Problem
Research questions and friction points this paper is trying to address.
tournament
loser
explanation
sub-tournaments
necessary losers
Characterizing Necessary Losers to Explain Tournaments Losers
🤖 AI Summary
研究通过识别子锦标赛来解释为何候选人在特定比赛规则下未被选中，定义了破坏性最小支持，并为六种常见比赛解决方案提供了必要失败者或可能胜利者的特征。
📝 Abstract
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-tournaments satisfying this property, which in formal explainable artificial intelligence correspond 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 the Borda rule which is suspected to be NP-complete.
Innovation
Methods, ideas, or system contributions that make the work stand out.
destructive minimal supports
formal explainable artificial intelligence
tournament solutions
polynomial-time algorithms
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