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Expected utility theory under non-classical uncertainty

Author

Listed:
  • Vladimir Ivanovitch Danilov

    (CEMI - Central Economic Mathematical Institute - RAS - Russian Academy of Sciences [Moscow])

  • Ariane Lambert-Mogiliansky

    (PSE - Paris-Jourdan Sciences Economiques - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - INRA - Institut National de la Recherche Agronomique - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique, PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement)

Abstract

In this article, Savage's theory of decision-making under uncertainty is extended from a classical environment into a non-classical one. The Boolean lattice of events is replaced by an arbitrary ortho-complemented poset. We formulate the corresponding axioms and provide representation theorems for qualitative measures and expected utility. Then, we discuss the issue of beliefs updating and investigate a transition probability model. An application to a simple game context is proposed.

Suggested Citation

  • Vladimir Ivanovitch Danilov & Ariane Lambert-Mogiliansky, 2010. "Expected utility theory under non-classical uncertainty," PSE-Ecole d'économie de Paris (Postprint) halshs-00754482, HAL.
    • Handle: RePEc:hal:pseptp:halshs-00754482
    DOI: 10.1007/s11238-009-9142-6
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    References listed on IDEAS

    as
    1. Danilov, V.I. & Lambert-Mogiliansky, A., 2008. "Measurable systems and behavioral sciences," Mathematical Social Sciences, Elsevier, vol. 55(3), pages 315-340, May.
    2. 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.
    3. Jacob Gyntelberg & Frank Hansen, 2004. "Expected utility theory with ”small worlds”," Discussion Papers 04-20, University of Copenhagen. Department of Economics, revised Jan 2005.
    4. Ehud Lehrer & Eran Shmaya, 2005. "A Subjective Approach to Quantum Probability," Game Theory and Information 0503002, University Library of Munich, Germany.
    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.
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    Cited by:

    1. Ariane Lambert-Mogiliansky & Adrian Calmettes, 2019. ""Phishing For (quantum-like) Phools" Theory and experimental evidence," Working Papers halshs-02146862, HAL.
    2. Danilov, V.I. & Lambert-Mogiliansky, A., 2018. "Targeting in quantum persuasion problem," Journal of Mathematical Economics, Elsevier, vol. 78(C), pages 142-149.
    3. Vladimir Ivanovitch Danilov & Ariane Lambert-Mogiliansky, 2017. "Preparing a (quantum) belief system," Working Papers halshs-01542068, HAL.
    4. V. I. Danilov & A. Lambert-Mogiliansky & V. Vergopoulos, 2018. "Dynamic consistency of expected utility under non-classical (quantum) uncertainty," Theory and Decision, Springer, vol. 84(4), pages 645-670, June.
    5. Thomas Boyer-Kassem & Sébastien Duchêne & Eric Guerci, 2016. "Quantum-like models cannot account for the conjunction fallacy," Theory and Decision, Springer, vol. 81(4), pages 479-510, November.
    6. 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.
    7. Ariane Lambert-Mogiliansky & Jerome Busemeyer, 2012. "Quantum Type Indeterminacy in Dynamic Decision-Making: Self-Control through Identity Management," Games, MDPI, vol. 3(2), pages 1-22, May.
    8. V. I. Yukalov & D. Sornette, 2012. "Quantum decision making by social agents," Papers 1202.4918, arXiv.org, revised Oct 2015.
    9. Ariane Lambert-Mogiliansky & François Dubois, 2015. "Our (represented) World: A Quantum-Like Object," PSE Working Papers halshs-01152332, HAL.
    10. Ariane Lambert-Mogiliansky & François Dubois, 2015. "Transparency in Public Life. A Quantum Cognition Perspective," PSE Working Papers halshs-01064980, HAL.
    11. Boyer-Kassem, Thomas & Duchêne, Sébastien & Guerci, Eric, 2016. "Testing quantum-like models of judgment for question order effect," Mathematical Social Sciences, Elsevier, vol. 80(C), pages 33-46.
    12. Ismaël Rafaï & Sébastien Duchêne & Eric Guerci & Irina Basieva & Andrei Khrennikov, 2022. "The triple-store experiment: a first simultaneous test of classical and quantum probabilities in choice over menus," Theory and Decision, Springer, vol. 92(2), pages 387-406, March.
    13. Haven, Emmanuel & Khrennikova, Polina, 2018. "A quantum-probabilistic paradigm: Non-consequential reasoning and state dependence in investment choice," Journal of Mathematical Economics, Elsevier, vol. 78(C), pages 186-197.
    14. Hammond, Peter J, 2011. "Laboratory Games and Quantum Behaviour: The Normal Form with a Separable State Space," The Warwick Economics Research Paper Series (TWERPS) 969, University of Warwick, Department of Economics.
    15. Danilov, V., 2016. "Utility Theory of General Lotteries," Journal of the New Economic Association, New Economic Association, vol. 32(4), pages 12-29.
    16. Haven, Emmanuel & Sozzo, Sandro, 2016. "A generalized probability framework to model economic agents' decisions under uncertainty," International Review of Financial Analysis, Elsevier, vol. 47(C), pages 297-303.

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