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Probability Weighting Functions

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  • Ali al-Nowaihi
  • Sanjit Dhami

Abstract

In this paper we begin by stressing the empirical importance of non-linear weighting of probabilities, which expected utility theory (EU) is unable to accommodate. We then go on to outline three stylized facts on non-linear weighting that any alternative theory of risk must address. These are that people: overweight small probabilities and underweight large ones (S1); do not choose stochastically dominated options when such dominance is obvious (S2); ignore very small probabilities and code extremely large probabilities as one (S3). We then show that the concept of a probability weighting function (PWF) is crucial in addressing S1-S3. A PWF is not, however, a theory of risk. PWF's need to be embedded within some theory of risk in order to have significant predictive content. We ouline the two main alternative theories that are relevant in this regard: rank dependent utility (RDU) and cumulative prospect theory (CP). RDU and CP explain S1,S2 but not S3. We conclude by outlining the recent proposal for composite prospect theory (CPP) that uses the composite Prelec probability weighting function (CPF). CPF is axiomatically founded, and is flexible and parsimonious. CPP can explain all three stylized facts S1,S2,S3.

Suggested Citation

  • Ali al-Nowaihi & Sanjit Dhami, 2010. "Probability Weighting Functions," Discussion Papers in Economics 10/10, Division of Economics, School of Business, University of Leicester.
    • Handle: RePEc:lec:leecon:10/10
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    File URL: https://www.le.ac.uk/economics/research/RePEc/lec/leecon/dp10-10.pdf
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    Cited by:

    1. Bernedo Del Carpio, María & Alpizar, Francisco & Ferraro, Paul J., 2022. "Time and risk preferences of individuals, married couples and unrelated pairs," Journal of Behavioral and Experimental Economics (formerly The Journal of Socio-Economics), Elsevier, vol. 97(C).
    2. Charles Bellemare & Sabine Kröger & Kouamé Marius Sossou, 2018. "Reporting probabilistic expectations with dynamic uncertainty about possible distributions," Journal of Risk and Uncertainty, Springer, vol. 57(2), pages 153-176, October.
    3. Ali al-Nowaihi & Sanjit Dhami, 2010. "The Behavioral Economics of Insurance," Discussion Papers in Economics 10/12, Division of Economics, School of Business, University of Leicester, revised Apr 2010.
    4. Changbo Zhu & Ke Zhou & Fengzhen Tang & Yandong Tang & Xiaoli Li & Bailu Si, 2022. "A Hierarchical Bayesian Model for Inferring and Decision Making in Multi-Dimensional Volatile Binary Environments," Mathematics, MDPI, vol. 10(24), pages 1-35, December.
    5. Ali al-Nowaihi & Sanjit Dhami, 2005. "Insurance and Probability Weighting Functions," Discussion Papers in Economics 05/19, Division of Economics, School of Business, University of Leicester, revised Sep 2006.
    6. Dhami, Sanjit & al-Nowaihi, Ali, 2013. "An extension of the Becker proposition to non-expected utility theory," Mathematical Social Sciences, Elsevier, vol. 65(1), pages 10-20.
    7. Dhami, Sanjit & al-Nowaihi, Ali, 2007. "Why do people pay taxes? Prospect theory versus expected utility theory," Journal of Economic Behavior & Organization, Elsevier, vol. 64(1), pages 171-192, September.
    8. Svetlozar Rachev & Frank J. Fabozzi & Boryana Racheva-Iotova & Abootaleb Shirvani, 2017. "Option Pricing with Greed and Fear Factor: The Rational Finance Approach," Papers 1709.08134, arXiv.org, revised Mar 2020.
    9. Ali al-Nowaihi & Sanjit Dhami, 2008. "A general theory of time discounting: The reference-time theory of intertemporal choice," Discussion Papers in Economics 08/34, Division of Economics, School of Business, University of Leicester.
    10. Sanjit Dhami & Ali al-Nowaihi, 2010. "The Behavioral Economics of Crime and Punishment," Discussion Papers in Economics 10/14, Division of Economics, School of Business, University of Leicester, revised Jul 2010.
    11. Martín Egozcue & Luis Fuentes García & Ričardas Zitikis, 2023. "The Slicing Method: Determining Insensitivity Regions of Probability Weighting Functions," Computational Economics, Springer;Society for Computational Economics, vol. 61(4), pages 1369-1402, April.
    12. Ali al-Nowaihi & Sanjit Dhami, 2010. "Composite Prospect Theory: A proposal to combine ‘prospect theory’ and ‘cumulative prospect theory’," Discussion Papers in Economics 10/11, Division of Economics, School of Business, University of Leicester.
    13. Sanjit Dhami & Ali al-Nowaihi, 2007. "Optimal income taxation in the presence of tax evasion: Expected utility versus prospect theory," Discussion Papers in Economics 07/10, Division of Economics, School of Business, University of Leicester.

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