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Decision Theory Without “Independence” or Without “Ordering”

What is the Difference?

Published online by Cambridge University Press:  05 December 2008

Teddy Seidenfeld
Teddy Seidenfeld
Affiliation:
Carnegie-Mellon University
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Extract

It is a familiar argument that advocates accommodating the so-called paradoxes of decision theory by abandoning the “independence” postulate. After all, if we grant that choice reveals preference, the anomalous choice patterns of the Allais and Ellsberg problems (reviewed in Section 3) violate postulate P2 (“sure thing”) of Savage's (1954) system. The strategy of making room for new preference patterns by relaxing independence is adopted in each of the following works: Samuelson (1950), Kahneman and Tversky's “Prospect Theory” (1979), Allais and Hagen (1979), Fishburn (1981), Chew and MacCrimmon (1979), McClennen (1983), and in closely argued essays by Machina (1982, 1983 [see the latter for an extensive bibliography]).

Type
Essays
Information
Economics & Philosophy , Volume 4 , Issue 2 , October 1988 , pp. 267 - 290
Copyright
Copyright © Cambridge University Press 1988

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References

REFERENCES

Allais, M. 1953. “Le comportement de l'homme rationnel devant le risque: Critique des postulats et axiomes de l'école americaine.” Econometrica 21:503–46.CrossRefGoogle Scholar
Allais, M. 1979. “The So-Called Allais Paradox and Rational Decisions Under Uncertainty.” In Expected Utility Hypotheses and the Allais Paradox, edited by Allais, & Hagen, , pp. 437–681. Dordrecht: Reidel.CrossRefGoogle Scholar
Allais, and Hagen, (editors). 1979. Expected Utility Hypotheses and the Allais Paradox. Dordrecht: Reidel.CrossRefGoogle Scholar
Anscombe, F. J., and Aumann, R. J. 1963. “A Definition of Subjective Probability.” Annals of Mathematical Statistics, 34:199–205.CrossRefGoogle Scholar
Bell, D. 1982. “Regret in Decision Making Under Uncertainty.” Operations Research 20:961–81.CrossRefGoogle Scholar
Bell, D., and Raiffa, H. 1979. “Decision Regret: A Component of Risk Aversion.” Unpublished manuscript, Harvard University.Google Scholar
Hong, Chew Soo. 1981, 4th revision. “A Mixture Set Axiomatization of Weighted Utility Theory.” Department of Economics, University of Arizona, Tucson.Google Scholar
Hong, Chew Soo. 1983. “A Generalization of the Quasilinear Mean with Applications to the Measurement of Income Inequality and Decision Theory Resolving the Allais Paradox.” Department of Economics, University of Arizona, Tuscon.CrossRefGoogle Scholar
Hong, Chew Soo, and MacCrimmon, K. R. 1979. “Alpha-Nu Choice Theory: A Generalization of Expected Utility Theory.” University of British Columbia working paper.Google Scholar
de Finetti, B. 1974. Theory of Probability. 2 volumes. New York: Wiley.Google Scholar
Debreu, G. 1959. Theory of Value. New Haven: Yale University Press.Google Scholar
Drèze, J. H. 1985. Decision Theory With Moral Hazard and State-Dependent Preferences. CORE Discussion paper #8545. Université Catholique de Louvain, Belgium: Center for Operations Research and Econometrics.Google Scholar
Ellsberg, D. 1961. “Risk, Ambiguity, and the Savage Axioms,” Quarterly journal of Economics, 75:643–99.CrossRefGoogle Scholar
Fishburn, P. C. 1970. Utility Theory for Decision Making. New York: Kriefer Publishing Company.CrossRefGoogle Scholar
Fishburn, P. C. 1981. “An Axiomatic Characterization of Skew-Symmetric Bilinear Functionals, With Applications to Utility Theory.” Economic Letters 8:311–13.CrossRefGoogle Scholar
Fishburn, P. C. 1983. “Nontransitive Measurable Utility.” Journal of Mathematical Psychology 26:31–67.CrossRefGoogle Scholar
Good, I. J. 1952. “Rational Decisions.” Journal of the Royal Statistical Society B, 14:107–14.Google Scholar
Hammond, P. J. 1976. “Changing Tastes and Coherent Dynamic Choice.” Review of Economic Studies 43:159–73.CrossRefGoogle Scholar
Hammond, P. J. 1984. “Consequentialist Behaviour in Decision Trees is Bayesian Rational.” Stanford University.Google Scholar
Herstein, I. N., and Milnor, J. 1953. “An Axiomatic Approach to Measurable Utility.” Econometrica 21:291–97.CrossRefGoogle Scholar
Jeffreys, H. 1971. Theory of Probability. 3rd ed.Oxford: Oxford University Press.Google Scholar
Jensen, N. E. 1967. “An Introduction to Bernoullian Utility Theory: I. Utility Functions” Swedish Journal of Economics 69:163–83.CrossRefGoogle Scholar
Kadane, J. 1986. “Toward a More Ethical Clinical Trial.” Journal of Medicine and Philosophy 11:385–404.CrossRefGoogle Scholar
Kadane, J., and Sedransk, N. 1980. “Toward a More Ethical Clinical Trial.” In Bayesian Statistics, edited by Bernardo, J., DeGroot, M. H., Lindley, D. V., and Smith, A. F. M., pp. 329–38. Valencia, Spain: University Press.Google Scholar
Kahneman, D., and Tversky, A. 1979. “Prospect Theory: An Analysis of Decision Under Risk.” Econometrica 47:263–91.CrossRefGoogle Scholar
LaValle, I. H., and Wapman, K. R. 1986. “Rolling Back Decision Trees Requires the Independence Axiom!” Management Science 32 (3):382–85.CrossRefGoogle Scholar
Levi, I. 1974. “On Indeterminate Probabilities.” Journal of Philosophy 71:391–418.CrossRefGoogle Scholar
Levi, I. 1980. The Enterprise of Knowledge. Cambridge: MIT Press.Google Scholar
Levi, I. 1986a. “The Paradoxes of Allais and Ellsberg,” Economics and Philosophy 2:23–53.CrossRefGoogle Scholar
Levi, I. 1986b. Hard Choices: Decision Making under Unresolved Conflict. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Levi, I. 1987. “The Demons of Decision.” The Monist 70:193–211.CrossRefGoogle Scholar
Lindley, D. V. 1972. Bayesian Statistics: A Review. Philadelphia: SIAM.CrossRefGoogle Scholar
Loomes, G., and Sugden, R. 1982. “Regret Theory: An Alternative Theory of Rational Choice Under Uncertainty.” Economic Journal 92:805–24.CrossRefGoogle Scholar
Luce, D., and Raiffa, H. 1957. Games and Decisions. New York: Wiley.Google Scholar
Machina, M. 1982. “Expected Utility Analysis Without the Independence Axiom.” Econometrica 50:277–323.CrossRefGoogle Scholar
Machina, M. 1983, 10. “The Economic Theory of Individual Behavior Toward Risk: Theory, Evidence and New Directions.” Department of Economics, University of California, San Diego. Technical report #433.Google Scholar
McClennen, E. F. 1983. “Sure-Thing Doubts.” In Foundations of Utility and Risk Theory with Applications, edited by Stigum, B. and Wenstop, F., pp. 117–36. Dordrecht: Reidel.CrossRefGoogle Scholar
McClennen, E. F. 1986. “Prisoner's Dilemma and Resolute Choice.” In Paradoxes of Rationality and Cooperation, edited by Campbell, R. and Sowden, L., pp. 94–104. Vancouver: University of British Columbia Press.Google Scholar
McClennen, E. F. 1988. “Dynamic Choice and Rationality.” In Risk, Decision, and Rationality, edited by Munier, B. R., pp. 517–36. Dordrecht: Reidel.CrossRefGoogle Scholar
McClennen, E. F.Rationality and Dynamic Choice: Foundational Explorations. Cambridge: Cambridge University Press. Forthcoming.Google Scholar
Raiffa, H. 1968. Decision Analysis: Introductory Lectures on Choices under Uncertainty. Reading, Mass: Addison-Wesley.Google Scholar
Samuelson, P. 1950. “Probability and the Attempts to Measure Utility.” Economic Review 1:167–73.Google Scholar
Savage, L. J. 1954. The Foundations of Statistics. New York: Wiley.Google Scholar
Schick, F. 1984. Having Reasons. Princeton: Princeton University Press.CrossRefGoogle Scholar
Schick, F. 1986. “Dutch Bookies and Money Pumps.” Journal of Philosophy 83:112–19.CrossRefGoogle Scholar
Seidenfeld, T. 1987. “Sequential Coherence without the ‘Ordering’ Postulate: Levi's Decision Theory.” Technical report. Department of Philosophy, Carnegie-Mellon University, Pittsburgh, Pa.Google Scholar
Seidenfeld, T., and Schervish, M. 1983. “A Conflict Between Finite Additivity and Avoiding Dutch Book.” Philosophy of Science 50:398–412.CrossRefGoogle Scholar
Seidenfeld, T., Schervish, M., and Kadane, J. 1987. “Decisions Without Ordering.” In Acting and Reflecting, edited by Sieg, W.. Dordrecht: Reidel. Forthcoming.Google Scholar
Sen, A. K. 1977. “Social Choice Theory: A Re-examination.” Econometrica 45:53–89.CrossRefGoogle Scholar
Shimony, A. 1955. “Coherence and the Axioms of Confirmation.” Journal of Symbolic Logic 20:1–28.CrossRefGoogle Scholar
Smith, C. A. B. 1961. “Consistency in Statistical Inference and Decision.” Journal of the Royal Statistical Society B, 23:1–25.Google Scholar
Suppes, P. 1974. “The Measurement of Belief.” Journal of the Royal Statistical Society B, 36:160–75.Google Scholar
von Neumann, J., and Morgenstern, O. 1947. Theory of Games and Economic behavior. 2nd ed.Princeton: Princeton University Press.Google Scholar
Walley, P., and Fine, T. L. 1979. “Varieties of Modal (Classificatory) and Comparative Probability.” Synthèse 41:321–74.CrossRefGoogle Scholar
Wolfenson, M., and Fine, T. 1982. “Bayes-like Decision Making with Upper and Lower Probabilities.” Journal of the American Statistical Association 77:80–88.CrossRefGoogle Scholar