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

Author

Listed:
  • 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 to restate, in a decision theory framework, the results of some significant contributions of the literature on probability discounting that followed the publication of the pioneering article by Rachlin et al. We provide a restatement of probability discounting, usually limited to the case of 2-issues lotteries, 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: a parameter related to impatience and pessimism, and a parameter related to time-consistency and the separation between non-optimism and non-pessimism. A simulation illustrates these results through the characteristics of the transformation of probabilities function.

Suggested Citation

  • Marc-Arthur Diaye & André Lapidus & Christian Schmidt, 2024. "From Decision in Risk to Decision in Time - and Return: A Restatement of Probability Discounting," Post-Print hal-03256606, HAL.
    • Handle: RePEc:hal:journl:hal-03256606
    DOI: 10.4236/tel.2024.145101
    Note: View the original document on HAL open archive server: https://paris1.hal.science/hal-03256606v2
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    References listed on IDEAS

    as
    1. 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.
    2. Quiggin, John, 1982. "A theory of anticipated utility," Journal of Economic Behavior & Organization, Elsevier, vol. 3(4), pages 323-343, December.
    3. 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.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Probability discounting; Time discounting; Logarithmic time perception; Rank-dependent utility; Rationality; Attitude toward probabilities; Attitude toward risk;
    All these keywords.

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