Skip to main content

Normative Theories of Decision Making under Risk and under Uncertainty

  • Chapter
Book cover Non-Conventional Preference Relations in Decision Making

Part of the book series: Lecture Notes in Economics and Mathematical Systems ((LNE,volume 301))

  • 153 Accesses

Abstract

Theories of rational preference and choice in situations of decision making under risk and under uncertainty that were developed during the 1940’s and 1950’s have come under increasing fire because of their inability to model certain types of reasonable and persistent patterns of preference. This essay outlines the standard theories, discusses defenses and criticisms of their axioms, and reviews recent efforts to generalize them in such a way that the new theories model a wider spectrum of reasonable behaviors without giving up too much of the mathematical convenience and elegance of the earlier theories.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Allais, M. “Le comportement de l’homme rationnel devant le risque: critique des postulats et axiomes de l’école Américaine.” Econometrica 21 (1953), pp. 503–546

    Article  Google Scholar 

  • Allais, M. “The Foundations of a Positive Theory of Choice Involving Risk and a Criticism of the Postulates and Axioms of the American School (1952).” In Expected Utility Hypotheses and the Allais Paradox, ed. by M. Allais and O. Hagen. Dordrecht, Holland: Reidel, 1979, pp. p27–145. a

    Chapter  Google Scholar 

  • Allais, M. “The So-Called Allais Paradox and Rational Decisions Under Uncertainty.” In Expected Utility Hypothesis Utility and the Allais Paradox, ed. by M. Allais and O. Hagen. Dordrecht, Holland: Reidel, 1979, pp. 437–681. b

    Chapter  Google Scholar 

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

    Article  Google Scholar 

  • Arrow, K. J. Aspects of the Theory of Risk Bearing Helsinki: Yrjö Jahssonin Säätiö, 1965.

    Google Scholar 

  • Bayes, T. “An Essay Towards Solving a Problem in the Doctrine of Chances.” Philosophical Transactions of the Royal Society 53 (1763), pp. 370–418. Reprinted with comments by E. C.

    Article  Google Scholar 

  • Molina in Facsimiles of Two Papers of Bayes Washington, D.C.: The Graduate School, Department of Agriculture, 1940.

    Google Scholar 

  • Bell, D. E. “Regret in Decision Making Under Uncertainty.” Operations Research 30 (1982), pp. 961–981.

    Article  Google Scholar 

  • Bernoulli, D. “Specimen theoriae novae de mensura sortis.” Commentarii Academiae Scientiarum Imperialis Petropolitanae 5 (1738), pp. 175–192. Translated by L. Sommer,

    Google Scholar 

  • Bernoulli, D. “Specimen theoriae novae de mensura sortis.” Econometrica 22 (1954), pp. 23–36.

    Article  Google Scholar 

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

    Google Scholar 

  • Chew, S. H. “A Mixture Set Axiomatization of Weighted Utility Theory.” College of Business & Public Administration Discussion Paper 82–4, University of Arizona, 1982.

    Google Scholar 

  • Chew, S. H. “A Generalization of the Quasilinear Mean with Applications to the Measurement of Income Inequality and Decision Theory Resolving the Allais Paradox.” Econometrica 51 (1983), pp. 1065–1092.

    Article  Google Scholar 

  • Chew, S. H., and MacCrimmon, K. R. “Alpha-Nu Choice Theory: A Generalization of Expected Utility Theory.” Faculty of Commerce and Business Administration Working Paper 669, University of British Columbia, 1979.

    Google Scholar 

  • Chipman, J. S. “The Foundations of Utility.” Econometrica 28 (1960), pp. 193–224.

    Article  Google Scholar 

  • de Finetti, B. “La prévision ses lois logiques, ses sources subjectives.” Annals de l’Institut Henri Poincaré 7 (1937), pp. 1–68.

    Google Scholar 

  • de Finetti, B. Translated by H. E. Kyburg in Studies in Subjective Probability, ed. by H. E. Kyburg and H. E. Smokier. New York: Wiley, 1964.

    Google Scholar 

  • Edwards, W. “The Theory of Decision Making.” Psychological Bulletin 51 (1954), pp. 380–417.

    Article  Google Scholar 

  • Ellsberg, D. “Risk, Ambiguity, and the Savage Axioms.” Quarterly Journal of Economics 75 (1961), pp. 643–669.

    Article  Google Scholar 

  • Fishburn, P. C. “Preference-Based Definitions of Subjective Probability.” Annals of Mathematical Statistics 38 (1967), pp. 1605–1617.

    Article  Google Scholar 

  • Fishburn, P. C. Utility Theory for Decision Making New York: Wiley, 1970.

    Google Scholar 

  • Fishburn, P. C. “Lexicographic Orders, Utilities, and Decision Rules: A Survey.” Management Science 20 (1974), pp. 1442–1471.

    Article  Google Scholar 

  • Fishburn, P. C. “Subjective Expected Utility: A Review of Normative Theories.” Theory and Decision 13 (1981), pp. 139–199.

    Article  Google Scholar 

  • Fishburn, P. C. The Foundations of Expected Utility Dordrecht, Holland: Reidel, 1982. a.

    Book  Google Scholar 

  • Fishburn, P. C. “Nontransitive Measurable Utility.” Journal of Mathematical Psychology 26 (1982), pp. 31–67. b.

    Article  Google Scholar 

  • Fishburn, P. C. “Transitive Measurable Utility.” Journal of Economic Theory 31 (1983), pp. 293–317. a.

    Article  Google Scholar 

  • Fishburn, P. C. “Ellsberg Revisited: A New Look at Comparative Probability.” Annals of Statistics 11 (1983), pp. 1047–1059. b.

    Google Scholar 

  • Fishburn, P. C. “Dominance in SSB Utility Theory.” Journal of Economic Theory 34 (1984), pp. 130–148. a.

    Article  Google Scholar 

  • Fishburn, P. C. “Probabilistic Social Choice Based on Simple Voting Comparisons.” Review of Economic Studies 51 (1984), pp. 683–692. b.

    Article  Google Scholar 

  • Fishburn, P. C. “SSB Utility Theory and Decision-Making under Uncertainty.” Mathematical Social Sciences 8 (1984), pp. 253–285. c.

    Article  Google Scholar 

  • Fishburn, P. C. “Nontransitive Preference Theory and the Preference Reversal Phenomenon.” International Review of Economics and Business 32 (1985), pp. 39–50.

    Google Scholar 

  • Fishburn, P. C. “Uncertainty Aversion and Separated Effects in Decision Making under Uncertainty.” Unpublished manuscript (1986).

    Google Scholar 

  • Friedman, M., and Savage, L. J. “The Utility Analysis of Choices Involving Risk.” Journal of Political Economy 56 (1948), pp. 279–304.

    Article  Google Scholar 

  • Gilboa, I. “Expected Utility with Purely Subjective Non-Additive Probabilities.” Working Paper 6–85, Foerder Institute for Economic Research, Tel-Aviv University, 1985.

    Google Scholar 

  • Hausner, M. “Multidimensional Utilities.” In Decision Processes, ed. by R. M. Thrall, C. H. Coombs, and R. L. Davis. New York: Wiley, 1954, pp. 167–180.

    Google Scholar 

  • Herstein, I. N., and Milnor, J. “An Axiomatic Approach to Measurable Utility.” Econometrica 21 (1953), pp. 291–297.

    Article  Google Scholar 

  • Kahneman, D., and Tversky, A. “Prospect Theory: An Analysis of Decision Under Risk.” Econometrica 47 (1979), pp. 263–291.

    Article  Google Scholar 

  • Libby, R., and Fishburn, P. C. “Behavioral Models of Risk Taking in Business Decisions: A Survey and Evaluation.” Journal of Accounting Research 15 (1977), pp. 272–292.

    Article  Google Scholar 

  • Loomes, G., and Sugden, R. “Regret Theory: An Alternative Theory of Rational Choice Under Uncertainty.” Economic Journal 92 (1982), pp. 805–824.

    Article  Google Scholar 

  • Loomes, G., and Sugden, R. “A Rationale for Preference Reversal.” American Economic Review 73 (1983), pp. 428–432.

    Google Scholar 

  • Luce, R. D., and Narens, L. “Classification of Concatenation Measurement Structures According to Scale Type.” Journal of Mathematical Psychology 29 (1985), pp. 1–72.

    Article  Google Scholar 

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

    Google Scholar 

  • MacCrimmon, K. R. “Descriptive and Normative Implications of the Decision-Theory Postulates.” In Risk and Uncertainty, ed. by K. Borch and J. Mossin. New York: Macmillan, 1968, pp. 3–32.

    Google Scholar 

  • MacCrimmon, K. R., and Larsson, S. “Utility Theory: Axioms versus ‘Paradoxes’.” In Expected Utility Hypotheses and the Allais Paradox, ed. by M. Allais and O. Hagen. Dordrecht, Holland: Reidel, 1979, pp. 333–409.

    Chapter  Google Scholar 

  • Machina, M. J. “‘Expected Utility’ Analysis Without the Independence Axiom.” Econometrica 50 (1982), pp. 277–323. a.

    Article  Google Scholar 

  • Machina, M. J. “A Stronger Characterization of Declining Risk Aversion.” Econometrica 50 (1982), pp. 1069–1079. b.

    Article  Google Scholar 

  • May, K. O. “Intransitivity, Utility, and the Aggregation of Preference Patterns.” Econometrica 22 (1954), pp. 1–13.

    Article  Google Scholar 

  • Morrison, D. G. “On the Consistency of Preferences in Allais’ Paradox.” Behavioral Science 12 (1967), pp. 373–383.

    Article  Google Scholar 

  • Mosteller, F., and Nogee, P. “An Experimental Measure of Utility.” Journal of Political Economy 59 (1951), pp. 371–404.

    Article  Google Scholar 

  • Payne, J. W. “Alternative Approaches to Decision Making Under Risk: Moments versus Risk Dimensions.” Psychological Bulletin 80 (1973), pp. 439–453.

    Article  Google Scholar 

  • Pratt, J. W. “Risk Aversion in the Small and in the Large.” Econometrica 32 (1964), pp. 122–136.

    Article  Google Scholar 

  • Pratt, J. W., Raiffa, H., and Schlaifer, R. “The Foundations of Decision Under Uncertainty: An Elementary Exposition.” Journal of the American Statistical Association 59 (1964), pp. 353–375.

    Article  Google Scholar 

  • Preston, M. G., and Baratta, P. “An Experimental Study of the Auction-Value of an Uncertain Outcome.” American Journal of Psychology 61 (1948), pp. 183–193.

    Article  Google Scholar 

  • Ramsey, F. P. “Truth and Probability.” In The Foundations of Mathematics and Other Logical Essays, by F. P. Ramsey. New York: Harcourt, Brace, 1931. Reprinted in Studies in Subjective Probability, ed. by H. E. Kyburg and H. E. Smokier. New York: Wiley, 1964, pp. 61–92.

    Google Scholar 

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

    Google Scholar 

  • Schmeidler, D. “Subjective Probability and Expected Utility Without Additivity.” Preprint #84, The Institute for Mathematics and its Applications, University of Minnesota, 1984.

    Google Scholar 

  • Slovic, P. “The Relative Influence of Probabilities and Payoffs upon Perceived Risk of a Gamble.” Psychonomic Science 9 (1967), pp. 223–224.

    Google Scholar 

  • Slovic, P., and Lichtenstein, S. “Preference Reversals: A Broader Perspective.” American Economic Review 73 (1983), pp. 596–605.

    Google Scholar 

  • Tversky, A. “Intransitivity of Preferences.” Psychological Review 76 (1969), pp. 31–48.

    Article  Google Scholar 

  • von Neumann, J., and Morgenstern, O. Theory of Games and Economic Behavior Princeton: Princeton University Press, 1944. Second edition, 1947; third edition, 1953.

    Google Scholar 

  • Whitmore, G. A., and Findlay, M. C. (eds.). Stochastic Dominance Lexington, Massachusetts: D. C. Heath, 1978.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1988 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Fishburn, P.C. (1988). Normative Theories of Decision Making under Risk and under Uncertainty. In: Kacprzyk, J., Roubens, M. (eds) Non-Conventional Preference Relations in Decision Making. Lecture Notes in Economics and Mathematical Systems, vol 301. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-51711-2_1

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-51711-2_1

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-18954-1

  • Online ISBN: 978-3-642-51711-2

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics