Abstract
A paradox is posed and analyzed in which people reverse their preferences for information on probabilities versus prizes once the range of the unknown probabilities is sufficiently narrowed. This reversal is shown to be incompatible with both objective expected utility (EU) as well as subjective versions in which the same probability transformation applies to all random variables. Experimental data are presented showing that the reversals occur with small, medium and large payoffs.
The present paradox is compared with those of Allais and Ellsberg, and found to differ in substantive ways. It raises further questions about the normative status of expected utility theory, especially its treatment of probability and value. The paradox specifically calls into question EU's substitution and compound probability axioms.
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References
Allais, M.: 1952, ‘The Foundations of A Positive Theory of Choice Involving Risk and A Criticism of the Postulates and Axioms of the American School’, translated in Allais, M. and Hagen, O. (Eds.), Expected Utility Hypotheses and the Allais Paradox, D. Reidel Publishing Co., Dordrecht, Holland, 1979.
Allais, M.: 1953, ‘Le comportement de l'homme rationnel devant le rísque: Critique des postulates et axioms de l'ecole Americaine’, Econometrica, 21, 503–546.
Bell, D. E.: 1982, ‘Regret in Decision Making Under Uncertainty’, Operations Research, 30, 961–981.
Bell, D. E. and Raiffa, H.: 1982, ‘Marginal Value and Intrinsic Risk Aversion’, in Risk: A Seminar Series, H. Kunreuther (Ed.), Laxenburg, Austria, International Institute for Applied Systems Analysis, pp. 325–350.
Camacho, A.: 1979, ‘Maximizing Expected Utility and The Rule of Long Run Success’, Expected Utility and the Allais Paradox, Maurice Allais and Ole Hagen (Eds.), D. Reidel Publishing Company, pp. 203–222.
Camerer, C.: 1989, ‘An Experimental Test of Several Generalized Utility Theories’, Journal of Risk and Uncertainty, 2, 61–104.
Chew, S. and MacCrimmon, K.: 1979, ‘Alpha-nu Choice Theory: A Generalization of Expected Utility Theory’, Working Paper No. 669, University of British Columbia.
Cooper, W. S.: 1987, ‘Decision Theory as a Branch of Evolutionary Theory: A Biological Derivation of the Savage Axioms’, Psychological Review, 94(4), 395–411.
Dyer, J. S. and Sarin, R. K.: 1982, ‘Relative Risk Aversion’, Management Science, 28(8), 875–886.
Einhorn, H. J. and Hogarth, R. M.: 1986, ‘Decision Making Under Ambiguity’, Journal of Business, 59(4), 5225–5255.
Ellsberg, D.: 1961, ‘Risk, Ambiguity and the Savage Axioms’, Quarterly Journal of Economics, 75, 643–669.
Garcia, C. B. and Zangwill, I.: 1984, ‘Experiential Origins of Utility’, University Chicago, Graduate School of Business, Working Paper.
Gould, J. P.: 1986, ‘Is the Rational Expectations Hypothesis Enough?’, The Journal of Business, 59(4(2)), 5371–5378.
Harrison, M. J.: 1977, ‘Independence and Calibration in Decision Analysis’, Management Science, 24(3), 320–328.
Hershey, J. C., Kunreuther, H. C., and Schoemaker, P. J. H.: 1982, ‘Sources of Bias in Assessment Procedures for Utility Functions’, Management Science, 28(8), 936–954.
Hogarth, R. M. and Einhorn, H. J.: 1990, ‘Venture Theory: Model of Decision Weights’, Management Science, 36(7), 780–803.
Kadane J. and Lichtenstein, S.: 1982, ‘A Subjectivist View of Calibration’, Decision Research Report 82–6, Perceptronics, Eugene, OR.
Kahneman, D. and Tversky, A.: 1979, ‘Prospect Theory: An Analysis of Decision Under Risk’, Econometrica, 47, 263–291.
Kripke, S.: 1971, ‘Semantical Considerations on Modal Logic’, in L. Linsky (Ed.), Reference and Modality, Oxford University Press, London.
Loomes, G. and Sugden, S.: 1982, ‘Regret Theory: An Alternative Approach to Rational Choice Under Uncertainty’, Economic Journal, 92, 805–824.
Loomes, C. and Sugden, S.: 1987, ‘Some Implications of a More General Form of Regret Theory’, Journal of Economic Theory, 41, 270–287.
MacCrimmon, K. R. and Larsson, S.: 1979, ‘Utility Theory: Axioms versus “Paradoxes”’, in Allais, M. and Hagen, O. (Eds.), Expected Utility Hypotheses and the Allais Paradox; D. Reidel Publishing Co. Dordrecht, Holland.
Machina, M. J.: 1982, ‘“Expected Utility Analysis” Without the Independence Axiom’, Econometrica, 50, 277–323.
Machina, M. J.: 1987, ‘Decision Making in the Presence of Risk’, Science, 537–543.
Machina, M.: 1989, ‘Dynamic Consistency and Non-Expected Utility Models of Choice Under Uncertainty’, Journal of Economic Literature, XXVII, 1622–1668.
Massy, W. F.: 1965, ‘On Methods: Discriminant Analysis of Audience Characteristics’, Journal of Advertising Research, 5, 39–48.
Quine, W. V. O.: 1976, The Ways of Paradox and Other Essays, Harvard University Press.
Quiggin, J.: 1982, ‘A Theory of Anticipated Utility’, Journal of Economic Behavior and Organization, 3, 323–343.
Samuelson, P.: 1950, ‘Probability and the Attempts to Measure Utility’, The Economic Review, July, 117–126.
Savage, L. J.: 1954, The Foundations of Statistics, New York: Wiley.
Schneeweis, H.: 1974, ‘Probability and Utility - Dual Concepts in Decision Theory’, in Information, Inference and Decision, G. Menges (Ed.), D. Reidel Publishing Co., Dordrecht-Holland.
Schoemaker, P. J. H.: 1980, Experiments on Decisions Under Risk: The Expected Utility Hypothesis, Martinus Nijhoff/Kluwer, Boston.
Schoemaker, P. J. H.: 1982, ‘The Expected Utility Model: Its Variants, Purposes, Evidence and Limitations’, Journal of Economic Literature, 20, 529–563.
Schoemaker, P. J. H.: 1989, ‘Preferences for Information on Probabilities versus Prizes: The Role of Risk-Taking Attitudes’, Journal of Risk and Uncertainty, 2, 37–60.
Schoemaker, P. J. H.: 1991, ‘Choices Involving Uncertain Probabilities: Tests of Generalized Utility Models’, Journal of Economic Behavior and Organization, 16, 295–317.
Segal, U.: 1990, ‘Two-Stage Lotteries Without the Reduction Axiom’, Econometrica, 58, 349–377.
Shafer, G.: 1988, ‘Savage Revisited’, Statistical Science, 1(4), 463–501.
Simon, H. A.: 1957, Models of Man: Social and Rational, New York, Wiley.
Sugden, R.: 1985, ‘Regret, Recrimination and Rationality’, Theory and Decision, 19, 77–99.
Thomas, J. C.: 1977, ‘Cognitive Psychology from the Perspective of Wilderness Survival’, Research Report, IBM Thomas J. Watson Research Laboratory, N.Y.
Tversky, A. and Kahneman, D.: 1981, ‘The Framing of Decisions and the Psychology of Choice’, Science, 211, 453–458.
Von Neumann, J. and Morgenstern, O.: 1947, Theory of Games and Economic Behavior, 2nd ed., Princeton University Press, Princeton, N.J.
Wakker, P.: 1988, ‘Nonexpected Utility as Aversion to Information’, Journal of Behavioral Decision Making, 1(3), 169–175.
Wothke, W.: 1985, ‘Allais' Paradox Revisited: The Implications of the Ambiguity Adjustment Model’, Unpublished Manuscript, Dept. of Psychology, Northwestern University, September.
Yaari, M. E.: 1987, ‘The Dual Theory of Choice Under Risk’, Econometrica, 55, 1, 95–115.
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Schoemaker, P.J.H. Subjective expected utility theory revisited: A reductio ad absurdum paradox. Theor Decis 33, 1–21 (1992). https://doi.org/10.1007/BF00133980
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DOI: https://doi.org/10.1007/BF00133980