Improvement sensitivity and invariance of solutions to group decision making problems with claims

Abstract

In this paper we have developed a very general framework for studying group decision making problems with claims which subsumes the set of problems studies in axiomatic models of bargaining. Subsequently we proceed to establish the improvement sensitivity of some solutions defined on a smaller domain. We also extend an earlier framework for studying multicriteria group decision making problems to incorporate claims as an additional parameter for reference. We define the concept of an equilibrated state for such problems and show that a solution which chooses only equilibrated state for such problems and show that a solution which chooses only equilibrated state is of necessity invariant under monotone increasing transformations of the value functions of respective agents.