On the cycle-transitive comparison of artificially coupled random variables

Given a collection of random variables, we build a probabilistic relation that, in the case of continuous random variables, expresses for each couple of random variables the probability that the first one takes a greater value than the second one. In order to compute this probability, the random variables are artificially coupled by means of a fixed commutative copula. The main result of this paper pertains to the transitivity of this probabilistic relation. Provided the commutative copula satisfies some additional condition, this transitivity can be described elegantly within the cycle-transitivity framework. It ranges between two known types of transitivity: TL-transitivity and partial stochastic transitivity.