Claim problems and egalitarian criteria

Abstract

The paper presents a unified framework where claim and cost sharing problems are jointly analyzed. Both problems have the following common characteristic: given a proposal the agents valuate the suitability of the proposal in two ways, checking how much they loss and how much they gain. Taking this into account, we construct the vector of awards and losses for any proposal and we use different egalitarian criteria to select among these vectors. We use the Lorenz, the Least Square and the lexicographic criteria and we analyze the solutions arising from the application of these criteria in the sets of vectors of awards-losses. In particular, we characterize the members of two families of solutions: the family of Weighted Least Square Solutions and the family of Imputation Selector Weighted Least Square Solutions. The second family includes between its members well-known solutions as Constrained Equal Awards and Constrained Equal Losses solutions.