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Mathematical Basis of Quantum Decision Theory

Author

Listed:
  • Vyacheslav I. Yukalov

    (ETH Zürich and Joint Institute for Nuclear Research)

  • Didier Sornette

    (ETH Zürich and Swiss Finance Institute)

Abstract

Following the ideas of Bohr, Von Neumann, and Benioff, we formulate quantum decision theory (QDT) as the quantum-mechanical theory of measurement for probability operators. QDT captures the effect of superposition of composite prospects, including many incorporated intentions. It is based on the hypothesis that the thought processes of real human beings involved in the definition and analysis of alternative prospects and scenarios do not necessarily separate them according to the recipes of standard probability theory and of classical utility theory. Our QDT formalizes systematically a broader class of decision making processes in which prospects can interact, interfere and remain entangled. The mathematical QDT is developed so as to be applicable to real-life decision making processes. We demonstrate that all known anomalies and paradoxes documented in the context of classical utility theory are reducible to just a few mathematical archetypes, all of which finding straightforward explanations in the framework of QDT. Interference terms, which are essential for resolving the paradoxes, quantify the aversion of human beings to uncertainty and/or to perceived potential loss resulting from their decisions.

Suggested Citation

  • Vyacheslav I. Yukalov & Didier Sornette, 2008. "Mathematical Basis of Quantum Decision Theory," Swiss Finance Institute Research Paper Series 08-25, Swiss Finance Institute.
    • Handle: RePEc:chf:rpseri:rp0825
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    File URL: http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1263853
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    Citations

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    Cited by:

    1. Ashtiani, Mehrdad & Azgomi, Mohammad Abdollahi, 2015. "A survey of quantum-like approaches to decision making and cognition," Mathematical Social Sciences, Elsevier, vol. 75(C), pages 49-80.
    2. Tanaka, Shigenori & Umegaki, Toshihito & Nishiyama, Akihiro & Kitoh-Nishioka, Hirotaka, 2022. "Dynamical free energy based model for quantum decision making," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 605(C).
    3. Mehrdad Ashtiani & Mohammad Abdollahi Azgomi, 2014. "Contextuality, Incompatibility And Biased Inference In A Quantum-Like Formulation Of Computational Trust," Advances in Complex Systems (ACS), World Scientific Publishing Co. Pte. Ltd., vol. 17(05), pages 1-61.
    4. Ferro, Giuseppe M. & Kovalenko, Tatyana & Sornette, Didier, 2021. "Quantum decision theory augments rank-dependent expected utility and Cumulative Prospect Theory," Journal of Economic Psychology, Elsevier, vol. 86(C).
    5. Didier SORNETTE, 2014. "Physics and Financial Economics (1776-2014): Puzzles, Ising and Agent-Based Models," Swiss Finance Institute Research Paper Series 14-25, Swiss Finance Institute.
    6. Yukalov, V.I. & Yukalova, E.P. & Sornette, D., 2022. "Role of collective information in networks of quantum operating agents," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 598(C).

    More about this item

    Keywords

    decision theory; quantum theory; Hilbert space; utility theory; emotions; loss aversion; uncertainty aversion; Allais paradox; independence paradox; inversion paradox; Ellsberg paradox; conjunction fallacy; disjunction effect; isolation effect;
    All these keywords.

    JEL classification:

    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • A12 - General Economics and Teaching - - General Economics - - - Relation of Economics to Other Disciplines

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