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Probability interference in expected utility theory

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  • Charles-Cadogan, G.

Abstract

Allais (1952) was one of the first to propose an outcome dependent probability weighting function to characterize probability distortions that explain violations of the linear probability model for expected utility theory (EUT). Quantum Probability Theory (QPT) extends the probability distortion paradigm with state dependent preferences, and non-Kolmogorov quantum probability measures, over a complex valued Hilbert space. Key innovations in QPT include representing vectors in Hilbert space as (mental) states, and a wave function comprised of a normalized linear combination of states. Born rule treats the real valued squared amplitude of the wave function as the associated probability often accompanied by a trigonometric probability interference factor addend. In this paper, we prove that the Born rule innovation of QPT which resolve, inter alia, violations of Savage’s sure thing principle, conjunction and disjunction fallacies, preference reversal, etc., can also be obtained by replacing EUT’s transitivity axiom with a weak harmonic transitivity (WHT) axiom in classic Kolmogorov probability space. The WHT axiom supports an abstract harmonic probability weighting function (HPWF) that mimics random fields driven by mental states, and it admits a harmonic addend akin to the trigonometric probability interference factor in QPT. By imposing suitable moment conditions on the underlying objective probability distribution, we derive a complex valued HPWF that satisfies Born rule. We calibrate the HPWF to a recent QPT probability measure derived from evaluation of state representation of binary choice, estimate it with harmonic regression, and show how heteroskedasticity correction has debiasing effects.

Suggested Citation

  • Charles-Cadogan, G., 2018. "Probability interference in expected utility theory," Journal of Mathematical Economics, Elsevier, vol. 78(C), pages 163-175.
    • Handle: RePEc:eee:mateco:v:78:y:2018:i:c:p:163-175
    DOI: 10.1016/j.jmateco.2018.03.006
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    1. Polkovnichenko, Valery & Zhao, Feng, 2013. "Probability weighting functions implied in options prices," Journal of Financial Economics, Elsevier, vol. 107(3), pages 580-609.
    2. Robin M. Hogarth & Hillel J. Einhorn, 1990. "Venture Theory: A Model of Decision Weights," Management Science, INFORMS, vol. 36(7), pages 780-803, July.
    3. Mohammed Abdellaoui & Aurelien Baillon & Laetitia Placido & Peter P. Wakker, 2011. "The Rich Domain of Uncertainty: Source Functions and Their Experimental Implementation," American Economic Review, American Economic Association, vol. 101(2), pages 695-723, April.
    4. Tversky, Amos & Kahneman, Daniel, 1992. "Advances in Prospect Theory: Cumulative Representation of Uncertainty," Journal of Risk and Uncertainty, Springer, vol. 5(4), pages 297-323, October.
    5. Nicholas Barberis & Ming Huang, 2008. "Stocks as Lotteries: The Implications of Probability Weighting for Security Prices," American Economic Review, American Economic Association, vol. 98(5), pages 2066-2100, December.
    6. Richard H. Thaler, 2008. "Mental Accounting and Consumer Choice," Marketing Science, INFORMS, vol. 27(1), pages 15-25, 01-02.
    7. Nathaniel T. Wilcox, 2023. "Unusual Estimates of Probability Weighting Functions," Research in Experimental Economics, in: Models of Risk Preferences: Descriptive and Normative Challenges, volume 22, pages 69-106, Emerald Group Publishing Limited.
    8. Blavatskyy, Pavlo, 2016. "Probability weighting and L-moments," European Journal of Operational Research, Elsevier, vol. 255(1), pages 103-109.
    9. 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..
    10. Machina, Mark J, 1985. "Stochastic Choice Functions Generated from Deterministic Preferences over Lotteries," Economic Journal, Royal Economic Society, vol. 95(379), pages 575-594, September.
    11. Ali E. Abbas, 2006. "Maximum Entropy Utility," Operations Research, INFORMS, vol. 54(2), pages 277-290, April.
    12. Kenneth R. Maccrimmon, 1968. "Descriptive and Normative Implications of the Decision-Theory Postulates," International Economic Association Series, in: Karl Borch & Jan Mossin (ed.), Risk and Uncertainty, chapter 0, pages 3-32, Palgrave Macmillan.
    13. Marc Rieger & Mei Wang, 2006. "Cumulative prospect theory and the St. Petersburg paradox," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 28(3), pages 665-679, August.
    14. Charness, Gary & Karni, Edi & Levin, Dan, 2010. "On the conjunction fallacy in probability judgment: New experimental evidence regarding Linda," Games and Economic Behavior, Elsevier, vol. 68(2), pages 551-556, March.
    15. Masanari Asano & Irina Basieva & Andrei Khrennikov & Masanori Ohya & Yoshiharu Tanaka, 2017. "A Quantum-like Model of Selection Behavior," Papers 1705.08536, arXiv.org.
    16. Mohammed Abdellaoui & Olivier L’Haridon & Horst Zank, 2010. "Separating curvature and elevation: A parametric probability weighting function," Journal of Risk and Uncertainty, Springer, vol. 41(1), pages 39-65, August.
    17. Lattimore, Pamela K. & Baker, Joanna R. & Witte, Ann D., 1992. "The influence of probability on risky choice: A parametric examination," Journal of Economic Behavior & Organization, Elsevier, vol. 17(3), pages 377-400, May.
    18. Robin P. Cubitt & Alistair Munro & Chris Starmer, 2004. "Testing explanations of preference reversal," Economic Journal, Royal Economic Society, vol. 114(497), pages 709-726, July.
    19. Drazen Prelec, 1998. "The Probability Weighting Function," Econometrica, Econometric Society, vol. 66(3), pages 497-528, May.
    20. Pamela K. Lattimore & Joanna R. Baker & A. Dryden Witte, 1992. "The Influence Of Probability on Risky Choice: A parametric Examination," NBER Technical Working Papers 0081, National Bureau of Economic Research, Inc.
    21. Einhorn, Hillel J & Hogarth, Robin M, 1986. "Decision Making under Ambiguity," The Journal of Business, University of Chicago Press, vol. 59(4), pages 225-250, October.
    22. Nathaniel T. Wilcox, 2017. "Random expected utility and certainty equivalents: mimicry of probability weighting functions," Journal of the Economic Science Association, Springer;Economic Science Association, vol. 3(2), pages 161-173, December.
    23. Tversky, Amos & Wakker, Peter, 1995. "Risk Attitudes and Decision Weights," Econometrica, Econometric Society, vol. 63(6), pages 1255-1280, November.
    24. Basieva, Irina & Khrennikova, Polina & Pothos, Emmanuel M. & Asano, Masanari & Khrennikov, Andrei, 2018. "Quantum-like model of subjective expected utility," Journal of Mathematical Economics, Elsevier, vol. 78(C), pages 150-162.
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    Cited by:

    1. Charles-Cadogan, G., 2021. "Market Instability, Investor Sentiment, And Probability Judgment Error in Index Option Prices," CRETA Online Discussion Paper Series 71, Centre for Research in Economic Theory and its Applications CRETA.
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    3. Charles-Cadogan, G., 2021. "Incoherent Preferences," CRETA Online Discussion Paper Series 69, Centre for Research in Economic Theory and its Applications CRETA.

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