Annals of Operations Research

, Volume 23, Issue 1, pp 201–212 | Cite as

Expected utility with nonlinear threshold

  • Yutaka Nakamura


This paper axiomatizes a nonlinear threshold representation for expected utility, which generalizes a linear threshold representation established by Nakamura [10]. The advantage of a nonlinear threshold lies in its applicability to the monetary context. When the consequence space is the real line, interpreted as wealth, the nonlinear threshold can account for the intransitivity of the indifference relation over gambles, whereas the threshold vanishes in the linear threshold representation.


Real Line Consequence Space Linear Threshold Indifference Relation Threshold Representation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. [1]
    R.J. Aumann, Utility theory without the completeness axiom, Econometrica 30(1962)445–462.Google Scholar
  2. [2]
    P.C. Fishburn, Semiorders and risky choices, J. Math. Psychol. 5(1968)358–361.Google Scholar
  3. [3]
    P.C. Fishburn, One-way expected utility with finite consequence spaces, Ann. Math. Statist. 42(1971)572–577.Google Scholar
  4. [4]
    P.C. Fishburn,The Foundations of Expected Utility (Reidel, Dordrecht, 1982).Google Scholar
  5. [5]
    P.C. Fishburn, Nontransitive measurable utility, J. Math. Psychol. 26(1982)31–67.Google Scholar
  6. [6]
    P.C. Fishburn,Interval orders and interval graphs (Wiley New York, 1985).Google Scholar
  7. [7]
    D.M. Grether and C.R. Plott, Economic theory of choice and the preference reversal phenomenon, Amer. Econ. Rev. 69(1979)623–638.Google Scholar
  8. [8]
    R.D. Luce, Semiorders and a theory of utility discrimination, Econometrica 24(1956)178–191.Google Scholar
  9. [9]
    R.D. Luce, Three axiom systems for additive semiordered structures, SIAM J. Appl. Math. 25(1973)41–53.Google Scholar
  10. [10]
    Y. Nakamura, Expected utility with an interval ordered structure, J. Math. Psychol. 32(1988)298–312.Google Scholar
  11. [11]
    Y. Nakamura, Bilinear utility and a threshold structure for nontransitive preferences, Math. Social. Sci. 19(1990)1–21.Google Scholar
  12. [12]
    P. Slovic and S. Lichtenstein, Preference reversals: A broader perspective, Amer. Econ. Rev. 73(1983) 596–605.Google Scholar
  13. [13]
    A. Tversky, Intransitivity of preferences, Psychol. Rev. 76(1969)31–48.Google Scholar
  14. [14]
    P. Vincke, Linear utility functions on semiordered mixture spaces, Econometrica 48(1980)771–775.Google Scholar

Copyright information

© J.C. Baltzer AG, Scientific Publishing Company 1990

Authors and Affiliations

  • Yutaka Nakamura
    • 1
  1. 1.Institute of Socio-Economic PlanningUniversity of TsukubaTsukuba, IbarakiJapan

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