Uniqueness of Maximum Scores in Countable-Outcome Round-Robin Tournaments
Gideon Amir, Yaakov Malinovsky
TL;DR
This paper proves that in countable-outcome round-robin tournaments with equally strong players, the maximum score is asymptotically unique with probability tending to 1. The authors extend the known result for the classical model to the general model $M_{[0,1]}$ by developing tail bounds for top scores, exploiting negative dependence among scores, and applying concentration inequalities to show the absence of top-score ties. The result also includes the finite-outcome family $M_k$ and holds for broad score distributions on [0,1], indicating robustness of the uniqueness phenomenon in large tournaments. The work connects to large-deviation techniques and provides a framework for understanding maximal-score behavior in paired-comparison models.
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 $[0,\,1]$.