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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

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

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    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

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