REFERENCE FUNCTIONS AND POSSIBILITY THEOREMS FOR CARDINAL SOCIAL CHOICE PROBLEMS

In this paper, we provide axiomatic foundations for social choice rule s on a domain of convex and comprehensive social choice problems when agents have cardinal utility functions. We translate the axioms of thr ee well known approaches in bargaining theory (Nash 1950; Kalai and Sm orodinsky 1975; Kalai 1977) to the domain of social choice problems an d provide an impossibility result for each. We then introduce the conc ept of a reference function which, for each social choice set, selects a point from which relative gains are measured. By restricting the in variance and comparison axioms so that they only apply to sets with th e same reference point, we obtain characterizations of social choice r ules that are natural analogues of the bargaining theory solutions.