[go: up one dir, main page]
More Web Proxy on the site http://driver.im/ Skip to main content
Springer Nature Link
Log in

Subjective expected utility: A review of normative theories

  • Published:
Theory and Decision Aims and scope Submit manuscript

Abstract

This paper reviews theories of subjective expected utility for decision making under uncertainty. It focuses on normative interpretations and discusses the primitives, axioms and representation-uniqueness theorems for a number of theories. Similarities and differences among the various theories are highlighted. The interplay between realistic decision structures and structural axioms that facilitate mathematical derivations is also emphasized.

The review attempts to be complete up to 1980. Among others, it includes theories developed by Ramsey; Savage; Suppes; Davidson and Suppes; Anscombe and Aumann; Pratt, Raiffa and Schlaifer; Fishburn; Bolker; Jeffrey; Pfanzagl; Luce and Krantz.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
£29.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (United Kingdom)

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Allais, M., 1953, ‘Le Comportement de l'Homme Rationnel Devant le Risque: Critique des Postulats et Axiomes de l'École Américaine’, Econometrica 21, 503–546.

    Google Scholar 

  • Anscombe, F. J. and Aumann, R. J., 1963, ‘A Definition of Subjective Probability’, Annals of Mathematical Statistics 34, 199–205.

    Google Scholar 

  • Arrow, K. J., 1951, ‘Alternative Approaches to the Theory of Choice in Risk-Taking Situations’, Econometrica 19, 404–437.

    Google Scholar 

  • Arrow, K. J., 1966, ‘Exposition of the Theory of Choice under Uncertainty’, Synthese 16, 253–269.

    Google Scholar 

  • Balch, M., 1974, ‘On Recent Developments in Subjective Expected Utility’, in M. Balch, D. McFadden and S. Wu (eds.), Essays on Economic Behavior Under Uncertainty, North-Holland, Amsterdam, pp. 45–54.

    Google Scholar 

  • Balch, M. and Fishburn, P. C., 1974, ‘Subjective Expected Utility for Conditional Primitives’, in M. Balch, D. McFadden and S. Wu (eds.), Essays on Economic Behavior Under Uncertainty, North-Holland, Amsterdam, pp. 57–69.

    Google Scholar 

  • Becker, G. M. and McClintock, C. G., 1967, ‘Value: Behavioral Decision Theory’, Annual Review of Psychology 18, 237–286.

    Google Scholar 

  • Blackwell, D. and Girshick, M. A., 1954, Theory of Games and Statistical Decisions, Wiley, New York.

    Google Scholar 

  • Bolker, E. D., 1966, ‘Functions Resembling Quotients of Measures’, Transactions of the American Mathematical Society 124, 292–312.

    Google Scholar 

  • Bolker, E. D., 1967, ‘A Simultaneous Axiomatization of Utility and Subjective Probability’, Philosophy of Science 34, 333–340.

    Google Scholar 

  • Chernoff, H., 1954, ‘Rational Selection of Decision Functions’, Econometrica 22, 422–443.

    Google Scholar 

  • Davidson, D. and Suppes, P., 1956, ‘A Finitistic Axiomatization of Subjective Probability and Utility’, Econometrica 24, 264–275.

    Google Scholar 

  • Davidson, D., Suppes, P. and Siegel, S., 1957, Decision Making: An Experimental Approach, Stanford University Press, Stanford, California.

    Google Scholar 

  • Debreu, G., 1959, ‘Cardinal Utility for Even-chance Mixtures of Pairs of Sure Prospects’, Review of Economic Studies 26, 174–177.

    Google Scholar 

  • Debreu, G., 1960, ‘Topological Methods in Cardinal Utility Theory’, in K. J. Arrow, S. Karlin and P. Suppes (eds.), Mathematical Methods in the Social Sciences, 1959, Stanford University Press, Stanford, California, pp. 16–26.

    Google Scholar 

  • de Finetti, B., 1937, ‘La Prévision ses Lois Logiques, ses Sources Subjectives’, Annales de l'Institut Henri Poincaré 7, 1–68. Translated by H. E. Kyburg as ‘Foresight: Its Logical Laws, Its Subjective Sources’, in H. E. Kyburg and H. E. Smokler (eds.), Studies in Subjective Probability, Wiley, New York, 1964, pp. 97–158.

    Google Scholar 

  • Domotor, Z., 1978, ‘Axiomatization of Jeffrey Utilities’, Synthese 39, 165–210.

    Google Scholar 

  • Dubins, L. E. and Savage, L. J., 1965, How to Gamble if You Must: Inequalities for Stochastic Processes, McGraw-Hill, New York.

    Google Scholar 

  • Edwards, W., 1954, ‘The Theory of Decision Making’, Psychological Bulletin 51, 380–417.

    Google Scholar 

  • Ellsberg, D., 1961, ‘Risk, Ambiguity, and the Savage Axioms’, Quarterly Journal of Economics 75, 643–669.

    Google Scholar 

  • Ferreira, P. E., 1972, ‘On Subjective Probability and Expected Utilities’, Annals of Mathematical Statistics 43, 928–933.

    Google Scholar 

  • Fishburn, P. C., 1964, Decision and Value Theory, Wiley, New York.

    Google Scholar 

  • Fishburn, P. C., 1967, ‘Preference-Based Definitions of Subjective Probability’, Annals of Mathematical Statistics 38, 1605–1617.

    Google Scholar 

  • Fishburn, P. C., 1969, ‘A General Theory of Subjective Probabilities and Expected Utilities’, Annals of Mathematical Statistics 40, 1419–1429.

    Google Scholar 

  • Fishburn, P. C., 1970, Utility Theory for Decision Making, Wiley, New York. Reprinted by Krieger Publishing Co., Huntington, New York, 1979.

    Google Scholar 

  • Fishburn, P. C., 1972, ‘Subjective Expected Utility with Mixture Sets and Boolean Algebras’, Annals of Mathematical Statistics, 43, 917–927.

    Google Scholar 

  • Fishburn, P. C., 1973, ‘A Mixture-Set Axiomatization of Conditional Subjective Expected Utility’, Econometrica 41, 1–25.

    Google Scholar 

  • Fishburn, P. C., 1974, ‘On the Foundations of Decision Making Under Uncertainty’, in M. Balch, D. McFadden and S. Wu (eds.), Essays on Economic Behavior Under Uncertainty, North-Holland, Amsterdam, pp. 25–44.

    Google Scholar 

  • Fishburn, P. C., 1975, ‘A Theory of Subjective Expected Utility with Vague Preferences’, Theory and Decision 6, 287–310.

    Google Scholar 

  • Fishburn, P. C., 1977, ‘Expected Utility Theories: A Review Note’, in R. Henn and O. Moeschlin (eds.), Mathematical Economics and Game Theory, Springer-Verlag, Berlin and New York, pp. 197–207.

    Google Scholar 

  • Fishburn, P. C. and Roberts, F. S., 1978, ‘Mixture Axioms in Linear and Multilinear Utility Theories’, Theory and Decision 9, 161–171.

    Google Scholar 

  • Friedman, M. and Savage, L. J., 1952, ‘The Expected Utility Hypothesis and the Measurability of Utility’, Journal of Political Economy 60, 463–474.

    Google Scholar 

  • Gibbard, A. and Harper, W. L., 1978, ‘Counterfactuals and Two Kinds of Expected Utility’, in C. A. Hooker, J. J. Leach and E. F. McClennen (eds.), Foundations and Applications of Decision Theory, Vol. I: Theoretical Foundations, Reidel, Dordrecht, Holland, pp. 125–162.

    Google Scholar 

  • Grether, D. M. and Plott, C. R., 1979, ‘Economic Theory of Choice and the Preference Reversal Phenomenon’, American Economic Review 69, 623–638.

    Google Scholar 

  • Hausdorff, F., 1957, Set Theory (translation), Chelsea, New York.

    Google Scholar 

  • Hausner, M., 1954, ‘Multidimensional Utilities’, in R. M. Thrall, C. H. Coombs and R. L. Davis (eds.), Decision Processes, Wiley, New York, pp. 167–180.

    Google Scholar 

  • Herstein, I. N. and Milnor, J., 1953, ‘An Axiomatic Approach to Measurable Utility’, Econometrica 21, 291–297.

    Google Scholar 

  • Jeffrey, R. C., 1965a, The Logic of Decision, McGraw-Hill, New York.

    Google Scholar 

  • Jeffrey, R. C., 1965b, ‘Ethics and the Logic of Decision’, Journal of Philosophy 62, 528–539.

    Google Scholar 

  • Jeffrey, R. C., 1974, ‘Frameworks for Preference’, in M. Balch, D. McFadden and S. Wu (eds.), Essays on Economic Behavior Under Uncertainty, North-Holland, Amsterdam, pp. 74–79.

    Google Scholar 

  • Jeffrey, R. C., ‘Axiomatizing the Logic of Decision’, in C. A. Hooker, J. J. Leach and E. F. McClennen (eds.), Foundations and Applications of Decision Theory, Vol. I: Theoretical Foundations, Reidel, Dordrecht, Holland, pp. 227–231.

  • Jensen, N. E., 1967, ‘An Introduction of Bernoullian Utility Theory. I. Utility Functions’, Swedish Journal of Economics 69, 163–183.

    Google Scholar 

  • Kahneman, D. and Tversky, A., 1979, ‘Prospect Theory: An Analysis of Decision Under Risk’, Econometrica 47, 263–291.

    Google Scholar 

  • Krantz, D. H., Luce, R. D., Suppes, P. and Tversky, A., 1971, Foundations of Measurement, Volume I, Academic Press, New York.

    Google Scholar 

  • Luce, R. D., 1956, ‘Semiorders and a Theory of Utility Discrimination’, Econometrica 24, 178–191.

    Google Scholar 

  • Luce, R. D., 1958, ‘A Probabilistic Theory of Utility’, Econometrica 26, 193–224.

    Google Scholar 

  • Luce, R. D., 1972, ‘Conditional Expected, Extensive Utility’, Theory and Decision 3, 101–106.

    Google Scholar 

  • Luce, R. D. and Krantz, D. H., 1971, ‘Conditional Expected Utility’, Econometrica 39, 253–271.

    Google Scholar 

  • Luce, R. D. and Raiffa, H., 1957, Games and Decisions, Wiley, New York.

    Google Scholar 

  • Luce, R. D. and Suppes, P., 1965, ‘Preference, Utility, and Subjective Probability’, in R. D. Luce, R. R. Bush and E. Galanter (eds.), Handbook of Mathematical Psychology, III, Wiley, New York, pp. 250–410.

    Google Scholar 

  • Luce, R. D. and Tukey, J. W., 1964, Simultaneous Conjoint Measurement: A New Type of Fundamental Measurement, Journal of Mathematical Psychology 1, 1–27.

    Google Scholar 

  • MacCrimmon, K. R., 1968, ‘Descriptive and Normative Implications of the Decision Theory Postulates’, in K. Borch and J. Mossin (eds.), Risk and Uncertainty, Macmillan, New York, pp. 3–32.

    Google Scholar 

  • Marschak, J., 1950, ‘Rational Behavior, Uncertain Prospects, and Measurable Utility’, Econometrica 18, 111–141.

    Google Scholar 

  • Maskin, E., 1979, ‘Decision Making under Ignorance with Implications for Social Choice’, Theory and Decision 11, 319–337.

    Google Scholar 

  • Milnor, J., 1954, ‘Games Against Nature’, in R. M. Thrall, C. H. Coombs and R. L. Davis (eds.), Decision Processes, Wiley, New York, pp. 49–59.

    Google Scholar 

  • Myerson, R. B., 1979, ‘An Axiomatic Derivation of Subjective Probability, Utility, and Evaluation Functions’, Theory and Decision 11, 339–352.

    Google Scholar 

  • Narens, L., 1976, Utility Uncertainty Trade-off Structures, Journal of Mathematical Psychology 13, 296–322.

    Google Scholar 

  • Pfanzagl, J., 1959, ‘A General Theory of Measurement: Applications to Utility’, Naval Research Logistics Quarterly 6, 283–294.

    Google Scholar 

  • Pfanzagl, J., 1967, ‘Subjective Probability Derived from the Morgenstern-von Neumann Utility Concept’, in M. Shubik (ed.), Essays in Mathematical Economics, Princeton University Press, Princeton, pp. 237–251.

    Google Scholar 

  • Pfanzagl, J., 1968, Theory of Measurement, Wiley, New York.

    Google Scholar 

  • Pratt, J. W., 1974, ‘Some Comments on Some Axioms for Decision Making Under Uncertainty’, in M. Balch, D. McFadden and S. Wu (eds.), Essays on Economic Behavior Under Uncertainty, North-Holland, Amsterdam, pp. 82–92.

    Google Scholar 

  • Pratt, J. W., Raiffa, H. and Schlaifer, R., 1964, ‘The Foundations of Decision under Uncertainty: An Elementary Exposition’, Journal of the American Statistical Association 59, 353–375.

    Google Scholar 

  • Pratt, J. W., Raiffa, H. and Schlaifer, R., 1965, Introduction to Statistical Decision Theory, McGraw-Hill, New York.

    Google Scholar 

  • Raiffa, H., 1961, ‘Risk, Ambiguity, and the Savage Axioms: Comment’, Quarterly Journal of Economics 75, 690–694.

    Google Scholar 

  • Ramsey, F. P., 1931, ‘Truth and Probability’, in F. P. Ramsey, The Foundations of Mathematics and Other Logical Essays, Harcourt, Brace and Co., New York, Reprinted in H. E. Kyburg and H. E. Smokler (eds.), Studies in Subjective Probability, Wiley, New York, 1964, pp. 61–92.

    Google Scholar 

  • Rapoport, A. and Wallsten, T. S., 1972, ‘Individual Decision Behavior’, Annual Review of Psychology 23, 131–176.

    Google Scholar 

  • Richter, M. K., 1975, ‘Rational Choice and Polynomial Measurement Models’, Journal of Mathematical Psychology 12, 99–113.

    Google Scholar 

  • Richter, M. K. and Shapiro, L., 1978, ‘Revelations of a Gambler’, Journal of Mathematical Economics 5, 229–244.

    Google Scholar 

  • Roberts, F. S., 1974, ‘Laws of Exchange and Their Applications’, SIAM Journal on Applied Mathematics 26, 260–284.

    Google Scholar 

  • Robinson, A., 1966, Non-standard Analysis, North-Holland, Amsterdam.

    Google Scholar 

  • Rubin, H., 1949, ‘Postulates for the Existence of Measurable Utility and Psychological Probability’ (abstract), Bulletin of the American Mathematical Society 55, 1050–1051.

    Google Scholar 

  • Savage, L. J., 1954, The Foundations of Statistics, Wiley, New York. Second revised edition, Dover Publications, New York, 1972.

    Google Scholar 

  • Savage, L. J., 1967, ‘Difficulties in the Theory of Personal Probability’, Philosophy of Science 34, 305–310. Discussions also by I. Hacking (pp. 311–325) and A. Shimony (pp. 326–332).

    Google Scholar 

  • Schick, F., 1967, Review of The Logic of Decision (by R. C. Jeffrey), Journal of Philosophy 64, 396–400.

    Google Scholar 

  • Scott, D. and Suppes, P., 1958, ‘Foundational Aspects of Theories of Measurement’, Journal of Symbolic Logic 23, 113–128.

    Google Scholar 

  • Shapiro, L., 1979, ‘Necessary and Sufficient Conditions for Expected Utility Maximization: The Finite Case, with a Partial Order’, Annals of Statistics 7, 1288–1302.

    Google Scholar 

  • Slovic, P. and Tversky, A., 1974, ‘Who Accepts Savage's Axiom?’, Behavioral Science 19, 368–373.

    Google Scholar 

  • Sneed, J. D., 1966, ‘Strategy and the Logic of Decision’, Synthese 16, 270–283.

    Google Scholar 

  • Spohn, W., 1977, ‘Where Luce and Krantz do Really Generalize Savage's Decision Model’, Erkenntnis 11, 113–134.

    Google Scholar 

  • Stigum, B. P., 1972, ‘Finite State Space and Expected Utility Maximization’, Econometrica 40, 253–259.

    Google Scholar 

  • Suppes, P., 1956, ‘The Role of Subjective Probability and Utility in Decision Making’, Proceedings of the Third Berkeley Symposium on Mathematical Statistics and Probability, 1954–1955 5, 61–73.

    Google Scholar 

  • Suppes, P. and Winet, M., 1955, ‘An Axiomatization of Utility Based on the Notion of Utility Differences’, Management Science 1, 259–270.

    Google Scholar 

  • Suppes, P. and Zinnes, J. L., 1963, ‘Basic Measurement Theory’, in R. D. Luce, R. R. Bush and E. Galanter (eds.), Handbook of Mathematical Psychology I, Wiley, New York, pp. 1–76.

    Google Scholar 

  • Tversky, A., 1967a, ‘A General Theory of Polynomial Conjoint Measurement’, Journal of Mathematical Psychology 4, 1–20.

    Google Scholar 

  • Tversky, A., 1967b, ‘Additivity, Utility, and Subjective Probability’, Journal of Mathematical Psychology 4, 175–201.

    Google Scholar 

  • Tversky, A., 1969, ‘Intransitivity of Preferences’, Psychological Review 76, 31–48.

    Google Scholar 

  • von Neumann, J. and Morgenstern, O., 1947, Theory of Games and Economic Behavior, 2nd ed., Princeton University Press, Princeton.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Bell Laboratories, New Jersey, USA

    Peter C. Fishburn

Authors
  1. Peter C. Fishburn
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Fishburn, P.C. Subjective expected utility: A review of normative theories. Theor Decis 13, 139–199 (1981). https://doi.org/10.1007/BF00134215

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00134215

Keywords

Search

Navigation