  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.
