Measures of the degree of contextuality and noncontextuality

Many if not all objects of research, be it in psychology, quantum physics, computer science, etc., can be presented by systems of random variables, in which each variable is identified by what it measures (what question it answers) and by contexts, the conditions under which it is recorded. Systems can be contextual and noncontextual, contextuality meaning that contexts force random variables answering the same question to be more dissimilar than they are in isolation. There is a consensus that it is useful to measure degree of contextuality when a system is contextual. Measures of noncontextuality, however, have not been proposed until very recently. We will outline a theory of contextuality measures and noncontextuality measures applied to an important class of systems, called cyclic. Using the example of a cyclic system of rank 2 (the smallest nontrivial system formalizing, e.g., the question order effects in psychology), we explain why measures of noncontextuality are as important as measures of contextuality. Literature: Dzhafarov, E.N., Kujala, J.V., & Cervantes, V.H. (2020). Contextuality and noncontextuality measures and generalized Bell inequalities for cyclic systems. Physical Review A 101:042119. (available as arXiv:1907.03328.) Erratum Note: Physical Review A 101:069902.