Uniqueness of Maximum Scores in Countable-Outcome Round-Robin Tournaments

TL;DR

This paper extends a recent result to show that in general round-robin tournaments with equally strong players and scores in [0,1], the maximum score is uniquely determined, ensuring a clear winner.

Contribution

It generalizes the uniqueness of maximum scores to broader tournament models with continuous score values and equal player strength.

Findings

Maximum score is unique in generalized models

Scores are within the [0,1] interval

Results apply to equally strong players

Abstract

In this note, we extend a recent result on the uniqueness of the maximum score in a classical round-robin tournament to general round-robin tournament models with equally strong players, where the scores take values in $[0,\,1]$.