Quantum-like modeling of the order effect in decision making: POVM viewpoint on the Wang-Busemeyer QQ-equality

• URL: http://arxiv.org/abs/1811.00045v2
• Date: Sat, 1 Apr 2023 19:10:42 GMT
• Title: Quantum-like modeling of the order effect in decision making: POVM viewpoint on the Wang-Busemeyer QQ-equality
• Authors: Aleksandr Lebedev and Andrei Khrennikov
• Abstract summary: Wang and Busemeyer invented a quantum model and approach as well as non-parametric equality (so-called QQ-equality) This note is to test the possibility to expand the Wang-Busemeyer model by considering questions which are mathematically represented by positive operator valued measures. But, we also showed that, in principle, it is possible to reduce expanded model to the original Wang-Busemeyer model by expanding the context of the questions.
• Score: 77.34726150561087
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In recent years, quantum mechanics has been actively used in areas outside of physics, such as psychology, sociology, theory of decision-making, game theory, and others. In particular, quantum mechanics is used to explain the paradoxes arising in cognitive psychology and decision making. Wang and Busemeyer invented a quantum model and approach as well as non-parametric equality (so-called QQ-equality), explaining the questions order effect. The primary objective of this note is to test the possibility to expand the Wang-Busemeyer model by considering questions which are mathematically represented by positive operator valued measures. We found that, for such observables, the QQ-equality can be violated. But, we also showed that, in principle, it is possible to reduce expanded model to the original Wang-Busemeyer model by expanding the context of the questions. This version of preprint is aimed to point out to annoying miscalculation in version 1. This miscalculation might mislead a reader who is not experienced in operating with POVMs. Otherwise the main line of construction and reasoning presented in version 1 is right and it can be easily completed by the reader on the basis of version 1 and the correction remark in version 2.

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