Order-distance and other metric-like functions on jointly distributed random variables

Abstract

We construct a class of real-valued nonnegative binary functions on a set of jointly distributed random variables, which satisfy the triangle inequality and vanish at identical arguments (pseudo-quasi-metrics). These functions are useful in dealing with the problem of selective probabilistic causality encountered in behavioral sciences and in quantum physics. The problem reduces to that of ascertaining the existence of a joint distribution for a set of variables with known distributions of certain subsets of this set. Any violation of the triangle inequality or its consequences by one of our functions when applied to such a set rules out the existence of this joint distribution. We focus on an especially versatile and widely applicable pseudo-quasi-metric called an order-distance and its special case called a classification distance.

14 pages, to appear in Proc. Amer. Math. Soc

Cited by in corpus (9)

• Contextuality is About Identity of Random Variables
• Contextuality in Three Types of Quantum-Mechanical Systems
• All-Possible-Couplings Approach to Measuring Probabilistic Context
• Embedding Quantum into Classical: Contextualization vs Conditionalization
• No-Forcing and No-Matching Theorems for Classical Probability Applied to Quantum Mechanics
• Generalizing Bell-type and Leggett-Garg-type Inequalities to Systems with Signaling
• Bell Inequalities for Continuously Emitting Sources
• Quantum Entanglement and the Issue of Selective Influences in Psychology: An Overview
• Noncontextuality with Marginal Selectivity in Reconstructing Mental Architectures