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Statistical and subjective interpretations of probability in quantum-like models of cognition and decision making
University of Leicester, UK.
Linnaeus University, Faculty of Technology, Department of Mathematics.ORCID iD: 0000-0002-9857-0938
2016 (English)In: Journal of mathematical psychology (Print), ISSN 0022-2496, E-ISSN 1096-0880, Vol. 74, 82-91 p.Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
2016. Vol. 74, 82-91 p.
National Category
Algebra and Logic
Research subject
Mathematics, Mathematics
Identifiers
URN: urn:nbn:se:lnu:diva-51801DOI: 10.1016/j.jmp.2016.02.005ISI: 000385057200008OAI: oai:DiVA.org:lnu-51801DiVA: diva2:916043
Available from: 2016-03-31 Created: 2016-03-31 Last updated: 2016-11-08Bibliographically approved

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Khrennikov, Andrei
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CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf