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De Finetti was Right: Probability Does Not Exist

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  • Robert Nau
Abstract
De Finetti's treatise on the theory of probability begins with the provocative statement PROBABILITY DOES NOT EXIST, meaning that probability does not exist in an objective sense. Rather, probability exists only subjectively within the minds of individuals. De Finetti defined subjective probabilities in terms of the rates at which individuals are willing to bet money on events, even though, in principle, such betting rates could depend on state-dependent marginal utility for money as well as on beliefs. Most later authors, from Savage onward, have attempted to disentangle beliefs from values by introducing hypothetical bets whose payoffs are abstract consequences that are assumed to have state-independent utility. In this paper, I argue that de Finetti was right all along: PROBABILITY, considered as a numerical measure of pure belief uncontaminated by attitudes toward money, does not exist. Rather, what exist are de Finetti's `previsions', or betting rates for money, otherwise known in the literature as `risk neutral probabilities'. But the fact that previsions are not measures of pure belief turns out not to be problematic for statistical inference, decision analysis, or economic modeling. Copyright Kluwer Academic Publishers 2001

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  • Robert Nau, 2001. "De Finetti was Right: Probability Does Not Exist," Theory and Decision, Springer, vol. 51(2), pages 89-124, December.
    • Handle: RePEc:kap:theord:v:51:y:2001:i:2:p:89-124
    DOI: 10.1023/A:1015525808214
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    References listed on IDEAS

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    1. Robert F. Nau, 1992. "Joint Coherence in Games of Incomplete Information," Management Science, INFORMS, vol. 38(3), pages 374-387, March.
    2. Ghirardato, Paolo & Marinacci, Massimo, 2002. "Ambiguity Made Precise: A Comparative Foundation," Journal of Economic Theory, Elsevier, vol. 102(2), pages 251-289, February.
    3. Harrison, J. Michael & Kreps, David M., 1979. "Martingales and arbitrage in multiperiod securities markets," Journal of Economic Theory, Elsevier, vol. 20(3), pages 381-408, June.
    4. Edi Karni & Philippe Mongin, 2000. "On the Determination of Subjective Probability by Choices," Management Science, INFORMS, vol. 46(2), pages 233-248, February.
    5. Joseph B. Kadane & Patrick D. Larkey, 1983. "The Confusion of Is and Ought in Game Theoretic Contexts," Management Science, INFORMS, vol. 29(12), pages 1365-1379, December.
    6. Joseph B. Kadane & Patrick D. Larkey, 1982. "Subjective Probability and the Theory of Games," Management Science, INFORMS, vol. 28(2), pages 113-120, February.
    7. Jackwerth, Jens Carsten, 2000. "Recovering Risk Aversion from Option Prices and Realized Returns," The Review of Financial Studies, Society for Financial Studies, vol. 13(2), pages 433-451.
    8. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-587, May.
    9. Ross, Stephen A, 1987. "The Interrelations of Finance and Economics: Theoretical Perspectives," American Economic Review, American Economic Association, vol. 77(2), pages 29-34, May.
    10. Aumann, Robert J, 1987. "Correlated Equilibrium as an Expression of Bayesian Rationality," Econometrica, Econometric Society, vol. 55(1), pages 1-18, January.
    11. James E. Smith & Robert F. Nau, 1995. "Valuing Risky Projects: Option Pricing Theory and Decision Analysis," Management Science, INFORMS, vol. 41(5), pages 795-816, May.
    12. Aumann, Robert J., 1974. "Subjectivity and correlation in randomized strategies," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 67-96, March.
    13. Sugden, Robert, 1991. "Rational Choice: A Survey of Contributions from Economics and Philosophy," Economic Journal, Royal Economic Society, vol. 101(407), pages 751-785, July.
    14. K. J. Arrow, 1964. "The Role of Securities in the Optimal Allocation of Risk-bearing," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 31(2), pages 91-96.
    15. Mark Machina, 2004. "Almost-objective uncertainty," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 24(1), pages 1-54, July.
    16. Nau, Robert F, 1995. "Coherent Decision Analysis with Inseparable Probabilities and Utilities," Journal of Risk and Uncertainty, Springer, vol. 10(1), pages 71-91, January.
    17. Cox, John C. & Ross, Stephen A., 1976. "The valuation of options for alternative stochastic processes," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 145-166.
    18. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    19. Nau, Robert F. & McCardle, Kevin F., 1990. "Coherent behavior in noncooperative games," Journal of Economic Theory, Elsevier, vol. 50(2), pages 424-444, April.
    20. Yaari, Menahem E., 1969. "Some remarks on measures of risk aversion and on their uses," Journal of Economic Theory, Elsevier, vol. 1(3), pages 315-329, October.
    21. F J Anscombe & R J Aumann, 2000. "A Definition of Subjective Probability," Levine's Working Paper Archive 7591, David K. Levine.
    22. Machina, Mark J & Schmeidler, David, 1992. "A More Robust Definition of Subjective Probability," Econometrica, Econometric Society, vol. 60(4), pages 745-780, July.
    23. Karni, Edi & Schmeidler, David & Vind, Karl, 1983. "On State Dependent Preferences and Subjective Probabilities," Econometrica, Econometric Society, vol. 51(4), pages 1021-1031, July.
    24. Larry G. Epstein, 1999. "A Definition of Uncertainty Aversion," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 66(3), pages 579-608.
    25. Cuoco, Domenico & Zapatero, Fernando, 2000. "On the Recoverability of Preferences and Beliefs," The Review of Financial Studies, Society for Financial Studies, vol. 13(2), pages 417-431.
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    Cited by:

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    2. Robert F. Nau, 2006. "Uncertainty Aversion with Second-Order Utilities and Probabilities," Management Science, INFORMS, vol. 52(1), pages 136-145, January.
    3. Edi Karni & David Schmeidler, 2016. "An expected utility theory for state-dependent preferences," Theory and Decision, Springer, vol. 81(4), pages 467-478, November.
    4. Robert Nau, 2015. "Risk-neutral equilibria of noncooperative games," Theory and Decision, Springer, vol. 78(2), pages 171-188, February.
    5. Robert Nau, 2011. "Risk, ambiguity, and state-preference theory," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 48(2), pages 437-467, October.
    6. Robert F. Nau, 2003. "A Generalization of Pratt-Arrow Measure to Nonexpected-Utility Preferences and Inseparable Probability and Utility," Management Science, INFORMS, vol. 49(8), pages 1089-1104, August.
    7. D. Johnstone, 2007. "The Value of a Probability Forecast from Portfolio Theory," Theory and Decision, Springer, vol. 63(2), pages 153-203, September.
    8. Colorni, Alberto & Tsoukiàs, Alexis, 2024. "What is a decision problem?," European Journal of Operational Research, Elsevier, vol. 314(1), pages 255-267.
    9. Tsoukias, Alexis, 2008. "From decision theory to decision aiding methodology," European Journal of Operational Research, Elsevier, vol. 187(1), pages 138-161, May.
    10. Casellina, Simone & Pandolfo, Giuseppe & Quagliariello, Mario, 2020. "Applying the Pre-Commitment Approach to bottom-up stress tests: A new old story," Journal of Economics and Business, Elsevier, vol. 112(C).

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