A new solution to the problem of adjudicating conflicting claims

Summary. For the problem of adjudicating conflicting claims, we consider the requirement that each agent should receive at least 1/n his claim truncated at the amount to divide, where n is the number of claimants (Moreno-Ternero and Villar, 2004a). We identify two families of rules satisfying this bound. We then formulate the requirement that for each problem, the awards vector should be obtainable in two equivalent ways, (i) directly or (ii) in two steps, first assigning to each claimant his lower bound and then applying the rule to the appropriately revised problem. We show that there is only one rule satisfying this requirement. We name it the “ rule”, as it is obtained by a recursion. We then undertake a systematic investigation of the properties of the rule.Received: 7 September 2004, Revised: 21 April 2005, JEL Classification Numbers: C79, D63, D74.William Thomson: Correspondence toWe thank Christopher Chambers, Youngsub Chun, Tarík Kara, Çağatay Kayí, Juan Moreno-Ternero, Toyotaka Sakai, and Michel Truchon for their comments. We also thank a referee for useful comments. This paper was presented at Columbia University, CORE, Bilkent University, Sabancí University, Université Laval, and Caltech, and at the Mallorca Review of Economic Design meeting. Thomson acknowledges support from the NSF under grant SES-0214691.