Experimental Design for Matching
匹配机制的实验设计AI 解读 ↓
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分类依据与纠错
AI 根据所提供的论文材料归类：摘要研究随机实验的设计与估计，并以匹配干扰和图上的路径、环结构为核心。
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匹配机制的实验设计
- 研究问题
- 在一个匹配中的分配会排斥另一个匹配分配的情况下，如何通过随机实验比较有限总体上的两个预先确定的匹配方案？
- 方法与思路
- 作者将匹配方案的差异集合分解为交替路径和环，沿其序贯随机化，并在极小极大框架下优化条件随机化概率。
- 材料陈述的贡献
- 摘要称设计支持无偏的 Horvitz–Thompson 估计及有限总体中心极限定理，并利用图论分解将结果扩展至多对一匹配。
- 阅读关注点
- 应核对比较目标、匹配干扰的形式、路径与环上的随机化规则，以及中心极限定理和多对一扩展所需的结构条件。
- 阅读边界
- 这是 arXiv 预印本，同行评审或期刊接收未核实；摘要未列出渐近条件，长路径上的最优概率也不能直接推广至所有结构。
原文摘要
Matching mechanisms play a central role in operations management across diverse fields including education, healthcare, and online platforms. However, experimentally comparing a new matching algorithm against a status quo presents some fundamental challenges due to matching interference, where assigning a unit in one matching may preclude its assignment in the other. In this work, we take a design-based perspective to study the design of randomized experiments to compare two predetermined matching plans on a finite population, without imposing outcome or behavioral models. We introduce the notation of a disagreement set, which captures the difference between the two matching plans, and show that it admits a unique decomposition into disjoint alternating paths and cycles with useful structural properties. Based on these properties, we propose the Alternating Path Randomized Design, which sequentially randomizes along these paths and cycles to effectively manage interference. Within a minimax framework, we optimize the conditional randomization probability and show that, for long paths, the optimal choice converges to $\sqrt{2}-1$, minimizing worst-case variance. We establish the unbiasedness of the Horvitz-Thompson estimator and derive a finite-population Central Limit Theorem that accommodates complex and unstable path and cycle structures as the population grows. Furthermore, we extend the design to many-to-one matchings, where capacity constraints fundamentally alter the structure of the disagreement set. Using graph-theoretic tools, including finding augmenting paths and Euler-tour decomposition on an auxiliary unbalanced directed graph, we construct feasible alternating path and cycle decompositions that allow the design and inference results to carry over.