On Round-Robin Tournaments with a Unique Maximum Score
Combinatorics
2024-04-17 v5 Probability
Abstract
Richard Arnold Epstein (1927-2016) published the first edition of "The Theory of Gambling and Statistical Logic" in 1967. He introduced some material on round-robin tournaments (complete oriented graphs) with n labeled vertices in Chapter 9; in particular, he stated, without proof, that the probability that there is a unique vertex with the maximum score tends to 1 as n tends to infinity. Our object here is to give a proof of this result along with some historical remarks and comments.
Keywords
Cite
@article{arxiv.2208.14932,
title = {On Round-Robin Tournaments with a Unique Maximum Score},
author = {Yaakov Malinovsky and John W. Moon},
journal= {arXiv preprint arXiv:2208.14932},
year = {2024}
}