Protective properties and the constrained equal awards rule for claims problems

We investigate the implications of two properties, sustainability and exemption, when imposed separately in conjunction with other basic properties for the resolution of conflicting claims. Under the protective properties, agents with sufficiently small claims in relation to the others are fully reimbursed. We base three characterizations of the constrained equal awards rule on the properties. Namely, (1) the constrained equal awards rule is the only rule satisfying sustainability and claims monotonicity, (2) it is the only rule satisfying sustainability and super-modularity, and (3) it is the only rule satisfying exemption, order preservation and consistency. Then, we extend the notions of the protective properties to groups of agents, and show that no rule satisfies any of these extensions.