A hierarchical approach to measuring contextuality

Many systems in which contextuality is studied have in common that their (non)contextuality is determined by particular configurations of pairwise correlations. Such systems are used to describe the question order effect in psychology, the Einstein-Podolsky-Rosen-Bohm paradigm in quantum physics, and many other situations. The prominence of pairwise correlations leads one to the incorrect intuitive idea that all contextuality appears on the level of pairwise associations, perhaps even only within cyclic subsystems. We present a new, hierarchical measure of (non)contextuality in which contextuality may arise at the level of pairwise, triple, quadruple, etc. associations of random variables. This measure allows one to look at (non)contextuality as varying not only in degree but also in pattern.