On Contextuality in Behavioral Data

TL;DR

This paper clarifies the relationship between contextuality and connectedness in behavioral data, showing that traditional definitions do not apply due to violations of certain conditions, and extends the understanding using CHSH inequalities.

Contribution

It provides a detailed analysis of how inconsistent connectedness affects the application of contextuality tests in behavioral data, extending the theoretical framework.

Findings

Behavioral data violate the condition of consistent connectedness.

Traditional contextuality definitions do not apply to these data.

Extended definitions clarify the relationship between connectedness and contextuality.

Abstract

Dzhafarov, Zhang, and Kujala (Phil. Trans. Roy. Soc. A 374, 20150099) reviewed several behavioral data sets imitating the formal design of the quantum-mechanical contextuality experiments. The conclusion was that none of these data sets exhibited contextuality if understood in the generalized sense proposed in Dzhafarov, Kujala, and Larsson (Found. Phys. 7, 762-782, 2015), 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-signaling 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 (CHSH) inequalities originally designed for detecting contextuality in entangled particles.