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Title: Statistical and subjective interpretations of probability in quantum-like models of cognition and decision making
Authors: Haven, Emmanuel Eugeen
Khrennikov, A.
First Published: 2016
Citation: Journal of Mathematical Psychology, 2016 (Accepted, In Press)
Abstract: 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.
DOI Link: 10.1016/
ISSN: 0022-2496
Embargo on file until: 1-Jan-10000
Version: Post-print
Status: Peer-reviewed
Type: Journal Article
Rights: Copyright © 2016 Elsevier Inc. All rights reserved. This manuscript version is made available after the end of the embargo period under the CC-BY-NC-ND 4.0 license 
Description: 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.
Appears in Collections:Published Articles, School of Management

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