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The triple-store experiment: a first simultaneous test of classical and quantum probabilities in choice over menus

Author

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  • Ismaël Rafaï

    (Université Côte d’Azur, CNRS, GREDEG
    CEE-M, Univ. Montpellier, CNRS, INRAE, Institut Agro)

  • Sébastien Duchêne

    (CEE-M, Univ. Montpellier, CNRS, INRAE, Institut Agro)

  • Eric Guerci

    (Université Côte d’Azur, CNRS, GREDEG)

  • Irina Basieva

    (City University)

  • Andrei Khrennikov

    (Linnaeus University)

Abstract

Recently quantum probability theory started to be actively used in studies of human decision-making, in particular for the resolution of paradoxes (such as the Allais, Ellsberg, and Machina paradoxes). Previous studies were based on a cognitive metaphor of the quantum double-slit experiment—the basic quantum interference experiment. In this paper, we report on an economics experiment based on a triple-slit experiment design, where the slits are menus of alternatives from which one can choose. The test of nonclassicality is based on the Sorkin equality (which was only recently tested in quantum physics). Each alternative is a voucher to buy products in one or more stores. The alternatives are obtained from all disjunctions including one, two or three stores. The participants have to reveal the amount for which they are willing to sell the chosen voucher. Interference terms are computed by comparing the willingness to sell a voucher built as a disjunction of stores and the willingness to sell the vouchers corresponding to the singleton stores. These willingness to sell amounts are used to estimate probabilities and to test both the law of total probabilities and the Born Rule. Results reject neither classical nor quantum probability. We discuss this initial experiment and our results and provide guidelines for future studies.

Suggested Citation

  • Ismaël Rafaï & Sébastien Duchêne & Eric Guerci & Irina Basieva & Andrei Khrennikov, 2022. "The triple-store experiment: a first simultaneous test of classical and quantum probabilities in choice over menus," Theory and Decision, Springer, vol. 92(2), pages 387-406, March.
    • Handle: RePEc:kap:theord:v:92:y:2022:i:2:d:10.1007_s11238-021-09823-2
    DOI: 10.1007/s11238-021-09823-2
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    More about this item

    Keywords

    Quantum cognition; Sorkin equality; Born rule; Law of total probability; Triple slit experiment;
    All these keywords.

    JEL classification:

    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • C67 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Input-Output Models
    • D57 - Microeconomics - - General Equilibrium and Disequilibrium - - - Input-Output Tables and Analysis
    • E17 - Macroeconomics and Monetary Economics - - General Aggregative Models - - - Forecasting and Simulation: Models and Applications
    • I18 - Health, Education, and Welfare - - Health - - - Government Policy; Regulation; Public Health
    • R15 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General Regional Economics - - - Econometric and Input-Output Models; Other Methods

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