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Quantum Adaptivity in Biology: From Genetics to Cognition pp 91–126Cite as

Application to Decision Making Theory and Cognitive Science

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Abstract

In this chapter the formalism of quantum probability and quantum information theory (in its generalized form based on theory of lifting) is applied to construct the QL-representations for cognitive processes, especially decision making in games of the prisoner’s dilemma type. Our modeling is based on the results of extended studies in the domain of cognitive psychology demonstrated that in some mental contexts players behave irrationally, i.e., they select mixed strategies which are different from the Nash equilibrium predicted by classical game theory. The simplest model of such irrational behavior is based on theory of open quantum systems and quantum master equation. More complex cognitive situations are modelled with aid quantum adaptive dynamics generalizing theory of open quantum systems. We also construct the QL-representation for bistable perception. We are able to construct quantum operators providing the adequate operational description of know statistical data. To check nonclassicality of these data we use a Bell-type inequality, namely, the Leggett-Garg inequality.

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Notes

  1. 1.

    Some of these problems were also studied by Cheon and Takahashi [20, 21], Khrennikov [22, 23], Fichtner et al. [24], Franco [25], Khrennikov and Haven [26], Pothos and Busemeyer [27, 28], Lambert-Mogiliansky et al. [29], Dzhafarov and Kujala [30, 31], and Wang et al. [32, 33], see also the special section on cognition, decision making and finances in the conference proceedings [34].

  2. 2.

    Of course, every probability in this case is subjective, so that we do not need to use classical probability theory in order to estimate this posterior probability. Instead of Bayes’ formulae, humans often use more heuristic inference, and there are many reports in psychology.

  3. 3.

    Similar interpretation for the Bell inequality was presented in the paper [50], the first paper which demonstrated that the Bell-type inequalities can be violated outside of physics, for the data collected from recognition of ambiguous figures; see also [51]; see [49] for the detailed presentation of the contextual viewpoint on quantum theory in general and on the Bell-type inequalities in particular.

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Author information

Authors and Affiliations

  1. Liberal Arts Division, Tokuyama College of Technology, Tokuyama, Japan

    Masanari Asano

  2. International Center for Mathematical Modeling in Physics and Cognitive Science, Linnaeus University, Växjö, Sweden

    Andrei Khrennikov

  3. Information Science, Tokyo University of Science, Tokyo, Japan

    Masanori Ohya & Yoshiharu Tanaka

  4. Department of Biological Science and Technology, Tokyo University of Science, Tokyo, Japan

    Ichiro Yamato

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  1. Masanari Asano
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  2. Andrei Khrennikov
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  3. Masanori Ohya
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  4. Yoshiharu Tanaka
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  5. Ichiro Yamato
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Correspondence to Masanari Asano .

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Asano, M., Khrennikov, A., Ohya, M., Tanaka, Y., Yamato, I. (2015). Application to Decision Making Theory and Cognitive Science. In: Quantum Adaptivity in Biology: From Genetics to Cognition. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-9819-8_6

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