IDEAS home Printed from https://ideas.repec.org/p/ces/ceswps/_7158.html
   My bibliography  Save this paper

Quantum Decision Theory and the Ellsberg Paradox

Author

Listed:
  • Ali al-Nowaihi
  • Sanjit Dhami
  • Mengxing Wei

Abstract

We formulate a simple quantum decision model of the Ellsberg paradox. We report the results of an experiment we performed to test the matching probabilities predicted by this model using an incentive compatible method. We find that the theoretical predictions of the model are in conformity with our experimental results. We compare the predictions of our quantum model with those of probably the most successful non-quantum model of ambiguity, namely, the source dependent model. The predictions of our quantum model are not statistically significantly different from those of the source dependent model. The source dependent model requires the specification of probability weighting functions in order to fit the evidence. On the other hand, our quantum model makes no recourse to probability weighting functions. This suggests that much of what is normally attributed to probability weighting may actually be due to quantum probability.

Suggested Citation

  • Ali al-Nowaihi & Sanjit Dhami & Mengxing Wei, 2018. "Quantum Decision Theory and the Ellsberg Paradox," CESifo Working Paper Series 7158, CESifo.
    • Handle: RePEc:ces:ceswps:_7158
    as

    Download full text from publisher

    File URL: https://www.cesifo.org/DocDL/cesifo1_wp7158.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Maurice Obstfeld & Kenneth Rogoff, 2001. "The Six Major Puzzles in International Macroeconomics: Is There a Common Cause?," NBER Chapters, in: NBER Macroeconomics Annual 2000, Volume 15, pages 339-412, National Bureau of Economic Research, Inc.
    2. 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.
    3. Segal, Uzi, 1990. "Two-Stage Lotteries without the Reduction Axiom," Econometrica, Econometric Society, vol. 58(2), pages 349-377, March.
    4. Kocher, Martin G. & Lahno, Amrei Marie & Trautmann, Stefan T., 2018. "Ambiguity aversion is not universal," European Economic Review, Elsevier, vol. 101(C), pages 268-283.
    5. Anna Conte & John D. Hey, 2018. "Assessing multiple prior models of behaviour under ambiguity," World Scientific Book Chapters, in: Experiments in Economics Decision Making and Markets, chapter 7, pages 169-188, World Scientific Publishing Co. Pte. Ltd..
    6. 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..
    7. 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.
    8. Drazen Prelec, 1998. "The Probability Weighting Function," Econometrica, Econometric Society, vol. 66(3), pages 497-528, May.
    9. 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.
    10. Gilboa, Itzhak, 1987. "Expected utility with purely subjective non-additive probabilities," Journal of Mathematical Economics, Elsevier, vol. 16(1), pages 65-88, February.
    11. Diebold, Francis X & Mariano, Roberto S, 2002. "Comparing Predictive Accuracy," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 134-144, January.
    12. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-587, May.
    13. Ali al-Nowaihi & Sanjit Dhami, 2016. "The Ellsberg paradox: A challenge to quantum decision theory?," Discussion Papers in Economics 16/08, Division of Economics, School of Business, University of Leicester.
    14. Craig R. Fox & Amos Tversky, 1995. "Ambiguity Aversion and Comparative Ignorance," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 110(3), pages 585-603.
    15. Gilboa,Itzhak, 2009. "Theory of Decision under Uncertainty," Cambridge Books, Cambridge University Press, number 9780521741231, September.
    16. John D. Hey & Gianna Lotito & Anna Maffioletti, 2018. "The descriptive and predictive adequacy of theories of decision making under uncertainty/ambiguity," World Scientific Book Chapters, in: Experiments in Economics Decision Making and Markets, chapter 8, pages 189-219, World Scientific Publishing Co. Pte. Ltd..
    17. Quiggin, John, 1982. "A theory of anticipated utility," Journal of Economic Behavior & Organization, Elsevier, vol. 3(4), pages 323-343, December.
    18. French, Kenneth R & Poterba, James M, 1991. "Investor Diversification and International Equity Markets," American Economic Review, American Economic Association, vol. 81(2), pages 222-226, May.
    19. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    20. Dhami, Sanjit, 2016. "The Foundations of Behavioral Economic Analysis," OUP Catalogue, Oxford University Press, number 9780198715535.
    21. Ghirardato, Paolo & Maccheroni, Fabio & Marinacci, Massimo, 2004. "Differentiating ambiguity and ambiguity attitude," Journal of Economic Theory, Elsevier, vol. 118(2), pages 133-173, October.
    22. Stephen G. Dimmock & Roy Kouwenberg & Peter P. Wakker, 2016. "Ambiguity Attitudes in a Large Representative Sample," Management Science, INFORMS, vol. 62(5), pages 1363-1380, May.
    23. Harrison, Glenn W., 1986. "An experimental test for risk aversion," Economics Letters, Elsevier, vol. 21(1), pages 7-11.
    24. Unknown, 1986. "Letters," Choices: The Magazine of Food, Farm, and Resource Issues, Agricultural and Applied Economics Association, vol. 1(4), pages 1-9.
    25. Amit Kothiyal & Vitalie Spinu & Peter Wakker, 2014. "An experimental test of prospect theory for predicting choice under ambiguity," Journal of Risk and Uncertainty, Springer, vol. 48(1), pages 1-17, February.
    26. 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.
    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. Mengxing Wei & Ali al-Nowaihi & Sanjit Dhami, 2019. "Quantum Decision Theory, Bounded Rationality and the Ellsberg Paradox," Studies in Microeconomics, , vol. 7(1), pages 110-139, June.

    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. Ali al-Nowaihi & Sanjit Dhami, 2016. "The Ellsberg paradox: A challenge to quantum decision theory?," Discussion Papers in Economics 16/08, Division of Economics, School of Business, University of Leicester.
    2. Amit Kothiyal & Vitalie Spinu & Peter Wakker, 2014. "An experimental test of prospect theory for predicting choice under ambiguity," Journal of Risk and Uncertainty, Springer, vol. 48(1), pages 1-17, February.
    3. Zhihua Li & Julia Müller & Peter P. Wakker & Tong V. Wang, 2018. "The Rich Domain of Ambiguity Explored," Management Science, INFORMS, vol. 64(7), pages 3227-3240, July.
    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. Stephen Dimmock & Roy Kouwenberg & Olivia Mitchell & Kim Peijnenburg, 2015. "Estimating ambiguity preferences and perceptions in multiple prior models: Evidence from the field," Journal of Risk and Uncertainty, Springer, vol. 51(3), pages 219-244, December.
    6. Junyi Chai & Zhiquan Weng & Wenbin Liu, 2021. "Behavioral Decision Making in Normative and Descriptive Views: A Critical Review of Literature," JRFM, MDPI, vol. 14(10), pages 1-14, October.
    7. 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.
    8. Tsang, Ming, 2020. "Estimating uncertainty aversion using the source method in stylized tasks with varying degrees of uncertainty," Journal of Behavioral and Experimental Economics (formerly The Journal of Socio-Economics), Elsevier, vol. 84(C).
    9. Aurélien Baillon & Zhenxing Huang & Asli Selim & Peter P. Wakker, 2018. "Measuring Ambiguity Attitudes for All (Natural) Events," Econometrica, Econometric Society, vol. 86(5), pages 1839-1858, September.
    10. 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.
    11. Chen Li & Uyanga Turmunkh & Peter P. Wakker, 2019. "Trust as a decision under ambiguity," Experimental Economics, Springer;Economic Science Association, vol. 22(1), pages 51-75, March.
    12. Gijs van de Kuilen & Peter P. Wakker, 2011. "The Midweight Method to Measure Attitudes Toward Risk and Ambiguity," Management Science, INFORMS, vol. 57(3), pages 582-598, March.
    13. repec:hal:journl:hal-03031751 is not listed on IDEAS
    14. Han Bleichrodt & Simon Grant & Jingni Yang, 2023. "Testing Hurwicz Expected Utility," Econometrica, Econometric Society, vol. 91(4), pages 1393-1416, July.
    15. Konstantinos Georgalos, 2019. "An experimental test of the predictive power of dynamic ambiguity models," Journal of Risk and Uncertainty, Springer, vol. 59(1), pages 51-83, August.
    16. Anna Conte & John D. Hey, 2018. "Assessing multiple prior models of behaviour under ambiguity," World Scientific Book Chapters, in: Experiments in Economics Decision Making and Markets, chapter 7, pages 169-188, World Scientific Publishing Co. Pte. Ltd..
    17. Gul, Faruk & Pesendorfer, Wolfgang, 2015. "Hurwicz expected utility and subjective sources," Journal of Economic Theory, Elsevier, vol. 159(PA), pages 465-488.
    18. Milos Borozan & Loreta Cannito & Barbara Luppi, 2022. "A tale of two ambiguities: A conceptual overview of findings from economics and psychology," Journal of Behavioral Economics for Policy, Society for the Advancement of Behavioral Economics (SABE), vol. 6(S1), pages 11-21, July.
    19. Ilke Aydogan & Loic Berger & Valentina Bosetti & Ning Liu, 2018. "Three layers of uncertainty: an experiment," Working Papers 623, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
    20. Aurélien Baillon & Han Bleichrodt & Umut Keskin & Olivier l’Haridon & Chen Li, 2018. "The Effect of Learning on Ambiguity Attitudes," Management Science, INFORMS, vol. 64(5), pages 2181-2198, May.
    21. Dillenberger, David & Segal, Uzi, 2017. "Skewed noise," Journal of Economic Theory, Elsevier, vol. 169(C), pages 344-364.

    More about this item

    Keywords

    quantum probability; the Ellsberg paradox; the source dependent model; the law of total probability; the law of reciprocity; the Feynman rules; projective expected utility; bounded rationality; Diebold-Mariano forecasting tests;
    All these keywords.

    JEL classification:

    • D03 - Microeconomics - - General - - - Behavioral Microeconomics: Underlying Principles

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    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:ces:ceswps:_7158. 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: Klaus Wohlrabe (email available below). General contact details of provider: https://edirc.repec.org/data/cesifde.html .

    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.