Skip to main content
Log in

Subjective utility with upper and lower probabilities on finite states

  • Published:
Journal of Risk and Uncertainty Aims and scope Submit manuscript

Abstract

This article is concerned with thresholds of discrimination of preference judgments under uncertainty. We establish an axiomatic characterization for a threshold representation, where thresholds are represented by inexact measurement of subjective probabilities, i.e., upper and lower probabilities. Since upper and lower probabilities need not be additive, the representational form adopts the Choquet integration.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Anscombe, F.J. and Robert J. Aumann. (1963). “A Definition of Subjective Probability,”Annals of Mathematical Statistics 34, 199–205.

    Google Scholar 

  • Choquet, Gustave. (1953–54). “Theory of Capacities,”Annales de l'Institut Fourier 5, 131–295.

    Google Scholar 

  • Fishburn, Peter C. (1968). “Semiorders and Risky Choices,”Journal of Mathematical Psychology 5, 358–361.

    Google Scholar 

  • Fishburn, Peter C. (1970).Utility Theory for Decision Making. New York: Wiley.

    Google Scholar 

  • Fishburn, Peter C. (1986). “The Axioms of Subjective Probability,”Statistical Science 1, 335–358.

    Google Scholar 

  • Fishburn, Peter C. and Yutaka Nakamura. (1991). “Nontransitive Measurable Utility with Constant Threshold,”Journal of Mathematical Psychology 35, 471–500.

    Google Scholar 

  • Gilboa, Itzhak. (1987). “Expected Utility with Purely Subjective Non-additive Probabilities,”Journal of Mathematical Economics 16, 65–88.

    Google Scholar 

  • Gilboa, Itzhak. (1989). “Duality in Non-additive Expected Utility Theory,”Annals of Operations Research 19, 405–414.

    Google Scholar 

  • Gurevich, E.S. and G.E. Naumov. (1987). “Interval Representation of Utility,”Automatika i Telemekhanika 10, 122–131 (in Russian) (translatedAutomation and Remote Control, 1988, 1371–1378).

    Google Scholar 

  • Luce, R. Duncan. (1956). “Semiorders and a Theory of Utility Discrimination,”Econometrica 24, 178–191.

    Google Scholar 

  • Nakamura, Yutaka. (1988). “Expected Utility with an Interval Ordered Structure,”Journal of Mathematical Psychology 32, 298–312.

    Google Scholar 

  • Nakamura, Yutaka. (1990a). “Expected Utility with Nonlinear Threshold,”Annals of Operations Research 23, 201–212.

    Google Scholar 

  • Nakamura, Yutaka. (1990b). “Bilinear Utility and Threshold Structures for Nontransitive Preferences,”Mathematical Social Sciences 19, 1–21.

    Google Scholar 

  • Nakamura, Yutaka. (1990c). “Subjective Expected Utility with Non-additive Probabilities on Finite State Spaces,”Journal of Economic Theory 51, 346–366.

    Google Scholar 

  • Nakamura, Yutaka. (1992a). “Multisymmetric Structures and Non-expected Utility,”Journal of Mathematical Psychology 36, 375–395.

    Google Scholar 

  • Nakamura, Yutaka. (1992b). “Threshold Representations of Transitive Preferences under Risk,” discussion paper, Institute of Socio-Economic Planning, University of Tsukuba, Ibaraki, Japan.

    Google Scholar 

  • Savage, Leonard J. (1954).The Foundations of Statistics. New York: Wiley. Second revised ed., New York: Dover, 1972.

    Google Scholar 

  • Schmeidler, David. (1984). “Subjective Probability and Expected Utility without Additivity,” Preprint 84, Institute of Mathematics and its Applications, University of Minnesota, Minneapolis.

    Google Scholar 

  • Schmeidler, David. (1989). “Subjective Probability and Expected Utility without Additivity,”Econometrica 57, 571–587.

    Google Scholar 

  • Suppes, Patrick. (1975). “Approximate Probability and Expectation of Gambles,”Erkenntnis 9, 153–161.

    Google Scholar 

  • Vincke, Philippe. (1980). “Linear Utility Function on Semiordered Mixture Spaces,”Econometrica 48, 771–775.

    Google Scholar 

  • Wakker, Peter. (1989a). “Continuous Subjective Expected Utility with Nonadditive Probabilities,”Journal of Mathematical Economics 18, 1–27.

    Google Scholar 

  • Wakker, Peter. (1989b).Additive Representation of Preferences. Boston: Kluwer Academic Publishers.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Nakamura, Y. Subjective utility with upper and lower probabilities on finite states. J Risk Uncertainty 6, 33–48 (1993). https://doi.org/10.1007/BF01065349

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01065349

Key words

Navigation