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Reference functions and possibility theorems for cardinal social choice problems

Author

Listed:
  • John P. Conley

    (Department of Economics, University of Illinois, Champaign, Ill 61820)

  • Simon Wilkie

    (Division of Humanities and Social Sciences, Caltech, Pasadena, CA 91125)

  • Richard P. McLean

    (Department of Economics, Rutgers University, New Brunswick, NJ 08903)

Abstract

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.

Suggested Citation

  • John P. Conley & Simon Wilkie & Richard P. McLean, 1996. "Reference functions and possibility theorems for cardinal social choice problems," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 14(1), pages 65-78.
    • Handle: RePEc:spr:sochwe:v:14:y:1996:i:1:p:65-78
    Note: Received: 8 August 1994/Accepted: 12 February 1996
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    Cited by:

    1. Attila Ambrus & Kareen Rozen, 2015. "Rationalising Choice with Multi‐self Models," Economic Journal, Royal Economic Society, vol. 125(585), pages 1136-1156, June.
    2. Yoshihara, Naoki, 2003. "Characterizations of bargaining solutions in production economies with unequal skills," Journal of Economic Theory, Elsevier, vol. 108(2), pages 256-285, February.
    3. Shiran Rachmilevitch, 2021. "Step-by-step negotiations and utilitarianism," International Journal of Game Theory, Springer;Game Theory Society, vol. 50(2), pages 433-445, June.
    4. Abraham Diskin & Dan Felsenthal, 2007. "Individual rationality and bargaining," Public Choice, Springer, vol. 133(1), pages 25-29, October.

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