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From Decision in Risk to Decision in Time - and Return: A Restatement of Probability Discounting

Author

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  • Marc-Arthur Diaye

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique)

  • André Lapidus

    (PHARE - Philosophie, Histoire et Analyse des Représentations Économiques - UP1 - Université Paris 1 Panthéon-Sorbonne)

  • Christian Schmidt

    (PHARE - Philosophie, Histoire et Analyse des Représentations Économiques - UP1 - Université Paris 1 Panthéon-Sorbonne)

Abstract

This paper aims at restating, in a decision theory framework, the results of some signicant contributions of the literature on probability discounting that followed the publication of the pioneering article by Rachlin et al. (1991). We provide a restatement of probability discounting in terms of rank-dependent utility, in which the utilities of the outcomes of n-issues lotteries are weighted by probabilities transformed after their transposition into time-delays. This formalism makes the typical cases of rationality in time and in risk mutually exclusive, but allows looser types of rationality. The resulting attitude toward probability and toward risk are then determined in relation to the values of the two parameters involved in the procedure of probability discounting.

Suggested Citation

  • Marc-Arthur Diaye & André Lapidus & Christian Schmidt, 2021. "From Decision in Risk to Decision in Time - and Return: A Restatement of Probability Discounting," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-03256606, HAL.
    • Handle: RePEc:hal:cesptp:hal-03256606
    Note: View the original document on HAL open archive server: https://paris1.hal.science/hal-03256606
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    References listed on IDEAS

    as
    1. Drazen Prelec & George Loewenstein, 1991. "Decision Making Over Time and Under Uncertainty: A Common Approach," Management Science, INFORMS, vol. 37(7), pages 770-786, July.
    2. Tversky, Amos & Kahneman, Daniel, 1992. "Advances in Prospect Theory: Cumulative Representation of Uncertainty," Journal of Risk and Uncertainty, Springer, vol. 5(4), pages 297-323, October.
    3. Takahashi, Taiki, 2011. "Psychophysics of the probability weighting function," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(5), pages 902-905.
    4. Mich�le Cohen, 2015. "Risk Perception, Risk Attitude, and Decision: A Rank-Dependent Analysis," Mathematical Population Studies, Taylor & Francis Journals, vol. 22(1), pages 53-70, March.
    5. Alain Chateauneuf & Michéle Cohen & Isaac Meilijson, 2005. "More pessimism than greediness: a characterization of monotone risk aversion in the rank-dependent expected utility model," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 25(3), pages 649-667, April.
    6. Diecidue, Enrico & Wakker, Peter P, 2001. "On the Intuition of Rank-Dependent Utility," Journal of Risk and Uncertainty, Springer, vol. 23(3), pages 281-298, November.
    7. George Loewenstein & Drazen Prelec, 1992. "Anomalies in Intertemporal Choice: Evidence and an Interpretation," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 107(2), pages 573-597.
    8. Chateauneuf, Alain & Cohen, Michele, 1994. "Risk Seeking with Diminishing Marginal Utility in a Non-expected Utility Model," Journal of Risk and Uncertainty, Springer, vol. 9(1), pages 77-91, July.
    9. Chateauneuf, Alain, 1999. "Comonotonicity axioms and rank-dependent expected utility theory for arbitrary consequences," Journal of Mathematical Economics, Elsevier, vol. 32(1), pages 21-45, August.
    10. María José Muñoz Torrecillas & Taiki Takahashi & Jesús Gil Roales-Nieto & Salvador Cruz Rambaud & Zaida Callejón Ruiz & Blas Torrecillas Jover, 2018. "Impatience and Inconsistency in Intertemporal Choice: An Experimental Analysis," Journal of Behavioral Finance, Taylor & Francis Journals, vol. 19(2), pages 190-198, April.
    11. Daniel Kahneman & Amos Tversky, 2013. "Prospect Theory: An Analysis of Decision Under Risk," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part I, chapter 6, pages 99-127, World Scientific Publishing Co. Pte. Ltd..
    12. Yaari, Menahem E, 1987. "The Dual Theory of Choice under Risk," Econometrica, Econometric Society, vol. 55(1), pages 95-115, January.
    13. Hong, Chew Soo & Karni, Edi & Safra, Zvi, 1987. "Risk aversion in the theory of expected utility with rank dependent probabilities," Journal of Economic Theory, Elsevier, vol. 42(2), pages 370-381, August.
    14. Michèle Cohen, 2008. "Risk perception, risk attitude and decision: a Rank-Dependent approach," Documents de travail du Centre d'Economie de la Sorbonne v08084, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    15. Quiggin, John, 1982. "A theory of anticipated utility," Journal of Economic Behavior & Organization, Elsevier, vol. 3(4), pages 323-343, December.
    16. repec:hal:pseose:halshs-00310491 is not listed on IDEAS
    17. Takahashi, Taiki, 2010. "A social discounting model based on Tsallis’ statistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(17), pages 3600-3603.
    18. Rachlin, Howard & Siegel, Eric, 1994. "Temporal Patterning in Probabilistic Choice," Organizational Behavior and Human Decision Processes, Elsevier, vol. 59(2), pages 161-176, August.
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    Keywords

    Probability discounting; time discounting; logarithmic time perception; rank-dependent utility; rationality; attitude toward probabilities; attitude toward risk;
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