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

Ismaël Rafaï (), Sébastien Duchêne (), Eric Guerci, Irina Basieva and Andrei Khrennikov ()
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Sébastien Duchêne: CEE-M - Centre d'Economie de l'Environnement - Montpellier - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement - Institut Agro Montpellier - Institut Agro - Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement - UM - Université de Montpellier
Irina Basieva: City University London
Andrei Khrennikov: ICMM - Iinternational Center for Mathematical Modeling - Växjö University

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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 three-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.

Date: 2022
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Published in Theory and Decision, 2022, 92 (387-406), ⟨10.1007/s11238-021-09823-2⟩

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Journal Article: The triple-store experiment: a first simultaneous test of classical and quantum probabilities in choice over menus (2022)
Working Paper: The Triple-Store Experiment: A First Simultaneous Test of Classical and Quantum Probabilities in Choice over Menus (2021)
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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-03227276

DOI: 10.1007/s11238-021-09823-2

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