Abstract
Clues from psychology indicate that human cognition is not only based on classical probability theory as explained by Kolmogorov’s axioms but additionally on quantum probability. We explore the relation between the law of total probability and its violation resulting in the law of total quantum probability. The violation results from an additional interference that influences the classical probabilities. Outgoing from this exploration we introduce a balanced Bayesian quantum-like model that is based on probability waves. The law of maximum uncertainty indicates how to choose a possible phase value of the wave resulting in a meaningful probability value.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Amico, L., Fazio, R., Osterloh, A., Vedral, V.: Entanglement in many-body systems. Rev. Mod. Phys. 80(2), 517–576 (2008)
Binney, J., Skinner, D.: The Physics of Quantum Mechanics. Oxford University Press, Oxford (2014)
Busemeyer, J., Matthew, M., Wang, Z.: A quantum information processing explanation of disjunction effects. In: Proceedings of the 28th Annual Conference of the Cognitive Science Society, pp. 131–135 (2006)
Busemeyer, J., Wang, Z.: Quantum cognition: key issues and discussion. Top. Cogn. Sci. 6, 43–46 (2014)
Busemeyer, J.R., Bruza, P.D.: Quantum Models of Cognition and Decision. Cambridge University Press, Cambridge (2012)
Busemeyer, J.R., Trueblood, J.: Comparison of quantum and Bayesian inference models. In: Bruza, P., Sofge, D., Lawless, W., van Rijsbergen, K., Klusch, M. (eds.) QI 2009. LNCS (LNAI), vol. 5494, pp. 29–43. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-00834-4_5
Busemeyer, J.R., Wang, Z., Lambert-Mogiliansky, A.: Empirical comparison of Markov and quantum models of decision making. J. Math. Psychol. 53(5), 423–433 (2009). https://doi.org/10.1016/j.jmp.2009.03.002
Busemeyer, J.R., Wang, Z., Townsend, J.T.: Quantum dynamics of human decision-making. J. Math. Psychol. 50(3), 220–241 (2006). https://doi.org/10.1016/j.jmp.2006.01.003
Ghosh, S., Rosenbaum, T.F., Aeppli, G., Coppersmith, S.N.: Entangled quantum state of magnetic dipoles. Nature 425, 48–51 (2003)
Hristova, E., Grinberg, M.: Disjunction effect in prisonner’s dilemma: evidences from an eye-tracking study. In: Proceedings of the 30th Annual Conference of the Cognitive Science Society, pp. 1225–1230 (2008)
Jaynes, E.T.: Information theory and statistical mechanics. Phys. Rev. Ser. II 106(4), 620–630 (1957)
Jaynes, E.T.: Information theory and statistical mechanics II. Phys. Rev. Ser. II 108(2), 171–190 (1957)
Jaynes, E.T.: Prior probabilities. IEEE Trans. Syst. Sci. Cybern. 4(3), 227–241 (1968)
Khrennikov, A.: Quantum-like model of cognitive decision making and information processing. J. BioSyst. 95, 179–187 (2009)
Kuhberger, A., Komunska, D., Josef, P.: The disjunction effect: does it exist for two-step gambles? Organ. Behav. Hum. Decis. Process. 85, 250–264 (2001)
Lambdin, C., Burdsal, C.: The disjunction effect reexamined: relevant methodological issues and the fallacy of unspecified percentage comparisons. Organ. Behav. Hum. Decis. Process. 103, 268–276 (2007)
Li, S., Taplin, J.: Examining whether there is a disjunction effect in prisoner’s dilemma game. Chin. J. Psychol. 44, 25–46 (2002)
Moreira, C., Wichert, A.: Quantum-like Bayesian networks for modeling decision making. Front. Psychol. 7, 11 (2016)
Shafir, E., Tversky, A.: Thinking through uncertainty: nonconsequential reasoning and choice. Cogn. Psychol. 24, 449–474 (1992)
Tversky, A., Shafir, E.: The disjunction effect in choice under uncertainty. J. Psychol. Sci. 3, 305–309 (1992)
Vedral, V.: Living in a quantum world. Sci. Am. 304(6), 38–43 (2011)
Yukalov, V., Sornette, D.: Decision theory with prospect interference and entanglement. Theor. Decis. 70, 283–328 (2011)
Acknowledgment
This work was supported by national funds through Fundação para a Ciência e a Tecnologia (FCT) with reference UID/CEC/50021/2013. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this paper
Cite this paper
Wichert, A., Moreira, C. (2019). Balanced Quantum-Like Model for Decision Making. In: Coecke, B., Lambert-Mogiliansky, A. (eds) Quantum Interaction. QI 2018. Lecture Notes in Computer Science(), vol 11690. Springer, Cham. https://doi.org/10.1007/978-3-030-35895-2_6
Download citation
DOI: https://doi.org/10.1007/978-3-030-35895-2_6
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-35894-5
Online ISBN: 978-3-030-35895-2
eBook Packages: Computer ScienceComputer Science (R0)