IDEAS home Printed from https://ideas.repec.org/p/hal/journl/halshs-00754482.html
   My bibliography  Save this paper

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," Post-Print halshs-00754482, HAL.
    • Handle: RePEc:hal:journl:halshs-00754482
    DOI: 10.1007/s11238-009-9142-6
    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. Danilov, V.I. & Lambert-Mogiliansky, A., 2008. "Measurable systems and behavioral sciences," Mathematical Social Sciences, Elsevier, vol. 55(3), pages 315-340, May.
    2. Jacob Gyntelberg & Frank Hansen, 2004. "Expected utility theory with ”small worlds”," Discussion Papers 04-20, University of Copenhagen. Department of Economics, revised Jan 2005.
    3. 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.
    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.
    as


    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. 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.
    6. 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.
    7. V. I. Yukalov & D. Sornette, 2012. "Quantum decision making by social agents," Papers 1202.4918, arXiv.org, revised Oct 2015.
    8. Ariane Lambert-Mogiliansky & François Dubois, 2015. "Transparency in Public Life. A Quantum Cognition Perspective," PSE Working Papers halshs-01064980, HAL.
    9. 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.
    10. 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.
    11. 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.
    12. Hammond, Peter J., 2011. "Laboratory Games and Quantum Behaviour: The Normal Form with a Separable State Space," Economic Research Papers 270755, University of Warwick - Department of Economics.
    13. Ariane Lambert-Mogiliansky & François Dubois, 2015. "Our (represented) World: A Quantum-Like Object," Working Papers halshs-01152332, HAL.
    14. 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.
    15. 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.
    16. Danilov, V., 2016. "Utility Theory of General Lotteries," Journal of the New Economic Association, New Economic Association, vol. 32(4), pages 12-29.
    17. 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.

    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. Vladimir Ivanovitch Danilov & Ariane Lambert-Mogiliansky, 2007. "Non-classical expected utility theory with application to type indeterminacy," Working Papers halshs-00587721, HAL.
    2. 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.
    3. 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.
    4. 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.
    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. Hammond, Peter J., 2011. "Laboratory Games and Quantum Behaviour: The Normal Form with a Separable State Space," Economic Research Papers 270755, University of Warwick - Department of Economics.
    7. Jerry Busemeyer & Ariane Lambert-Mogiliansky, 2009. "TI-games I: An exploration of Type Indeterminacy in strategic decision-making," Working Papers halshs-00566780, HAL.
    8. Ariane Lambert-Mogiliansky & François Dubois, 2015. "Transparency in Public Life. A Quantum Cognition Perspective," PSE Working Papers halshs-01064980, HAL.
    9. Vladimir Danilov, 2009. "Modelling of Non-Commuting Measurements," Journal of the New Economic Association, New Economic Association, issue 1-2, pages 10-36.
    10. V. I. Yukalov & D. Sornette, 2012. "Quantum decision making by social agents," Papers 1202.4918, arXiv.org, revised Oct 2015.
    11. Siegfried K. Berninghaus & Lora R. Todorova & Bodo Vogt, 2012. "How Sensitive is Strategy Selection in Coordination Games?," FEMM Working Papers 120020, Otto-von-Guericke University Magdeburg, Faculty of Economics and Management.
    12. 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.
    13. Adam Brandenburger, 2008. "The Relationship Between Classical and Quantum Correlation in Games," Levine's Working Paper Archive 122247000000002312, David K. Levine.
    14. Emmanuel Haven, 2008. "Private Information and the ‘Information Function’: A Survey of Possible Uses," Theory and Decision, Springer, vol. 64(2), pages 193-228, March.
    15. 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.
    16. Ariane Lambert-Mogiliansky & François Dubois, 2015. "Our (represented) World: A Quantum-Like Object," PSE Working Papers halshs-01152332, HAL.
    17. Godfrey Cadogan, 2012. "Representation theory for risk on markowitz-tversky-kahneman topology," Economics Bulletin, AccessEcon, vol. 32(4), pages 1-34.
    18. Danilov, V., 2016. "Utility Theory of General Lotteries," Journal of the New Economic Association, New Economic Association, vol. 32(4), pages 12-29.
    19. 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.
    20. Ariane Lambert-Mogiliansky, 2010. "Endogenous preferences in games with type indeterminate players," PSE Working Papers halshs-00564895, HAL.

    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:halshs-00754482. 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.