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

Marc-Arthur Diaye (marc-arthur.diaye@univ-paris1.fr), André Lapidus (andre.lapidus@univ-paris1.fr) and Christian Schmidt
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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

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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.

Keywords: Probability discounting; Time discounting; Logarithmic time perception; Rank-dependent utility; Rationality; Attitude toward probabilities; Attitude toward risk (search for similar items in EconPapers)
Date: 2024-10
Note: View the original document on HAL open archive server: https://paris1.hal.science/hal-03256606v2
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Published in Theoretical Economics Letters, 2024, 14 (5), pp.2036-2065. ⟨10.4236/tel.2024.145101⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-03256606

DOI: 10.4236/tel.2024.145101

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