发表机构
Institut de Recherche en Informatique de Toulouse (IRIT); Université de Toulouse; Université Toulouse Capitole（图卢兹计算机科学研究所; 图卢兹大学; 图卢兹第一大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究通过定义破坏性最小支撑集，刻画六种锦标赛解下候选人成为必要失败者或可能获胜者的情形，确定最小支撑集规模并给出计算算法，以解释锦标赛中候选人未被选中的原因。
AI 中文摘要
我们研究的问题是，通过识别子锦标赛中候选人的失利情况（无论锦标赛其余部分如何完成），从形式上解释为何某一候选人未被给定锦标赛规则选中。我们将满足该属性的任意最小子锦标赛定义为破坏性最小支撑集，在形式可解释人工智能中，这对应于对“为何该失败者会输掉锦标赛”这一问题的溯因解释。针对六种常见的锦标赛解（maximin、uncovered set及其加权变体、top-cycle、Copeland、Borda），我们刻画了候选人是必要失败者或可能获胜者的情形，确定了最小破坏性最小支撑集的规模，补充了用于计算这些支撑集的多项式时间算法，仅Borda规则的情况除外，该情况被怀疑为NP完全问题。
英文摘要
We study the problem of formally explaining why a candidate was not selected by a given tournament rule, by identifying sub-tournaments in which the candidate loses independently of how the rest of the tournament is completed. We define destructive minimal supports as any minimal sub-tournament satisfying this property, which in formal explainable artificial intelligence corresponds to abductive explanations for the question "Why does the loser lose the tournament?". For six common tournament solutions (maximin, uncovered set and its weighted variant, top cycle, Copeland, and Borda) we provide characterizations of when a candidate is either a necessary loser or a possible winner, we determine the size of the smallest destructive minimal supports, complemented by polynomial-time algorithms for their computation except for the case of Borda and Copeland rules which we conjecture to also be polynomial.
CommentsThis paper is the extended version of Contet, Grandi, Mengin. Characterizing Necessary Losers to Explain Tournaments Losers. In: Proceedings of the 9th International Conference on Algorithmic Decision Theory (ADT) (2026)
