AI 中文总结
本研究针对单调联盟排序，探究词典序最优（lex-cel）与L^(1)两种联盟排序解的组合联系，给出其参数向量计算式与最坏情况运行时间，通过模拟验证单调性假设不会造成排序冗余。
AI 中文摘要
近期关于联盟场景下社会排序的研究引入了通过词典序比较个体在按强度排序的联盟中出现次数向量来对个体排序的方法。本研究聚焦于其中两种解：词典序最优（lex-cel）解，其忽略联盟规模；以及L^(1)解，其通过双重词典序比较额外优先考虑较小联盟。我们研究了这两种解在单调联盟排序上的组合联系，其中等价类通过集合包含关系下的最小联盟集紧凑表示。在引入从这些最小联盟计算lex-cel和L^(1)参数向量的通用公式后，我们还给出了最坏情况运行时间结果。最后，为进一步探究两种解的行为，我们设计了评估其生成排序距离的模拟，结果显示单调性假设不会导致两种解生成的排序存在实际冗余。
英文摘要
Recent studies on social rankings in coalitional settings have introduced methods that rank individuals by lexicographically comparing vectors of their occurrences across coalitions ordered according to their strength. In this work, we focus on two such solutions: the lexicographical excellence (lex-cel) solution, which disregards coalition size, and the L^(1) solution, which additionally prioritizes smaller coalitions through a double lexicographic comparison. We investigate the combinatorial connections between these two solutions on monotonic coalitional rankings, where equivalence classes are compactly represented through sets of minimal (with respect to set inclusion) coalitions. After introducing general formulas for computing the lex-cel and L^(1) parameter vectors from these minimal coalitions, we also present worst-case running time results. Finally, to further explore the behavior of the two solutions through simulations designed to assess the distance of the rankings they produce, we show that the monotonicity assumption does not lead to actual redundancy in the rankings produced by the two solutions.
Comments18 pages, 1 figure, slightly modified version to be published in ADT 2026 - 9th International conference on Algorithmic Decision Theory
