Testing Contextuality in Cyclic Psychophysical Systems of High Ranks

TL;DR

This paper applies the Contextuality-by-Default theory to a psychophysical experiment involving double detection, finding no evidence of contextuality but highlighting influence of context on response distributions.

Contribution

It extends the application of cyclic system contextuality analysis to behavioral data, demonstrating the theory's relevance beyond quantum systems.

Findings

No evidence of contextuality in the psychophysical system

Context influences response distributions without indicating contextuality

The role of context is limited to lack of selectiveness

Abstract

The Contextuality-by-Default (CbD) theory allows one to separate contextuality from context-dependent errors and violations of selective influences (aka "no-signaling" or "no-disturbance" principles). This makes the theory especially applicable to behavioral systems, where violations of selective influences are ubiquitous. For cyclic systems with binary random variables, CbD provides necessary and sufficient conditions for noncontextuality, and these conditions are known to be breached in certain quantum systems. We apply the theory of cyclic systems to a psychophysical double-detection experiment, in which observers were asked to determine presence or absence of a signal property in each of two simultaneously presented stimuli. The results, as in all other behavioral and social systems previous analyzed, indicate lack of contextuality. The role of context in double-detection is confined to lack of selectiveness: the distribution of responses to one of the stimuli is influenced by the state of the other stimulus.