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Expected utility theory with non-commutative probability theory

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  • Dino Borie

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 axioms 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. Copyright Springer-Verlag 2013

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  • Dino Borie, 2013. "Expected utility theory with non-commutative probability theory," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 8(2), pages 295-315, October.
    • Handle: RePEc:spr:jeicoo:v:8:y:2013:i:2:p:295-315
    DOI: 10.1007/s11403-012-0098-1
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    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.
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    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..
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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; C60; D03; D81;
    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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