Reflecting inequality of claims in gains and losses

We consider the problem of dividing a resource among a group of agents who have conflicting claims on it. We follow the axiomatic approach and investigate the class of rules satisfying claims-inequality and claims-order preservation in gains and losses. We show that these axioms single out the proportional rule when there are more than three agents. This result confirms the central role of this rule and furthers our understanding of it in claims problems.