IDEAS home Printed from https://ideas.repec.org/a/nea/journl/y2009i1-2p10-36.html
   My bibliography  Save this article

Modelling of Non-Commuting Measurements

Author

Listed:
  • Vladimir Danilov

    (Central Economics and Mathematics Institute, RAS, Moscow, Russia)

Abstract

In the paper we propose an approach which allows to discuss on formal level non-commuting measurements. Such measurements 'disturb' a measured system and change its states. The key structure used in the description of such measurements is the structure of ortho-poset (which is a Boolean lattice in the classical case of commuting measurements). States of the system are realized as probabilistic measures on the ortho-poset. We give an application of the proposed approach to decision-making under 'non-classical' indeterminacy and to modelling 'non-classical' preferences.

Suggested Citation

  • Vladimir Danilov, 2009. "Modelling of Non-Commuting Measurements," Journal of the New Economic Association, New Economic Association, issue 1-2, pages 10-36.
    • Handle: RePEc:nea:journl:y:2009:i:1-2:p:10-36
    as

    Download full text from publisher

    File URL: http://www.econorus.org/journal/doc/Danilov%201-2.pdf
    Download Restriction: no
    File URL: http://www.econorus.org/repec/journl/2009-1-2-10-36r.pdf
    Download Restriction: no
    ---><---

    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.
    Full references (including those not matched with items on IDEAS)

    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. 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.
    2. 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.
    3. 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.
    4. 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.
    5. V. Danilov & A. Lambert-Mogiliansky, 2010. "Expected utility theory under non-classical uncertainty," Theory and Decision, Springer, vol. 68(1), pages 25-47, February.
    6. Jerry Busemeyer & Ariane Lambert-Mogiliansky, 2009. "TI-games I: An exploration of Type Indeterminacy in strategic decision-making," Working Papers halshs-00566780, HAL.
    7. Ariane Lambert-Mogiliansky & François Dubois, 2015. "Transparency in Public Life. A Quantum Cognition Perspective," PSE Working Papers halshs-01064980, HAL.
    8. V. I. Yukalov & D. Sornette, 2012. "Quantum decision making by social agents," Papers 1202.4918, arXiv.org, revised Oct 2015.
    9. 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.
    10. 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.
    11. Adam Brandenburger, 2008. "The Relationship Between Classical and Quantum Correlation in Games," Levine's Working Paper Archive 122247000000002312, David K. Levine.
    12. 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.
    13. 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.
    14. 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.
    15. Ariane Lambert-Mogiliansky & François Dubois, 2015. "Our (represented) World: A Quantum-Like Object," PSE Working Papers halshs-01152332, HAL.
    16. Godfrey Cadogan, 2012. "Representation theory for risk on markowitz-tversky-kahneman topology," Economics Bulletin, AccessEcon, vol. 32(4), pages 1-34.
    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.
    18. Ariane Lambert-Mogiliansky, 2010. "Endogenous preferences in games with type indeterminate players," PSE Working Papers halshs-00564895, HAL.
    19. Khrennikov, Andrei, 2015. "Quantum version of Aumann’s approach to common knowledge: Sufficient conditions of impossibility to agree on disagree," Journal of Mathematical Economics, Elsevier, vol. 60(C), pages 89-104.
    20. Jerome R. Busemeyer & Jörg Rieskamp, 2014. "Psychological research and theories on preferential choice," Chapters, in: Stephane Hess & Andrew Daly (ed.), Handbook of Choice Modelling, chapter 3, pages 49-72, Edward Elgar Publishing.

    More about this item

    Keywords

    First-kind measurement; inconsistent measurements; event; orthoposet; transition probability space;
    All these keywords.

    JEL classification:

    • C44 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Operations Research; Statistical Decision Theory
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

    Statistics

    Access and download statistics

    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:nea:journl:y:2009:i:1-2:p:10-36. 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: Alexey Tcharykov (email available below). General contact details of provider: https://edirc.repec.org/data/nearuea.html .

    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.