IDEAS home Printed from https://ideas.repec.org/p/hal/journl/hal-01341722.html
   My bibliography  Save this paper

Expected utility theory with non-commutative probability theory

Author

Listed:
  • Dino Borie

    (GREDEG - Groupe de Recherche en Droit, Economie et Gestion - UNS - Université Nice Sophia Antipolis (1965 - 2019) - CNRS - Centre National de la Recherche Scientifique - UniCA - Université Côte d'Azur)

Abstract

In this paper, we extend von Neumann and Morgenstern's expected utility approach to a non-commutative probability theory. We introduce a new representation of the decision maker's set of events which extends the canonical representation. We reformulate von Neumann and Morgenstern's approach to modeling decision maker behavior by non-commutative probability theory. We introduce a set of preference axi- oms similar to von Neumann and Morgenstern's axioms, and show that they lead to a generalization of the expected utility theorem. Our generalization allows for decision makers to make an intuitive distinction between representations of a set of events. We find that this methodology enables several paradoxes and inconsistencies in traditional expected utility theory (e.g., Allais paradox, etc.) to be solved or better understood.

Suggested Citation

  • Dino Borie, 2013. "Expected utility theory with non-commutative probability theory," Post-Print hal-01341722, HAL.
    • Handle: RePEc:hal:journl:hal-01341722
    DOI: 10.1007/s11403-012-0098-1
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a search for a similarly titled item that would be available.

    Other versions of this item:

    References listed on IDEAS

    as
    1. L. Lambertini, 2000. "Quantum Mechanics and Mathematical Economics are Isomorphic. John von Neumann between Physics and Economics," Working Papers 370, Dipartimento Scienze Economiche, Universita' di Bologna.
    2. Aerts, Diederik & Broekaert, Jan & Czachor, Marek & D'Hooghe, Bart, 2011. "A Quantum-Conceptual Explanation of Violations of Expected Utility in Economics," MPRA Paper 41792, University Library of Munich, Germany.
    3. V. Danilov & A. Lambert-Mogiliansky, 2010. "Expected utility theory under non-classical uncertainty," Theory and Decision, Springer, vol. 68(1), pages 25-47, February.
    4. Loomes, Graham & Sugden, Robert, 1982. "Regret Theory: An Alternative Theory of Rational Choice under Uncertainty," Economic Journal, Royal Economic Society, vol. 92(368), pages 805-824, December.
    5. V. I. Danilov & A. Lambert-Mogiliansky, 2005. "Non-classical Measurement Theory: a Framework for Behavioral Sciences," Levine's Working Paper Archive 122247000000000899, David K. Levine.
    6. Quiggin, John, 1982. "A theory of anticipated utility," Journal of Economic Behavior & Organization, Elsevier, vol. 3(4), pages 323-343, December.
    7. 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..
    8. Machina, Mark J, 1982. ""Expected Utility" Analysis without the Independence Axiom," Econometrica, Econometric Society, vol. 50(2), pages 277-323, March.
    9. Ariane Lambert Mogiliansky & Shmuel Zamir & Herve Zwirn, 2003. "Type Indeterminacy: A Model of the KT(Kahneman-Tversky)-man," Discussion Paper Series dp343, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
    10. Frank Hansen, 2003. "A General Theory of Decision Making," Discussion Papers 03-38, University of Copenhagen. Department of Economics, revised Aug 2005.
    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. Kavitha Ranganathan, 2018. "Does Global Shapes Of Utility Functions Matter For Investment Decisions?," Bulletin of Economic Research, Wiley Blackwell, vol. 70(4), pages 341-361, October.

    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. repec:cup:judgdm:v:16:y:2021:i:6:p:1324-1369 is not listed on IDEAS
    2. Trabelsi, Mohamed Ali, 2006. "Les nouveaux modèles de décision dans le risque et l’incertain : quel apport ? [The new models of decision under risk or uncertainty : What approach?]," MPRA Paper 25442, University Library of Munich, Germany.
    3. Graham Loomes & Ganna Pogrebna, 2014. "Testing for independence while allowing for probabilistic choice," Journal of Risk and Uncertainty, Springer, vol. 49(3), pages 189-211, December.
    4. Belianin, A., 2017. "Face to Face to Human Being: Achievements and Challenges of Behavioral Economics," Journal of the New Economic Association, New Economic Association, vol. 34(2), pages 166-175.
    5. Marc Willinger, 1990. "La rénovation des fondements de l'utilité et du risque," Revue Économique, Programme National Persée, vol. 41(1), pages 5-48.
    6. Delli Gatti,Domenico & Fagiolo,Giorgio & Gallegati,Mauro & Richiardi,Matteo & Russo,Alberto (ed.), 2018. "Agent-Based Models in Economics," Cambridge Books, Cambridge University Press, number 9781108400046, October.
    7. Gaudeul, Alexia, 2009. "A (micro) course in microeconomic theory for MSc students," MPRA Paper 15388, University Library of Munich, Germany.
    8. Moshe Levy, 2022. "An evolutionary explanation of the Allais paradox," Journal of Evolutionary Economics, Springer, vol. 32(5), pages 1545-1574, November.
    9. Sudeep Bhatia & Graham Loomes & Daniel Read, 2021. "Establishing the laws of preferential choice behavior," Judgment and Decision Making, Society for Judgment and Decision Making, vol. 16(6), pages 1324-1369, November.
    10. 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.
    11. Michal Skořepa, 2007. "Zpochybnění deskriptivnosti teorie očekávaného užitku [Doubts about the descriptive validity of the expected utility theory]," Politická ekonomie, Prague University of Economics and Business, vol. 2007(1), pages 106-120.
    12. Kontek, Krzysztof, 2015. "Fanning-Out or Fanning-In? Continuous or Discontinuous? Estimating Indifference Curves Inside the Marschak-Machina Triangle using Certainty Equivalents," MPRA Paper 63965, University Library of Munich, Germany.
    13. Charles-Cadogan, G., 2016. "Expected utility theory and inner and outer measures of loss aversion," Journal of Mathematical Economics, Elsevier, vol. 63(C), pages 10-20.
    14. Han Bleichrodt & Peter P. Wakker, 2015. "Regret Theory: A Bold Alternative to the Alternatives," Economic Journal, Royal Economic Society, vol. 0(583), pages 493-532, March.
    15. Andrew J. Keith & Darryl K. Ahner, 2021. "A survey of decision making and optimization under uncertainty," Annals of Operations Research, Springer, vol. 300(2), pages 319-353, May.
    16. Kircher, Philipp & Sandroni, Alvaro & Ludwig, Sandra, 2009. "Fairness: A Critique to the Utilitarian Approach," Discussion Paper Series of SFB/TR 15 Governance and the Efficiency of Economic Systems 288, Free University of Berlin, Humboldt University of Berlin, University of Bonn, University of Mannheim, University of Munich.
    17. Trabelsi, Mohamed Ali, 2019. "The new models of decision in risk: A review of the critical literature," MPRA Paper 92693, University Library of Munich, Germany, revised 2019.
    18. Phillips Peter J. & Pohl Gabriela, 2018. "The Deferral of Attacks: SP/A Theory as a Model of Terrorist Choice when Losses Are Inevitable," Open Economics, De Gruyter, vol. 1(1), pages 71-85, February.
    19. Trabelsi, Mohamed Ali, 2006. "Les nouveaux modèles de décision dans le risque et l’incertain : quel apport ? [The new models of decision under risk or uncertainty : What approach?]," MPRA Paper 25442, University Library of Munich, Germany.
    20. Jean Baccelli, 2018. "Risk attitudes in axiomatic decision theory: a conceptual perspective," Theory and Decision, Springer, vol. 84(1), pages 61-82, January.
    21. Liang Zou, 2006. "An Alternative to Prospect Theory," Annals of Economics and Finance, Society for AEF, vol. 7(1), pages 1-28, May.

    More about this item

    Keywords

    Expected utility; Decision theory; Non-expected utility; Quantum decision theory;
    All these keywords.

    JEL classification:

    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General
    • D03 - Microeconomics - - General - - - Behavioral Microeconomics: Underlying Principles
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

    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:hal:journl:hal-01341722. 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: CCSD (email available below). General contact details of provider: https://hal.archives-ouvertes.fr/ .

    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.