Axiomatic Foundations for Compromise Theory†

We provide a characterization of the symmetric and weighted versions of the Euclidean compromise solution for multiobjective optimization problems first proposed by P.L.Yu. These solutions minimize a measure of the distance between a feasible set and the utopia point of that set, and are closely related to solutions that have been proposed in the bargaining with claims literature. We provide new axiomatizations of the symmetric and weighted Nash Bargaining Solutions. Our characterizations of the compromise solutions employ axioms that are, in a certain sense, dual to those used in these new axiomatizations of the Nash solutions. We also provide characterizations for solutions that are dual to the Egalitarian and Kalai-Smorodinsky solutions.