Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Modeling Combination of Question Order Effect, Response Replicability Effect, and QQ-Equality with Quantum Instruments

Version 1 : Received: 16 October 2020 / Approved: 19 October 2020 / Online: 19 October 2020 (08:05:59 CEST)

A peer-reviewed article of this Preprint also exists.

Journal reference: Journal of Mathematical Psychology 2021, 100, 102491
DOI: 10.1016/


We continue to analyze basic constraints on human's decision making from the viewpoint of quantum measurement theory (QMT). As has been found, the conventional QMT based on the projection postulate cannot account for combination of the question order effect (QOE) and the response replicability effect (RRE). This was an alarm signal for quantum-like modeling of decision making. Recently, it was shown that this objection to quantum-like modeling can be removed on the basis of the general QMT based on quantum instruments. In the present paper we analyse the problem of combination of QOE, RRE, and the famous QQ-equality (QQE). This equality was derived by Busemeyer and Wang and it was shown (in the joint paper with Solloway and Shiffrin) that statistical data from many social opinion polls satisfies it. Now, we construct quantum instruments satisfying QOE, RRE, and QQE. The general features of our approach are formalized with postulates which generalize {\it Wang-Busemeyer} postulates for quantum-like modeling of decision making. Moreover, we show that our model closely reproduces the statistics of the famous Clinton-Gore Poll data with a prior belief state independent of the question order. This model successfully removes the order effect from the data to determine the genuine distribution of the opinions in the Poll. The paper also provides a psychologist-friendly introduction to the theory of quantum instruments - the most general mathematical framework for quantum measurements. We hope that this theory will attract attention of psychologists and will stimulate further applications.

Subject Areas

quantum-like models; decision making; social science; quantum instruments; order effect; response replicability effect; QQ-equality

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