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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, Department of Economics, University of Leicester.
  • Handle: RePEc:lec:leecon:10/10
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    File URL: http://www.le.ac.uk/economics/research/repec/lec/leecon/dp10-10.pdf
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    References listed on IDEAS

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    1. 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, Department of Economics, University of Leicester.
    2. Avner Bar-Ilan & Bruce Sacerdote, 2001. "The Response to Fines and Probability of Detection in a Series of Experiments," NBER Working Papers 8638, National Bureau of Economic Research, Inc.
    3. Bar-Ilan, Avner & Sacerdote, Bruce, 2004. "The Response of Criminals and Noncriminals to Fines," Journal of Law and Economics, University of Chicago Press, vol. 47(1), pages 1-17, April.
    4. Ali al-Nowaihi & Ian Bradley & Sanjit Dhami, 2006. "The Utility Function Under Prospect Theory," Discussion Papers in Economics 06/15, Department of Economics, University of Leicester.
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    Cited by:

    1. Ali al-Nowaihi & Sanjit Dhami, 2005. "Insurance and Probability Weighting Functions," Discussion Papers in Economics 05/19, Department of Economics, University of Leicester, revised Sep 2006.
    2. 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.
    3. 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.
    4. 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, Department of Economics, University of Leicester.
    5. Sanjit Dhami & Ali al-Nowaihi, 2010. "The Behavioral Economics of Crime and Punishment," Discussion Papers in Economics 10/14, Department of Economics, University of Leicester, revised Jul 2010.
    6. 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, Department of Economics, University of Leicester.
    7. 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, Department of Economics, University of Leicester.
    8. Ali al-Nowaihi & Sanjit Dhami, 2010. "The Behavioral Economics of Insurance," Discussion Papers in Economics 10/12, Department of Economics, University of Leicester, revised Apr 2010.

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