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Expected utility theory with non-commutative probability theory

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  • 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
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    References listed on IDEAS

    as
    1. V. Danilov & A. Lambert-Mogiliansky, 2010. "Expected utility theory under non-classical uncertainty," Theory and Decision, Springer, vol. 68(1), pages 25-47, February.
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    5. 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..
    6. 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.
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    8. 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.
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    10. Frank Hansen, 2003. "A General Theory of Decision Making," Discussion Papers 03-38, University of Copenhagen. Department of Economics, revised Aug 2005.
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    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.

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    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

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