On negative dependence inequalities and maximal scores in round-robin tournaments

TL;DR

This paper extends a classical inequality to negative dependent scores in round-robin tournaments, leading to broader convergence results for the maximum scores in such competitions.

Contribution

It generalizes Huber's inequality for negative dependence, enabling more comprehensive analysis of maximum scores in round-robin tournaments.

Findings

Extended Huber's inequality for negative dependence

Proved convergence in probability of maximal scores

Applicable to more general tournament settings

Abstract

We extend Huber's (1963) inequality for the joint distribution function of negative dependent scores in round-robin tournaments. As a byproduct, this extension implies convergence in probability of the maximal score in round-robin tournaments in a more general setting.