IDEAS home Printed from https://ideas.repec.org/a/eee/mateco/v78y2018icp186-197.html
   My bibliography  Save this article

A quantum-probabilistic paradigm: Non-consequential reasoning and state dependence in investment choice

Author

Listed:
  • Haven, Emmanuel
  • Khrennikova, Polina

Abstract

Seminal findings involving payoffs (Shafir and Tversky, 1992; Tversky and Shafir, 1992; Shafir, 1994) showed that individuals exhibit state-dependent behaviour in different informational contexts. In particular, in the condition of ambiguity as well as risk, individuals tend to exhibit ambiguity aversion. The core principle of rational (consequential) behaviour conceived by Savage (1954), that is the ‘Savage Sure Thing’ principle, has been shown to be violated. In mathematical language, this violation is equivalent to the violation of the “Law of total probability”, (Kolmogorov, 1933). Given the importance of original findings in the call for a generalization of classical expected utility, we perform in this paper a set of experiments related to expressing investment preferences: (i) under objective risk, (ii) after a preceding gain, or loss. In accordance with previous findings we detected state dependence in human judgement (previous gain or loss changed the preference state of the participants) as well as violation of consequential reasoning under risk. We propose a quantum probabilistic model of agents’ preferences, where non-consequentialism and state dependence can be well explained via interference of complex probability amplitudes. A geometric depiction of the experimental findings with a state reconstruction procedure from statistical data via the inverse Born’s rule (1926), allows for an accurate representation of agents’ preference formation in risky investment choice.

Suggested Citation

  • Haven, Emmanuel & Khrennikova, Polina, 2018. "A quantum-probabilistic paradigm: Non-consequential reasoning and state dependence in investment choice," Journal of Mathematical Economics, Elsevier, vol. 78(C), pages 186-197.
    • Handle: RePEc:eee:mateco:v:78:y:2018:i:c:p:186-197
    DOI: 10.1016/j.jmateco.2018.04.003
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304406818300442
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmateco.2018.04.003?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Aurelien Baillon & Olivier L'Haridon & Laetitia Placido, 2011. "Ambiguity Models and the Machina Paradoxes," American Economic Review, American Economic Association, vol. 101(4), pages 1547-1560, June.
    2. Lambdin, Charles & Burdsal, Charles, 2007. "The disjunction effect reexamined: Relevant methodological issues and the fallacy of unspecified percentage comparisons," Organizational Behavior and Human Decision Processes, Elsevier, vol. 103(2), pages 268-276, July.
    3. 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.
    4. V. Danilov & A. Lambert-Mogiliansky, 2010. "Expected utility theory under non-classical uncertainty," Theory and Decision, Springer, vol. 68(1), pages 25-47, February.
    5. Amos Tversky & Daniel Kahneman, 1991. "Loss Aversion in Riskless Choice: A Reference-Dependent Model," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 106(4), pages 1039-1061.
    6. Maroussia Favre & Amrei Wittwer & Hans Rudolf Heinimann & Vyacheslav I Yukalov & Didier Sornette, 2016. "Quantum Decision Theory in Simple Risky Choices," PLOS ONE, Public Library of Science, vol. 11(12), pages 1-29, December.
    7. repec:bla:jfinan:v:53:y:1998:i:5:p:1775-1798 is not listed on IDEAS
    8. Gilboa, Itzhak, 1987. "Expected utility with purely subjective non-additive probabilities," Journal of Mathematical Economics, Elsevier, vol. 16(1), pages 65-88, February.
    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. Bagarello, F. & Haven, E., 2014. "The role of information in a two-traders market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 404(C), pages 224-233.
    11. Khrennikov, Andrei, 2015. "Quantum version of Aumann’s approach to common knowledge: Sufficient conditions of impossibility to agree on disagree," Journal of Mathematical Economics, Elsevier, vol. 60(C), pages 89-104.
    12. Raymond J. Hawkins & B. Roy Frieden, 2012. "Asymmetric Information and Quantization in Financial Economics," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2012, pages 1-11, December.
    13. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-587, May.
    14. Peter Klibanoff & Massimo Marinacci & Sujoy Mukerji, 2005. "A Smooth Model of Decision Making under Ambiguity," Econometrica, Econometric Society, vol. 73(6), pages 1849-1892, November.
    15. Daniel Kahneman, 2003. "Maps of Bounded Rationality: Psychology for Behavioral Economics," American Economic Review, American Economic Association, vol. 93(5), pages 1449-1475, December.
    16. Shefrin, Hersh & Statman, Meir, 1985. "The Disposition to Sell Winners Too Early and Ride Losers Too Long: Theory and Evidence," Journal of Finance, American Finance Association, vol. 40(3), pages 777-790, July.
    17. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    18. Shlomo Benartzi & Richard H. Thaler, 1995. "Myopic Loss Aversion and the Equity Premium Puzzle," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 110(1), pages 73-92.
    19. Mehra, Rajnish & Prescott, Edward C., 1985. "The equity premium: A puzzle," Journal of Monetary Economics, Elsevier, vol. 15(2), pages 145-161, March.
    20. Karni, Edi & Schmeidler, David & Vind, Karl, 1983. "On State Dependent Preferences and Subjective Probabilities," Econometrica, Econometric Society, vol. 51(4), pages 1021-1031, July.
    21. Brandenburger, Adam, 2010. "The relationship between quantum and classical correlation in games," Games and Economic Behavior, Elsevier, vol. 69(1), pages 175-183, May.
    22. Haven, Emmanuel & Sozzo, Sandro, 2016. "A generalized probability framework to model economic agents' decisions under uncertainty," International Review of Financial Analysis, Elsevier, vol. 47(C), pages 297-303.
    23. Tversky, Amos & Slovic, Paul & Kahneman, Daniel, 1990. "The Causes of Preference Reversal," American Economic Review, American Economic Association, vol. 80(1), pages 204-217, March.
    24. Matthew Rabin & Richard H. Thaler, 2013. "Anomalies: Risk aversion," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part I, chapter 27, pages 467-480, World Scientific Publishing Co. Pte. Ltd..
    25. Croson, Rachel T. A., 1999. "The Disjunction Effect and Reason-Based Choice in Games, , , , , , , , , , , , ," Organizational Behavior and Human Decision Processes, Elsevier, vol. 80(2), pages 118-133, November.
    26. Richard H. Thaler & Eric J. Johnson, 1990. "Gambling with the House Money and Trying to Break Even: The Effects of Prior Outcomes on Risky Choice," Management Science, INFORMS, vol. 36(6), pages 643-660, June.
    27. Daniel Ellsberg, 1961. "Risk, Ambiguity, and the Savage Axioms," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 75(4), pages 643-669.
    28. Machina, Mark J, 1982. ""Expected Utility" Analysis without the Independence Axiom," Econometrica, Econometric Society, vol. 50(2), pages 277-323, March.
    29. Maroussia Favre & Amrei Wittwer & Hans Rudolf Heinimann & Vyacheslav I. Yukalov & Didier Sornette, 2016. "Quantum Decision Theory in Simple Risky Choices," Swiss Finance Institute Research Paper Series 16-09, Swiss Finance Institute.
    30. Mark Machina, 2005. "‘Expected utility / subjective probability’ analysis without the sure-thing principle or probabilistic sophistication," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 26(1), pages 1-62, July.
    31. Machina, Mark J, 1987. "Choice under Uncertainty: Problems Solved and Unsolved," Journal of Economic Perspectives, American Economic Association, vol. 1(1), pages 121-154, Summer.
    32. Kuhberger, Anton & Komunska, Dagmara & Perner, Josef, 2001. "The Disjunction Effect: Does It Exist for Two-Step Gambles?," Organizational Behavior and Human Decision Processes, Elsevier, vol. 85(2), pages 250-264, July.
    33. Holt, Charles A, 1986. "Preference Reversals and the Independence Axiom," American Economic Review, American Economic Association, vol. 76(3), pages 508-515, June.
    34. Ehtibar N Dzhafarov & Janne V Kujala, 2013. "All-Possible-Couplings Approach to Measuring Probabilistic Context," PLOS ONE, Public Library of Science, vol. 8(5), pages 1-9, May.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Khrennikova, Polina & Patra, Sudip, 2019. "Asset trading under non-classical ambiguity and heterogeneous beliefs," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 521(C), pages 562-577.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. Izhakian, Yehuda, 2017. "Expected utility with uncertain probabilities theory," Journal of Mathematical Economics, Elsevier, vol. 69(C), pages 91-103.
    3. Zvi Safra & Uzi Segal, 2005. "Are Universal Preferences Possible? Calibration Results for Non-Expected Utility Theories," Boston College Working Papers in Economics 633, Boston College Department of Economics.
    4. Laurent Denant-Boemont & Olivier L’Haridon, 2013. "La rationalité à l'épreuve de l'économie comportementale," Revue française d'économie, Presses de Sciences-Po, vol. 0(2), pages 35-89.
    5. Eddie Dekel & Barton L. Lipman, 2010. "How (Not) to Do Decision Theory," Annual Review of Economics, Annual Reviews, vol. 2(1), pages 257-282, September.
    6. Eduard Marinov, 2017. "The 2017 Nobel Prize in Economics," Economic Thought journal, Bulgarian Academy of Sciences - Economic Research Institute, issue 6, pages 117-159.
    7. Committee, Nobel Prize, 2017. "Richard H. Thaler: Integrating Economics with Psychology," Nobel Prize in Economics documents 2017-1, Nobel Prize Committee.
    8. Michał Lewandowski, 2017. "Prospect Theory Versus Expected Utility Theory: Assumptions, Predictions, Intuition and Modelling of Risk Attitudes," Central European Journal of Economic Modelling and Econometrics, Central European Journal of Economic Modelling and Econometrics, vol. 9(4), pages 275-321, December.
    9. Shaw, W. Douglass & Woodward, Richard T., 2008. "Why environmental and resource economists should care about non-expected utility models," Resource and Energy Economics, Elsevier, vol. 30(1), pages 66-89, January.
    10. Fan Wang, 2022. "Rank-Dependent Utility Under Multiple Priors," Management Science, INFORMS, vol. 68(11), pages 8166-8183, November.
    11. Mohammed Abdellaoui & Horst Zank, 2023. "Source and rank-dependent utility," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 75(4), pages 949-981, May.
    12. Yehuda Izhakian, 2012. "Ambiguity Measurement," Working Papers 12-01, New York University, Leonard N. Stern School of Business, Department of Economics.
    13. Robin Cubitt & Gijs van de Kuilen & Sujoy Mukerji, 2020. "Discriminating Between Models of Ambiguity Attitude: a Qualitative Test," Journal of the European Economic Association, European Economic Association, vol. 18(2), pages 708-749.
    14. Blavatskyy, Pavlo R., 2013. "Two examples of ambiguity aversion," Economics Letters, Elsevier, vol. 118(1), pages 206-208.
    15. Ilke Aydogan & Loïc Berger & Valentina Bosetti & Ning Liu, 2023. "Three Layers of Uncertainty," Journal of the European Economic Association, European Economic Association, vol. 21(5), pages 2209-2236.
    16. Izhakian, Yehuda, 2020. "A theoretical foundation of ambiguity measurement," Journal of Economic Theory, Elsevier, vol. 187(C).
    17. Alexander Zimper, 2011. "Do Bayesians Learn Their Way Out of Ambiguity?," Decision Analysis, INFORMS, vol. 8(4), pages 269-285, December.
    18. Wang, Jianli & Liu, Liqun & Neilson, William S., 2020. "The participation puzzle with reference-dependent expected utility preferences," Insurance: Mathematics and Economics, Elsevier, vol. 93(C), pages 278-287.
    19. Dillenberger, David & Segal, Uzi, 2017. "Skewed noise," Journal of Economic Theory, Elsevier, vol. 169(C), pages 344-364.
    20. Diederik Aerts & Emmanuel Haven & Sandro Sozzo, 2018. "A proposal to extend expected utility in a quantum probabilistic framework," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 65(4), pages 1079-1109, June.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:mateco:v:78:y:2018:i:c:p:186-197. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/jmateco .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.