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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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    1. Stan Lipovetsky, 2015. "Analytical closed-form solution for binary logit regression by categorical predictors," Journal of Applied Statistics, Taylor & Francis Journals, vol. 42(1), pages 37-49, January.
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    7. Benedict G. C. Dellaert & Joffre Swait & Wiktor L. Vic Adamowicz & Theo A. Arentze & Elizabeth E. Bruch & Elisabetta Cherchi & Caspar Chorus & Bas Donkers & Fred M. Feinberg & A. A. J. Marley & Linda , 2018. "Individuals’ Decisions in the Presence of Multiple Goals," Customer Needs and Solutions, Springer;Institute for Sustainable Innovation and Growth (iSIG), vol. 5(1), pages 51-64, March.
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    9. Stan Lipovetsky, 2010. "Supercritical Pitchfork Bifurcation in Implicit Regression Modeling," International Journal of Artificial Life Research (IJALR), IGI Global, vol. 1(4), pages 1-9, October.
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    1. Stan Lipovetsky, 2021. "Predictor Analysis in Group Decision Making," Stats, MDPI, vol. 4(1), pages 1-14, February.
    2. Stan Lipovetsky & Michael Conklin, 2018. "Decreasing Respondent Heterogeneity by Likert Scales Adjustment via Multipoles," Stats, MDPI, vol. 1(1), pages 1-7, November.
    3. Stan Lipovetsky, 2023. "Quantum-like Data Modeling in Applied Sciences: Review," Stats, MDPI, vol. 6(1), pages 1-9, February.
    4. 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.
    5. 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.
    6. 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.
    7. 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).
    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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