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 liquidation 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 satisfy 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. JEL classification: C71; D31; H24.