AI 中文总结
该研究证明效率调整延期接受（EADA）机制及所有弱帕累托占优于延期接受（DA）的帕累托有效机制，可将匹配市场中学生期望平均排名的渐近阶从对数阶降至双对数阶，突破了DA的对数排名壁垒。
AI 中文摘要
我们研究了独立同分布匹配市场中效率调整延期接受（EADA）机制实现的期望平均排名。由学生提议的延期接受（DA）机制为学生提供的期望平均排名为对数阶，而我们证明EADA的期望平均排名至多为$4\log\log n+O(1)$，因此EADA改进了学生分配的渐近阶。以更弱的界$O((\log\log n)^2)$为代价，我们将该结论扩展到更大一类机制：每个弱帕累托占优于DA的帕累托有效机制都突破了DA的对数壁垒。这些是关于EADA及更广泛的DA帕累托有效改进类的期望平均排名的首批渐近保证，结论可扩展到有界配额的多对一市场和偏好相关的随机市场。
英文摘要
We study the expected average rank achieved by the Efficiency-Adjusted Deferred Acceptance (EADA) mechanism in i.i.d.\ matching markets. While student-proposing Deferred Acceptance gives students an expected average rank of logarithmic order, we prove that EADA's expected average rank is at most $4\log\log n+O(1)$. Therefore, EADA improves the asymptotic order of students' assignments. At the cost of a weaker bound, $O((\log\log n)^2)$, we extend this conclusion to a much larger class of mechanisms. Namely, every Pareto-efficient mechanism that weakly Pareto-dominates DA breaks DA's logarithmic barrier. These are the first asymptotic guarantees for the expected average rank of EADA and of the broader class of Pareto-efficient improvements of DA. The conclusions extend to many-to-one markets with bounded quotas and random markets with correlated preferences.
