Subjectively Expected State-Independent Utility on State-Dependent Consequence Domains

  • Peter J. Hammond
Chapter
Part of the Theory and Decision Library book series (TDLB, volume 40)

Abstract

The standard decision theories of Savage (1954) and of Anscombe and Aumann (1963) both rely on the assumption that there are “constant acts” yielding the same consequence in all states of the world. More precisely, they postulate that the domain of consequences is state independent. But there are many decision problems where this hypothesis makes no sense — for instance, where there is a risk of death or serious injury. The point was first made by Drèze (1958, 1961) that such problems do not fit well with Savage’s (1954) assumption that all consequences are possible in every state of the world.

Keywords

Subjective Probability Expect Utility Theory Consequence Domain Universal Domain Contingent Preference 
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References

  1. Anscombe, F.J. and R.J. Aumann: “A Definition of Subjective Probability,” Annals of Mathematical Statistics 34, (1963) 199–205.CrossRefGoogle Scholar
  2. Arrow, K.J.: “Optimal Insurance and Generalized Deductibles,” Scandinavian Actuarial Journal 1 (1974), 1–42. Reprinted in The Collected Papers of Kenneth J. Arrow, 3: Individual Choice under Certainty and Uncertainty. The Belknap Press of Harvard University Press: Cambridge, MA, 1983, ch. 12, pp. 212–260.Google Scholar
  3. Blume, L., A. Brandenburger and E. Dekel: “Lexicographic Probabilities and Choice Under Uncertainty,” Econometrics 59, (1991) 61–79.CrossRefGoogle Scholar
  4. Drèze, J.H.: Individual Decision Making under Partially Controllable Uncertainty. Unpublished Ph.D. dissertation, Columbia University, 1958.Google Scholar
  5. Drèze, J.H.: “Fondements logiques de la probabilité subjective et de l’utilité,” in La Décision. Paris: CNRS, 1961, pp. 73–87; translated as “Logical Foundations of Cardinal Utility and Subjective Probability” with postscript in Drèze (1987a), ch. 3, pp. 90–104.Google Scholar
  6. Drèze, J.H. Essays on Economic Decisions under Uncertainty. Cambridge University Press: Cambridge, 1987a.CrossRefGoogle Scholar
  7. Fishburn, P.C. Utility Theory for Decision Making. John Wiley: New York, 1970.Google Scholar
  8. Hammond, P.J. “Consequentialist Foundations for Expected Utility,” Theory and Decision 25, (1988) 25–78.CrossRefGoogle Scholar
  9. Jensen, N.E. “An Introduction to Bernoullian Utility Theory, I: Utility Functions,” Swedish Journal of Economics 69, (1967) 163–183.CrossRefGoogle Scholar
  10. Jones-Lee, M.W. “The Expected Conditional Utility Theorem for the Case of Personal Probabilities and State-Conditional Utililty Functions: A Proof and Some Notes,” Economic Journal 89, (1979) 834–849.CrossRefGoogle Scholar
  11. Karni, E. Decision Making under Uncertainty: The Case of State-Dependent Preferences. Harvard University Press: Cambridge MA, 1985.Google Scholar
  12. Karni, E. “State-Dependent Preferences,” in Eatwell, J., Milgate, M. and P. Newman (eds.) The New Palgrave: A Dictionary of Economics. Macmillan: London, 1987; reprinted in Eatwell, J., Milgate, M. and P. Newman (eds.) The New Palgrave: Utility and Probability. Macmillan: London, 1990, pp. 242–247.Google Scholar
  13. Karni, E. “A Definition of Subjective Probabilities with State-Dependent Preferences,” Econometrics 61, (1993a) 187–198.CrossRefGoogle Scholar
  14. Karni, E. “Subjective Expected Utility Theory with State-Dependent Preferences,” Journal of Economic Theory 60, (1993b) 428–438.CrossRefGoogle Scholar
  15. Karni, E. and P. Mongin, E. and P. Mongin “More on State-Dependent Preferences and the Uniqueness of Subjective Probability,” preprint, 1997.Google Scholar
  16. Karni, E., and D. Schmeidler “Utility Theory with Uncertainty,” in W. Hildenbrand and H. Sonnenschein (eds.) Handbook of Mathematical Economics, Vol. IV. North-Holland: Amsterdam, 1991, ch. 33, pp. 1763–1831.Google Scholar
  17. Karni, E., Schmeidler, D. and K. Vind “On State Dependent Preferences and Subjective Probabilities,” Econometrica 51, (1983) 1021–1031.CrossRefGoogle Scholar
  18. Machina, M.J. “Choice under Uncertainty: Problems Solved and Unsolved,” Journal of Economic Perspectives 1,(1987, No. 1, Summer) 121–154.Google Scholar
  19. Mongin, P. “The Paradox of Bayesian Experts and State-Dependent Utility Theory,” Journal of Mathematical Economics,in press (1997).Google Scholar
  20. Myerson, R..B. “An Axiomatic Derivation of Subjective Probability, Utility, and Evaluation Functions,” Theory and Decision 11, (1979) 339–352.CrossRefGoogle Scholar
  21. R.aiffa, H. “Risk, Ambiguity, and the Savage Axioms: Comment,” Quarterly Journal of Economics 75, (1961) 690–694.CrossRefGoogle Scholar
  22. Savage, L.J. The Foundations of Statistics. John Wiley: New York, 1954; and Dover Publications: New York, 1972.Google Scholar
  23. Schervish, M.J., Seidenfeld, T., and J.B. Kadane “State-Dependent Utilities,” Journal of the American Statistical Association 85, (1990) 840–847.CrossRefGoogle Scholar
  24. Wilson, RB. “The Theory of Syndicates,” Econometrics 36, (1968) 119–132.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1999

Authors and Affiliations

  • Peter J. Hammond
    • 1
  1. 1.Department of EconomicsStanford UniversityUSA

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