Contextuality and Dichotomizations of Random Variables

Foundations of Physics 52 (1):1-25 (2021)
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Abstract

The Contextuality-by-Default approach to determining and measuring the contextuality of a system of random variables requires that every random variable in the system be represented by an equivalent set of dichotomous random variables. In this paper we present general principles that justify the use of dichotomizations and determine their choice. The main idea in choosing dichotomizations is that if the set of possible values of a random variable is endowed with a pre-topology, then the allowable dichotomizations split the space of possible values into two linked subsets. We primarily focus on two types of random variables most often encountered in practice: categorical and real-valued ones. A categorical variable is represented by all of its possible dichotomizations. If the values of a random variable are real numbers, then they are dichotomized by intervals above and below a variable cut point.

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