Testing Contextuality in Cyclic Psychophysical Systems of High Ranks

Contextuality-by-Default (CbD) is a mathematical framework for understanding the role of context in systems with deterministic inputs and random outputs. A necessary and sufficient condition for contextuality was derived for cyclic systems with binary outcomes. In quantum physics, the cyclic systems of ranks n = 5, 4, and 3 are known as systems of Klyachko-type, EPR-Bell-type, and Leggett-Garg-type, respectively. In earlier publications, we examined data collected in various behavioral and social scenarios, from polls of public opinion to our own experiments with psychophysical matching. No evidence of contextuality was found in these data sets. However, those studies were confined to cyclic systems of lower ranks (n ≤ 4). In this paper, contextuality of higher ranks (n = 6, 8) was tested on our data with psychophysical matching, and again, no contextuality was found. This may indicate that many if not all of the seemingly contextual effects observed in behavioral sciences are merely violations of consistent connectedness (selectiveness of influences).