An application of contextuality-by-default in a psychophysical double detection experiment
The Contextuality-by-Default (CbD) theory allows one to separate contextuality from context-dependent errors and violations of selective influences. This makes the theory especially applicable to behavioral systems, where violations of selective influences are ubiquitous. For a system with categorical random variables there is a principled way, using linear programming, to measure the degree of contextuality in this systems. For an especially important special case of cyclic systems with binary random variables, CbD provides necessary and sufficient conditions for (non-)contextuality, and these conditions are known to be breached in certain quantum systems. We apply the contextuality analysis of systems with binary random variables, both cyclic and more general, 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 previously analyzed, indicate lack of contextuality. We conclude that 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.^
Ehtibar N. Dzhafarov, Purdue University.