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.

翻译：匹配机制在教育、医疗和在线平台等不同领域的运营管理中发挥着核心作用。然而，由于匹配干扰的存在，实验性地比较新匹配算法与现状算法面临一些根本性挑战——在一个匹配中分配某个单元可能会阻止其在另一个匹配中被分配。在本研究中，我们采用基于设计的视角，研究在有限总体中比较两个预定匹配方案的随机实验设计，而不施加结果或行为模型。我们引入了分歧集的概念，用以捕捉两个匹配方案之间的差异，并证明其可唯一分解为具有有用结构特性的不相交交替路径和循环。基于这些特性，我们提出了交替路径随机设计，该设计沿着这些路径和循环顺序进行随机化，以有效管理干扰。在极小极大框架下，我们优化了条件随机化概率，并证明对于长路径，最优选择收敛于 $\sqrt{2}-1$，从而最小化最坏情况方差。我们建立了霍维茨-汤普森估计量的无偏性，并推导出一个有限总体中心极限定理，该定理在总体增长时能适应复杂且不稳定的路径和循环结构。此外，我们将该设计扩展到多对一匹配，其中容量约束从根本上改变了分歧集的结构。利用图论工具，包括在辅助的非平衡有向图上寻找增广路径和欧拉回路分解，我们构建了可行的交替路径和循环分解，从而使设计和推断结果得以延续。