of claims problems.

Abstract

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.

Problem

• claims problems
• proportionality
• egalitarianism
• fair allocation
• resource distribution

Innovation

• claims problems
• compromise rules
• axiomatic characterization
• proportionality
• egalitarianism