Violation of contextual generalization of the Leggett–Garg inequality for recognition of ambiguous figures

Asano, Masanari; Hashimoto, Takahisa; Khrennikov, Andrei; Ohya, Masanori; Tanaka, Yoshiharu

doi:10.1088/0031-8949/2014/t163/014006

Cited by 68 publications

(81 citation statements)

References 54 publications

(86 reference statements)

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“…So, R 1 1 and R 2 2 are essentially the same random variable, say X. But, from (10), this X equals R 2 1 with probability 3/4, whereas from the c 2 -distribution in (7), this X equals R 2 1 with probability 2a − 1/4, which is not 3/4 if a = 1/2. The conclusion is that the joint distributions along the two rows of the content-context matrix (6) prevent the responses to the same questions in the two columns of the matrix to be as close to each other as they can be if the two columns are viewed separately.…”

Section: A Numerical Example and Interpretationmentioning

confidence: 99%

True contextuality beats direct influences in human decision making.

Basieva¹,

Cervantes²,

Dzhafarov³

et al. 2019

Journal of Experimental Psychology: General

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In quantum physics there are well-known situations when measurements of the same property in different contexts (under different conditions) have the same probability distribution, but cannot be represented by one and the same random variable. Such systems of random variables are called contextual. More generally, true contextuality is observed when different contexts force measurements of the same property (in psychology, responses to the same question) to be more dissimilar random variables than warranted by the difference of their distributions. The difference in distributions is itself a form of context-dependence, but of another nature: it is attributable to direct causal influences exerted by contexts upon the random variables. The Contextuality-by-Default (CbD) theory allows one to separate true contextuality from direct influences in the overall context-dependence. The CbD analysis of numerous previous attempts to demonstrate contextuality in human judgments shows that all context-dependence in them can be accounted for by direct influences, with no true contextuality present. However, contextual systems in human behavior can be found. In this paper we present a series of crowdsourcing experiments that exhibit true contextuality in simple decision making. The design of these experiments is an elaboration of one introduced in the "Snow Queen" experiment (Decision 5, 193-204, 2018), where contextuality was for the first time demonstrated unequivocally.

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Section: A Numerical Example and Interpretationmentioning

confidence: 99%

True contextuality beats direct influences in human decision making.

Basieva¹,

Cervantes²,

Dzhafarov³

et al. 2019

Journal of Experimental Psychology: General

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“…Some examples of such systems are: for n = 2, question order effects (Wang & Busemeyer, 2013;Wang, Solloway, Shiffrin, & Busemeyer, 2014); for n = 3, the Suppes-Zanotti (Suppes & Zanotti, 1981), original Bell (1964), and Leggett-Garg (Leggett & Garg, 1985) systems in quantum mechanics, and simple decision making systems in cognition (Asano, Hashimoto, Khrennikov, Ohya, & Tanaka, 2014;Basieva et al, in press); for n = 4, the EPR/Bohm-Bell-CHSH systems (Bell, 1966;Bohm & Aharonov, 1957;Clauser & Horne, 1974;Clauser, Horne, Shimony, & Holt, 1969;Fine, 1982a, b), and decision making and psychophysical systems (Bruza, Kitto, Nelson, & McEvoy, 2009;Bruza, Kitto, Ramm, & Sitbon, 2015;Cervantes & Dzhafarov, 2017; for n = 5, the KCBS system (Klyachko et al, 2008;Lapkiewicz, Li, Schaeff, Langford, Ramelow, Wieśniak, & Zeilinger, 2011); for n > 5, some psychophysical systems . The main theoretical result here is Theorem 1.1 .…”

Section: Dichotomous Random Variablesmentioning

confidence: 99%

True contextuality in a psychophysical experiment

Cervantes

Dzhafarov

2019

Journal of Mathematical Psychology

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Recent crowdsourcing experiments have shown that true contextuality of the kind found in quantum mechanics can also be present in human behavior. In these experiments simple human choices were aggregated over large numbers of respondents, with each respondent dealing with a single context (set of questions asked). In this paper we present experimental evidence of contextuality in individual human behavior, in a psychophysical experiment with repeated presentations of visual stimuli in randomly varying conteXts (arrangements of stimuli). The analysis is based on the Contextuality-by-Default (CbD) theory whose relevant aspects are reviewed in the paper. CbD allows one to detect contextuality in the presence of direct influences, i.e., when responses to the same stimuli have different distributions in different contexts. The experiment presented is also the first one in which contextuality is demonstrated for responses that are not dichotomous, with five options to choose among. CbD requires that random variables representing such responses be dichotomized before they are subjected to contextuality analysis. A theorem says that a system consisting of all possible dichotomizations of responses has to be contextual if these responses violate a certain condition, called nominal dominance. In our experiment nominal dominance was violated in all data sets, with very high statistical reliability established by bootstrapping.

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“…In quantum physics the Leggett-Garg inequality was explored to test compatibility of macroscopic realism with QM. Harald Atmanspacher and Thomas Filk used this inequality [28] to study the problem of bistable perception (see also [88]). …”

Section: Short Review On Various Directions Of Research On Quantum Momentioning

confidence: 99%

Quantum-like modeling of cognition

Khrennikov

2015

Front. Phys.

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This paper begins with a historical review of the mutual influence of physics and psychology, from Freud's invention of psychic energy inspired by von Boltzmann' thermodynamics to the enrichment quantum physics gained from the side of psychology by the notion of complementarity (the invention of Niels Bohr who was inspired by William James), besides we consider the resonance of the correspondence between Wolfgang Pauli and Carl Jung in both physics and psychology. Then we turn to the problem of development of mathematical models for laws of thought starting with Boolean logic and progressing toward foundations of classical probability theory. Interestingly, the laws of classical logic and probability are routinely violated not only by quantum statistical phenomena but by cognitive phenomena as well. This is yet another common feature between quantum physics and psychology. In particular, cognitive data can exhibit a kind of the probabilistic interference effect. This similarity with quantum physics convinced a multi-disciplinary group of scientists (physicists, psychologists, economists, sociologists) to apply the mathematical apparatus of quantum mechanics to modeling of cognition. We illustrate this activity by considering a few concrete phenomena: the order and disjunction effects, recognition of ambiguous figures, categorization-decision making. In Appendix 1 of Supplementary Material we briefly present essentials of theory of contextual probability and a method of representations of contextual probabilities by complex probability amplitudes (solution of the "inverse Born's problem") based on a quantum-like representation algorithm (QLRA).

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Violation of contextual generalization of the Leggett–Garg inequality for recognition of ambiguous figures

Cited by 68 publications

References 54 publications

True contextuality beats direct influences in human decision making.

True contextuality beats direct influences in human decision making.

True contextuality in a psychophysical experiment

Quantum-like modeling of cognition

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