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Testing Contextuality in Cyclic Psychophysical Systems of High Ranks

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Quantum Interaction (QI 2016)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10106))

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Abstract

Contextuality-by-Default (CbD) is a mathematical framework for understanding the role of context in systems with deterministic inputs and random outputs. A necessary and sufficient condition for contextuality was derived for cyclic systems with binary outcomes. In quantum physics, the cyclic systems of ranks \(n=\) 5, 4, and 3 are known as systems of Klyachko-type, EPR-Bell-type, and Leggett-Garg-type, respectively. In earlier publications, we examined data collected in various behavioral and social scenarios, from polls of public opinion to our own experiments with psychophysical matching. No evidence of contextuality was found in these data sets. However, those studies were confined to cyclic systems of lower ranks (\(n\le 4\)). In this paper, contextuality of higher ranks (\(n=6,8\)) was tested on our data with psychophysical matching, and again, no contextuality was found. This may indicate that many if not all of the seemingly contextual effects observed in behavioral sciences are merely violations of consistent connectedness (selectiveness of influences).

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Acknowledgments

This research has been supported by NSF grant SES-1155956, AFOSR grant FA9550-14-1-0318.

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Authors and Affiliations

  1. Purdue University, West Lafayette, USA

    Ru Zhang & Ehtibar N. Dzhafarov

  2. Indiana University, Bloomington, USA

    Ru Zhang

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  1. Ru Zhang
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  2. Ehtibar N. Dzhafarov
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Correspondence to Ru Zhang .

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Editors and Affiliations

  1. San Francisco State University, San Francisco, California, USA

    Jose Acacio de Barros

  2. University of Oxford, Oxford, United Kingdom

    Bob Coecke

  3. City University of London, London, United Kingdom

    Emmanuel Pothos

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Zhang, R., Dzhafarov, E.N. (2017). Testing Contextuality in Cyclic Psychophysical Systems of High Ranks. In: de Barros, J., Coecke, B., Pothos, E. (eds) Quantum Interaction. QI 2016. Lecture Notes in Computer Science(), vol 10106. Springer, Cham. https://doi.org/10.1007/978-3-319-52289-0_12

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  • DOI: https://doi.org/10.1007/978-3-319-52289-0_12

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  • Online ISBN: 978-3-319-52289-0

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