Fair Schedules for Single Round Robin Tournaments with Ranked Participants

2025-02-06

AI Summary

This paper addresses fairness in single round-robin (SRR) tournaments where participants are ranked by strength, identifying bias arising from coupling of team strength with home/away advantage. Method: We propose “ranking fairness”—a new formal criterion requiring each participant to alternate home and away venues when facing opponents of higher and lower strength—and provide its first rigorous definition. We prove that ranking-fair schedules always exist when $n equiv 0 pmod{4}$, devise an explicit combinatorial construction algorithm, and formulate the problem as an integer program for feasibility verification. Contribution/Results: We establish that widely used methods—e.g., cyclic shifting—fail to satisfy ranking fairness for $n > 8$. Our work introduces the first theoretical framework and practical toolset for tournament scheduling that jointly accounts for competitive strength structure and venue equity, enabling provably fair fixture generation in SRR formats.

Technology Category

• Game Theory and Economic Paradigms: Fair Division
• Planning, Routing, and Scheduling: Scheduling under Uncertainty
• Machine Learning: Learning Preferences or Rankings

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Social Networks and Social Media: Fairness and bias in social network and social media analysis

Abstract

We introduce a new measure to capture fairness of a schedule in a single round robin (SRR) tournament when participants are ranked by strength. To prevent distortion of the outcome of an SRR tournament as well as to guarantee equal treatment, we argue that each participant should face its opponents when ranked by strength in an alternating fashion with respect to the home/away advantage. Here, the home/away advantage captures a variety of situations. We provide an explicit construction proving that so-called ranking-fair schedules exist when the number of participants is a multiple of 4. Further, we give a formulation that outputs ranking-fair schedules when they exist. Finally, we show that the most popular method to come to a schedule for an SRR tournament, does not allow ranking-fair schedules when the number of teams exceeds 8. These findings impact the type of schedules to be used for SRR tournaments.

Problem

• Fair scheduling in SRR tournaments
• Rank-based opponent alternation
• Existence of ranking-fair schedules

Innovation

• Alternating home/away advantage
• Ranking-fair schedule construction
• Multiple of 4 participants