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Open AccessArticle

Balanced Quantum-Like Bayesian Networks

Department of Computer Science and Engineering, INESC-ID & Instituto Superior Técnico, University of Lisbon, 2740-122 Porto Salvo, Portugal
School of Information Systems, Science and Engineering Faculty, Queensland University of Technology, QLD 4000 Brisbane, Australia
Author to whom correspondence should be addressed.
Entropy 2020, 22(2), 170;
Received: 15 December 2019 / Revised: 29 January 2020 / Accepted: 30 January 2020 / Published: 2 February 2020
(This article belongs to the Special Issue Quantum Information Revolution: Impact to Foundations)
Empirical findings from cognitive psychology indicate that, in scenarios under high levels of uncertainty, many people tend to make irrational decisions. To address this problem, models based on quantum probability theory, such as the quantum-like Bayesian networks, have been proposed. However, this model makes use of a Bayes normalisation factor during probabilistic inference to convert the likelihoods that result from quantum interference effects into probability values. The interpretation of this operation is not clear and leads to extremely skewed intensity waves that make the task of prediction of these irrational decisions challenging. This article proposes the law of balance, a novel mathematical formalism for probabilistic inferences in quantum-like Bayesian networks, based on the notion of balanced intensity waves. The general idea is to balance the intensity waves resulting from quantum interference in such a way that, during Bayes normalisation, they cancel each other. With this representation, we also propose the law of maximum uncertainty, which is a method to predict these paradoxes by selecting the amplitudes of the wave with the highest entropy. Empirical results show that the law of balance together with the law of maximum uncertainty were able to accurately predict different experiments from cognitive psychology showing paradoxical or irrational decisions, namely in the Prisoner’s Dilemma game and the Two-Stage Gambling Game. View Full-Text
Keywords: decision making; quantum cognition; quantum-like Bayesian networks; law of total probability; probability waves decision making; quantum cognition; quantum-like Bayesian networks; law of total probability; probability waves
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MDPI and ACS Style

Wichert, A.; Moreira, C.; Bruza, P. Balanced Quantum-Like Bayesian Networks. Entropy 2020, 22, 170.

AMA Style

Wichert A, Moreira C, Bruza P. Balanced Quantum-Like Bayesian Networks. Entropy. 2020; 22(2):170.

Chicago/Turabian Style

Wichert, Andreas; Moreira, Catarina; Bruza, Peter. 2020. "Balanced Quantum-Like Bayesian Networks" Entropy 22, no. 2: 170.

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