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. A typical situation is when a firm goes bankrupt and its liqui-dation value has to be divided among its creditors. We follow the axiomatic approach. Our main axioms are inequality preservation in gains and inequality preservation in losses (Hougaard and Thorlund-Petersen, 2001; Hougaard and Østerdal, 2005). We characterize the family of rules that are continuous, order preserving in gains and losses, and inequality preserving in gains and losses: (i) for two agents, these axioms hardly restrict rules (in particular, all central rules considered in the literature sat-isfy them); (ii) for three agents, they are significantly more restrictive but they are satisfied by a family containing a continuum of rules; and (iii) for more than three agents, they single out the proportional rule; this result confirms the central role of this rule and furthers our understanding of it in claims problems