A Characterization of a Family of Rules for the Adjudication of Conflicting Claims

We consider the problem of adjudicating conflicting claims, and characterize the family of rules satisfying four standard invariance requirements, homogeneity, two composition properties, and consistency. It takes as point of departure the characterization of the family of two-claimant rules satisfying the first three requirements, and describes the restrictions imposed by consistency on this family and the further implications of this requirement for problems with three or more claimants. The proof, which is an alternative to Moulin's original proof (Econometrica, 2000), is based on a general method of constructing consistent extensions of two-claimant rules (Thomson, 2001), which exploits geometric properties of paths of awards, seen in their entirety.