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Statistical and subjective interpretations of probability in quantum-like models of cognition and decision making
journal contribution
posted on 2016-03-16, 10:13 authored by Emmanuel Eugeen Haven, A. KhrennikovThe paper starts with an introduction to the basic mathematical model of classical probability (CP), i.e. the Kolmogorov (1933) measure-theoretic model. Its two basic interpretations are discussed: statistical and subjective. We then present the probabilistic structure of quantum mechanics (QM) and discuss the problem of interpretation of a quantum state and the corresponding probability given by Born’s rule. Applications of quantum probability (QP) to modeling of cognition and decision making (DM) suffer from the same interpretational problems as QM. Here the situation is even more complicated than in physics. We analyze advantages and disadvantages of the use of subjective and statistical interpretations of QP. The subjective approach to QP was formalized in the framework of Quantum Bayesianism (QBism) as the result of efforts from C. Fuchs and his collaborators. The statistical approach to QP was presented in a variety of interpretations of QM, both in nonrealistic interpretations, e.g., the Copenhagen interpretation (with the latest version due to A. Plotnitsky), and in realistic interpretations (e.g., the recent Växjö interpretation). At present, we cannot make a definite choice in favor of any of the interpretations. Thus, quantum-like DM confronts the same interpretational problem as quantum physics does.
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Citation
Journal of Mathematical Psychology, 2016, 74, pp. 82–91Author affiliation
/Organisation/COLLEGE OF SOCIAL SCIENCES, ARTS AND HUMANITIES/School of ManagementVersion
- AM (Accepted Manuscript)
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Journal of Mathematical Psychologyissn
0022-2496Acceptance date
2016-02-03Copyright date
2016Available date
2018-03-09Publisher DOI
Publisher version
http://www.sciencedirect.com/science/article/pii/S0022249616000213Notes
The file associated with this record is under a 24-month embargo from publication in accordance with the publisher's self-archiving policy. The full text may be available through the publisher links provided above.Language
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