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Psychophysics of the probability weighting function

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  • Takahashi, Taiki

Abstract

A probability weighting function w(p) for an objective probability p in decision under risk plays a pivotal role in Kahneman–Tversky prospect theory. Although recent studies in econophysics and neuroeconomics widely utilized probability weighting functions, psychophysical foundations of the probability weighting functions have been unknown. Notably, a behavioral economist Prelec (1998) [4] axiomatically derived the probability weighting function w(p)=exp(−(−lnp)α) (0<α<1 and w(0)=1,w(1e)=1e,w(1)=1), which has extensively been studied in behavioral neuroeconomics. The present study utilizes psychophysical theory to derive Prelec’s probability weighting function from psychophysical laws of perceived waiting time in probabilistic choices. Also, the relations between the parameters in the probability weighting function and the probability discounting function in behavioral psychology are derived. Future directions in the application of the psychophysical theory of the probability weighting function in econophysics and neuroeconomics are discussed.

Suggested Citation

  • Takahashi, Taiki, 2011. "Psychophysics of the probability weighting function," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(5), pages 902-905.
    • Handle: RePEc:eee:phsmap:v:390:y:2011:i:5:p:902-905
    DOI: 10.1016/j.physa.2010.10.004
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    References listed on IDEAS

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    1. 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..
    2. C. Anteneodo & C. Tsallis & A. S. Martinez, 2001. "Risk aversion in economic transactions," Papers cond-mat/0109203, arXiv.org, revised Jun 2002.
    3. Drazen Prelec, 1998. "The Probability Weighting Function," Econometrica, Econometric Society, vol. 66(3), pages 497-528, May.
    4. Takahashi, Taiki & Oono, Hidemi & Radford, Mark H.B., 2007. "Empirical estimation of consistency parameter in intertemporal choice based on Tsallis’ statistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 381(C), pages 338-342.
    5. Takahashi, Taiki, 2007. "A probabilistic choice model based on Tsallis’ statistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 386(1), pages 335-338.
    6. Cajueiro, Daniel O., 2006. "A note on the relevance of the q-exponential function in the context of intertemporal choices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 364(C), pages 385-388.
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    2. dos Santos, Lindomar Soares & Destefano, Natália & Martinez, Alexandre Souto, 2018. "Decision making generalized by a cumulative probability weighting function," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 490(C), pages 250-259.
    3. Hu, Xiangmin & Chen, Tao & Deng, Kaifeng & Wang, Guanning, 2023. "Effects of aggressiveness on pedestrian room evacuation using extended cellular automata model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 619(C).
    4. 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.
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    8. repec:plo:pone00:0154083 is not listed on IDEAS

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