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Quantum paradigm of probability amplitude and complex utility in entangled discrete choice modeling

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  • Lipovetsky, Stan

Abstract

The main idea of this paper is motivated by a paradigm from quantum physics where the probability amplitude is built as a superposition of the wave functions of states, and the squared modulus of amplitude defines the probability of state membership. Similar linear aggregates are used in classical physics for description of wave interference effects. In contrast to regular techniques of probability estimation in social-economic research (such as logistic regression, multinomial-logit (MNL), discrete choice modeling (DCM), conjoint, best-worst scaling (BWS), and other methods), the proposed approach of probability amplitude modeling permits finding choice probabilities themselves and demonstrates possible interference phenomena of entanglement of different choices. Particularly, a BWS example evaluated by complex utility MNL demonstrates how a choice of each item is composed from its pure-state and mix-state probabilities. The obtained numerical results are supportive of theoretical considerations and practical applications of the probability amplitude modeling, and can serve for better understanding and evaluation of choice decisions.

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  • Lipovetsky, Stan, 2018. "Quantum paradigm of probability amplitude and complex utility in entangled discrete choice modeling," Journal of choice modelling, Elsevier, vol. 27(C), pages 62-73.
    • Handle: RePEc:eee:eejocm:v:27:y:2018:i:c:p:62-73
    DOI: 10.1016/j.jocm.2017.10.003
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    References listed on IDEAS

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    3. 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.
    4. 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).
    5. Stan Lipovetsky, 2023. "Quantum-like Data Modeling in Applied Sciences: Review," Stats, MDPI, vol. 6(1), pages 1-9, February.
    6. 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.
    7. Wei Nai & Zan Yang & Dan Li & Lu Liu & Yuting Fu & Yuao Guo, 2024. "Urban Day-to-Day Travel and Its Development in an Information Environment: A Review," Sustainability, MDPI, vol. 16(6), pages 1-29, March.
    8. Di Gangi, Massimo & Vitetta, Antonino, 2021. "Quantum utility and random utility model for path choice modelling: Specification and aggregate calibration from traffic counts," Journal of choice modelling, Elsevier, vol. 40(C).

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