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arXiv:1508.03686 · Journal of Mathematical Psychology

Beyond-quantum modeling of question order effects and response replicability in psychological measurements

Diederik Aerts, Massimiliano Sassoli de Bianchi

Published May 2, 2017• 19 citations
arXivHTMLPDF
DOI
10.1016/j.jmp.2017.03.004

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We continue to analyze matching of some basic constraints on human's decision making with quantum theory of measurement. As was found, quantum measurement theory based on the projection postulate does not match with combination of the question order effect (QOE) and the response replicability effect (RRE). This was the 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 measurement theory based on quantum instruments. In the present paper, the problem of combination QOE, RRE with the famous QQ-equality is analyzed. 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 QQE, RRE, and QQ-inequality. Moreover, we show that this model reproduces the statistics of the famous Clinton-Gore Poll data almost faithfully 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 opinion to the Poll. Independently of modeling of the concrete psychological effects, the paper provides psychologist-friendly presentation of the theory of quantum instruments - the most general mathematical framework for quantum measurements. We hope that this theory will attract attention of psychologists and generate further psychological applications.
Recently, quantum formalism started to be actively used outside of quantum physics: in psychology, decision-making, economics, finances, and social science. Human psychological behavior is characterized by a few basic effects; one of them is the question order effect (QOE). This effect was successfully modeled (Busemeyer–Wang) by representing questions A and B by Hermitian observables and mental-state transformations (back action of answering) by orthogonal projectors. However, then it was demonstrated that such representation cannot be combined with another psychological effect, known as the response replicability effect (RRE). Later, this no-go result was generalized to representation of questions and state transformations by quantum instruments of the atomic type. In light of these results, the possibility of using quantum formalism in psychology was questioned. In this paper, we show that, nevertheless, the combination of the QOE and RRE can be modeled within quantum formalism, in the framework of theory of non-atomic quantum instruments.