Contextuality and Noncontextuality in Human Choice Behavior

Abstract

The Contextuality-by-Default theory describes the contextual effects on random variables: how the identity of random variables changes from one context to another. Direct influences and true contextuality constitute different types of effects of contexts upon sets of random variables. Changes in the distributions of random variables across contexts define direct influences. True contextuality is defined by the impossibility of sewing all the variables of a system of random variables into a particular overall joint distribution. In the absence of direct influences, the theory specializes to the theory of selective influences in psychology and the traditional treatment of contextuality in quantum mechanics. Consistently connected (i.e., with no direct influences) noncontextual systems are the systems with selective influences. However, observable systems of human behavior are seldom consistently connected. Contextuality-by-Default allows one to classify and measure the degree of deviation from or adherence to the pattern of selective influences, both for consistently and inconsistently connected systems.The papers here included follow the development of the Contextuality-by-Default theory. The theory is presented for cyclic systems of binary random variables, for arbitrary systems of binary random variables, and for systems that include categorical random variables. Although contextuality has been searched for in human behavior since at least the 1990s, I report here the first experiments that have demonstrated contextuality in choice behavior without making the mistake of ignoring the direct influences present in the systems of random variables. A psychophysical experiment was conducted and then analyzed using the theory for systems of binary random variables. Its results showed no contextuality in a double-detection paradigm, that is, in an experiment in which each participant was asked to make dual conjoint judgments of signal detection for two stimuli at a time. Several crowdsourcing experiments wereconducted and analyzed using the theory for cyclic systems of binary random variables. These experiments demonstrate contextuality using a between-subjects experimental design. Among them, the Snow Queen experiment, in which each participant made two conjoint choices in accordance with a simple story line, provided a methodological template (used afterward to design the other crowdsourcing experiments) forsystematically exploring contextuality. Lastly, another psychophysical experiment was conducted and then analyzed using the theory for systems with categorical random variables. This one is the first experiment that demonstrates contextuality in a within-subject design.In addition to the experimental work reported in these papers, I also present the development of the Contextuality-by-Default theory from the theory for cyclic systems to the theory for systems with categorical random variables. The nominal dominance theorem, which states a necessary condition for noncontextuality of systems where all dichotomizations of categorical variables are considered, is the most relevant theoretical result of this development. The role that the notion of contextuality can play in psychology is difficult to fully understand at our present stage of knowledge. Most obviously, contextuality analysis is a generalization of the traditional psychological problem of selective influences. It is, in fact, the only existing theoretical tool for classifying and quantifying patterns of deviations from the hypothesis of selective influences. It is less evident whether the degree of (non)contextuality correlates with specific aspects of behavior that may be of interest. Although some such correlations seem to suggest themselves, to be certain and precise in identifying them, we need to expand our knowledge of the degree of (non)contextuality to a broader class of behavioral systems.