Journal of Risk and Uncertainty

, Volume 1, Issue 4, pp 355–387 | Cite as

Ordinal independence in nonlinear utility theory

  • Jerry R. Green
  • Bruno Jullien


Individual behavior under uncertainty is characterized using a new axiom, ordinal independence, which is a weakened form of the von Neumann-Morgenstern independence axiom It states that if two distributions share a tail in common, then this tail can be modified without altering the individual's preference between these distributions. Preference is determined by the tail on which the distributions differ. This axiom implies an appealing and simple functional form for a numerical representation of preferences. It generalizes the form of anticipated utility, and it explains some well-known forms of behavior, such as the Friedman-Savage paradox, that anticipated utility cannot.

Key words

ordinal independence nonlinear utility theory preferences 


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  1. Chew, S.H., and L.G. Epstein, (1987), “A Unifying Approach to Axiomatic Non-Expected Utility Theories”, mimeo, University of Toronto.Google Scholar
  2. Chew, S.H., E. Karni and Z. Safra, (1987), “Risk Aversion in the Theory of Expected Utility with Rank- Dependent Probabilities,” Journal of Economic Theory 42, 370–381.Google Scholar
  3. Chew, S.H. and K.R. MacCrimmon (1979). “Alpha Utility Theory: A Generalization of Expected Utility Theory,” Faculty of Commerce and Business Administration Working Paper #669, University of British Columbia.Google Scholar
  4. Dekel, E. (1986). “An Axiomatic Characterization of Preferences under Uncertainty: Weakening the Independence Axiom”, Journal of Economic Theory 40, 304–318.Google Scholar
  5. Gorman, W.M. (1968), “The Structure of Utility Functions”, Review of Economic Studies 35, 367–390.Google Scholar
  6. Gul, F. (1988), “Neo-Bernoullian Extensions and the Expected Utility Hypotheses and a Theory of Disappointment”, mimeo., Stanford Graduate School of Business.Google Scholar
  7. Friedman, M. and L.J. Savage (1948). “The Utility Analysis of Choices Involving Risk”, Journal of Political Economy 56, 279–304.Google Scholar
  8. Kahneman, D. and A. Tversky (1984), “Choices, Values and Frames”, American Psychologist 39, 341–350.Google Scholar
  9. Kahneman, D. and A. Tversky (1979), “Prospect Theory: An Analysis of Decision under Risk”, Econometrica 47, 263–291.Google Scholar
  10. Loomes, G. and R. Sugden (1982), “Regret Theory: An Alternative Theory of Rational Choice under Uncertainty”, Economic Journal 92, 805–824.Google Scholar
  11. Machina, M. (1982), “‘Expected Utility’ Analysis without the Independence Axiom”, Econometrica 50, 277–323.Google Scholar
  12. MacCrimmon, K. and S. Larsen (1979), “Utility Theory: Axioms versus ‘Paradoxes’” in Expected Utility Hypotheses and the Allais Paradox M. Allais and O. Hager (eds.) Holland: D. Reidel.Google Scholar
  13. Quiggin, J. (1982), “A Theory of Anticipated Utility”, Journal of Economic Behavior and Organization 3, 323–343.Google Scholar
  14. Royden, H. (1963), Real Analysis, Macmillan, New York.Google Scholar
  15. Segal, U. (1987). “Two-Stage Lotteries without the Reduction Axiom”. University of Toledo working paper no. 8708.Google Scholar
  16. Segal, U. (1984), “Nonlinear Decision Weights With the Independence Axiom”, UCLA Working Paper #353.Google Scholar
  17. Yaari, M. (1987) “The Dual Theory of Choice Under Risk”, Econometrica 55, 96–115.Google Scholar

Copyright information

© Kluwer Academic Publishers 1988

Authors and Affiliations

  • Jerry R. Green
    • 1
  • Bruno Jullien
    • 2
  1. 1.Harvard UniversityUSA
  2. 2.Harvard UniversityUSA

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