A constructive method to minimize couple matchings

TL;DR

This paper introduces a constructive approach to minimize couple matchings by using indeterminacy coupling, which reduces the expected number of consecutive equal pairs, and explores its properties and implications.

Contribution

It presents a novel constructive method for indeterminacy coupling, offering an alternative to independence coupling and analyzing its effect on couple matchings.

Findings

Indeterminacy coupling reduces expected consecutive matchings.

The Janson Vegelius coefficient measures deviation from indeterminacy.

As modalities increase, the coefficient tends to zero.

Abstract

This paper provides constructive procedures for the indeterminacy coupling between two marginal distributions, an alternative to independence coupling. It also introduces a drawing under indeterminacy into a mixture of three independent couplings. Leveraging on this decomposition it states that indeterminacy optimally reduces couple matchings, minimizing the expected number of equal couples drawn in a row. Besides it is seen that the Janson Vegelius coefficient is nothing but a deviation to indeterminacy and it is shown that it tends to 0 when the number of modalities increases.