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Empirical Comparison of Markov and Quantum models of decision-making

Author

Listed:
  • Jérôme Busemeyer

    (Indiana University - Indiana University [Bloomington] - Indiana University System)

  • Ariane Lambert-Mogiliansky

    (PJSE - Paris-Jourdan Sciences Economiques - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique, PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement)

  • Zheng Wang

    (OSU - The Ohio State University [Columbus])

Abstract

There are at least two general theories for building probabilistic-dynamical systems: one is Markov theory and another is quantum theory. These two mathematical frameworks share many fundamental ideas, but they also differ in some key properties. On the one hand, Markov theory obeys the law of total probability, but quantum theory does not; on the other hand, quantum theory obeys the doubly stochastic law, but Markov theory does not. Therefore, the decision about whether to use a Markov or a quantum system depends on which of these laws are empirically obeyed in an application. This article derives two general methods for testing these theories that are parameter free, and presents a new experimental test. The article concludes with a review of experimental findings from cognitive psychology that evaluate these two properties.

Suggested Citation

  • Jérôme Busemeyer & Ariane Lambert-Mogiliansky & Zheng Wang, 2009. "Empirical Comparison of Markov and Quantum models of decision-making," PSE-Ecole d'économie de Paris (Postprint) halshs-00754332, HAL.
    • Handle: RePEc:hal:pseptp:halshs-00754332
    DOI: 10.1016/j.jmp.2009.03.002
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    Citations

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    Cited by:

    1. Khrennikov, Andrei, 2015. "Quantum version of Aumann’s approach to common knowledge: Sufficient conditions of impossibility to agree on disagree," Journal of Mathematical Economics, Elsevier, vol. 60(C), pages 89-104.
    2. Xiaoyang Xin & Mengdan Sun & Bo Liu & Ying Li & Xiaoqing Gao, 2022. "A More Realistic Markov Process Model for Explaining the Disjunction Effect in One-Shot Prisoner’s Dilemma Game," Mathematics, MDPI, vol. 10(5), pages 1-23, March.
    3. Thomas Boyer-Kassem & Sébastien Duchêne & Eric Guerci, 2016. "Quantum-like models cannot account for the conjunction fallacy," Theory and Decision, Springer, vol. 81(4), pages 479-510, November.
    4. Yu, Jiangbo Gabriel & Jayakrishnan, R., 2018. "A quantum cognition model for bridging stated and revealed preference," Transportation Research Part B: Methodological, Elsevier, vol. 118(C), pages 263-280.
    5. Andreas Wichert, 2021. "Quantum-Like Sampling," Mathematics, MDPI, vol. 9(17), pages 1-11, August.
    6. Ashtiani, Mehrdad & Azgomi, Mohammad Abdollahi, 2015. "A survey of quantum-like approaches to decision making and cognition," Mathematical Social Sciences, Elsevier, vol. 75(C), pages 49-80.
    7. Xiao Tan & Jianjun Zhu & Tong Wu, 2022. "Dynamic Reference Point-Oriented Consensus Mechanism in Linguistic Distribution Group Decision Making Restricted by Quantum Integration of Information," Group Decision and Negotiation, Springer, vol. 31(2), pages 491-528, April.
    8. Jingmei Xiao & Mei Cai & Yu Gao, 2022. "A VIKOR-Based Linguistic Multi-Attribute Group Decision-Making Model in a Quantum Decision Scenario," Mathematics, MDPI, vol. 10(13), pages 1-23, June.
    9. Ana Njegovanovic, 2018. "Hilbert Space / Quantum Theory of the Financial Decision and Role of the Prefrontal Cortex with a View to Emotions," International Journal of Social and Administrative Sciences, Asian Economic and Social Society, vol. 3(1), pages 42-54, March.
    10. Loretta Mastroeni & Maurizio Naldi & Pierluigi Vellucci, 2023. "Personal Finance Decisions with Untruthful Advisors: An Agent-Based Model," Computational Economics, Springer;Society for Computational Economics, vol. 61(4), pages 1477-1522, April.
    11. Boyer-Kassem, Thomas & Duchêne, Sébastien & Guerci, Eric, 2016. "Testing quantum-like models of judgment for question order effect," Mathematical Social Sciences, Elsevier, vol. 80(C), pages 33-46.
    12. Hancock, Thomas O. & Broekaert, Jan & Hess, Stephane & Choudhury, Charisma F., 2020. "Quantum probability: A new method for modelling travel behaviour," Transportation Research Part B: Methodological, Elsevier, vol. 139(C), pages 165-198.
    13. Hancock, Thomas O. & Broekaert, Jan & Hess, Stephane & Choudhury, Charisma F., 2020. "Quantum choice models: A flexible new approach for understanding moral decision-making," Journal of choice modelling, Elsevier, vol. 37(C).
    14. Khrennikova, Polina, 2016. "Application of quantum master equation for long-term prognosis of asset-prices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 450(C), pages 253-263.
    15. Luke Snow & Shashwat Jain & Vikram Krishnamurthy, 2022. "Lyapunov based Stochastic Stability of Human-Machine Interaction: A Quantum Decision System Approach," Papers 2204.00059, arXiv.org.

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