Explaining Tournament Solutions with Minimal Supports

Explainability can be achieved through minimal evidence: The paper demonstrates that for most common decision-making rules in tournaments (competitions with pairwise matchups), researchers can identify the smallest possible subset of comparisons needed to guarantee a winner—providing "certified explanations" for why someone won, rather than just stating the outcome.

Different rules require different amounts of explanation: The complexity of explaining a decision varies significantly depending on which tournament rule is used. For most rules studied (top cycle, uncovered set, Copeland, Borda, and maximin), explanations can be computed efficiently, but for the weighted uncovered set rule, finding minimal explanations becomes computationally difficult—a finding relevant to choosing explainable decision-making systems in practice.

Minimal explanations are more trustworthy and practical: By identifying the smallest sub-set of relevant information needed to justify a winner, this approach produces "compact, certified, and intuitive explanations"—meaning stakeholders can verify the reasoning is sound and understand it without being overwhelmed by irrelevant details, which is crucial for responsible AI deployment in high-stakes decisions.

This framework applies broadly to real-world ranking problems: Since tournaments model any situation involving pairwise comparisons between options (hiring candidates, ranking alternatives, evaluating teams), these explainability methods could improve transparency in diverse decision-making contexts where people need to understand why one option was chosen over others.