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Statistical and subjective interpretations of probability in quantum-like models of cognition and decision making

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journal contribution
posted on 16.03.2016, 10:13 by Emmanuel Eugeen Haven, A. Khrennikov
The 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.

History

Citation

Journal of Mathematical Psychology, 2016, 74, pp. 82–91

Author affiliation

/Organisation/COLLEGE OF SOCIAL SCIENCES, ARTS AND HUMANITIES/School of Management

Version

AM (Accepted Manuscript)

Published in

Journal of Mathematical Psychology

issn

0022-2496

Acceptance date

03/02/2016

Copyright date

2016

Available date

09/03/2018

Publisher version

http://www.sciencedirect.com/science/article/pii/S0022249616000213

Notes

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

en