On the average-of-awards rule for solving claims problems

I. Núñez Lugilde, E. Sánchez Rodríguez

A claims problem arises when an amount has to be divided among a set of agents with claims that, in aggregate, exceed what is available. A division rule must satisfy three natural requirements: no claimant is asked to pay; no claimant receives more than her claim; and the entire endowment is allocated. The set of all the allocations that meet these basic properties is the set of awards vectors, which is a polytope obtained by the intersection of an n-rectangle with a hyperplane x1+. . .+xn=b. The average-of-awards rule selects the expected value of the uniform distribution over the set of awards vectors. We explore the geometry of a polytope of this type and compute its volume and its centroid. We obtain a procedure to compute the average-of-awards rule directly from the parameters of the problem. We incorporate the average-of-awards rule to the ranking of the standard rules. Finally, we present an application to the distribution of CO2 emissions among the 20 most polluting regions.

Keywords: Claims problems, Average-of-awards rule, Lorenz-domination, Global carbon budget

GT19.GAMES3
November 9, 2023  3:30 PM
CC2: Conference Room

L. A. Guardiola Alcalá, A. Meca, J. Puerto

R. Acosta Vega, E. Algaba, J. SANCHEZ SORIANO

J. M. Alonso-Meijide, J. Costa, I. García Jurado, J. C. Gonçalves Dosantos