On contextuality in behavioural data

Ehtibar N Dzhafarov; Janne V Kujala; Víctor H Cervantes; Ru Zhang; Matt Jones

doi:10.1098/rsta.2015.0234

On contextuality in behavioural data

Philos Trans A Math Phys Eng Sci. 2016 May 28;374(2068):20150234. doi: 10.1098/rsta.2015.0234.

Authors

Ehtibar N Dzhafarov¹, Janne V Kujala², Víctor H Cervantes³, Ru Zhang³, Matt Jones⁴

Affiliations

¹ Department of Psychological Sciences, Purdue University, West Lafayette, IN, USA ehtibar@purdue.edu.
² Department of Mathematical Information Technology, University of Jyväskylä, Jyväskylä, Finland.
³ Department of Psychological Sciences, Purdue University, West Lafayette, IN, USA.
⁴ Department of Psychology and Neuroscience, University of Colorado, Boulder, CO, USA.

Abstract

Dzhafarovet al.(Dzhafarovet al.2016Phil. Trans. R. Soc. A374, 20150099. (doi:10.1098/rsta.2015.0099)) reviewed several behavioural datasets imitating the formal design of the quantum-mechanical contextuality experiments. The conclusion was that none of these datasets exhibited contextuality if understood in the generalized sense proposed by Dzhafarovet al.(2015Found. Phys.7, 762-782. (doi:10.1007/s10701-015-9882-9)), while the traditional definition of contextuality does not apply to these data because they violate the condition of consistent connectedness (also known as marginal selectivity, no-signalling condition, no-disturbance principle, etc.). In this paper, we clarify the relationship between (in)consistent connectedness and (non)contextuality, as well as between the traditional and extended definitions of (non)contextuality, using as an example the Clauser-Horn-Shimony-Holt inequalities originally designed for detecting contextuality in entangled particles.

Keywords: consistent connectedness; contextuality; cyclic systems.

Publication types

Research Support, Non-U.S. Gov't
Research Support, U.S. Gov't, Non-P.H.S.