Quantum like modelling of decision making: quantifying uncertainty with the aid of the Heisenberg-Robertson inequality

Khrennikov, A., Bagarello, F., Basieva, I. & Pothos, E. M. (2018). Quantum like modelling of decision making: quantifying uncertainty with the aid of the Heisenberg-Robertson inequality. Journal of Mathematical Psychology,

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Abstract

This paper contributes to quantum-like modeling of decision making (DM) under uncertainty through application of Heisenberg’s uncertainty principle (in the form of the Robertson inequality). In this paper we apply this instrument to quantify uncertainty in DM performed by quantum-like agents. As an example, we apply the Heisenberg uncertainty principle to the determination of mutual interrelation of uncertainties for “incompatible questions” used to be asked in political opinion pools. We also consider the problem of representation of decision problems, e.g., in the form of questions, by Hermitian operators, commuting and noncommuting, corresponding to compatible and incompatible questions respectively. Our construction unifies the two different situations (compatible versus incompatible mental observables), by means of a single Hilbert space and of a deformation parameter which can be tuned to describe these opposite cases. One of the main foundational consequences of this paper for cognitive psychology is formalization of the mutual uncertainty about incompatible questions with the aid of Heisenberg’s uncertainty principle implying the mental state dependence of (in)compatibility of questions.

Item Type: Article
Additional Information: © 2018 Elsevier. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/
Uncontrolled Keywords: Compatible and incompatible questions; decision making; Heisenberg uncertainty principle; mental state; order effect
Divisions: School of Social Sciences > Department of Psychology
URI: http://openaccess.city.ac.uk/id/eprint/19334

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