Reference functions and possibility theorems for cardinal social choice problems

John P. Conley, Richard P. McLean, Simon Wilkie

Research output: Contribution to journalArticleResearchpeer-review

6 Citations (Scopus)


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

Original languageEnglish
Pages (from-to)65-78
Number of pages14
JournalSocial Choice and Welfare
Issue number1
Publication statusPublished - Dec 1996
Externally publishedYes


  • utility function
  • reference point
  • social choice
  • reference function
  • theory solution

Cite this