arXiv 28 Jan 2026 · Statistics — Methodology
arXiv:2601.21036 · PDF · DOI · OpenAlex · Extracted main text
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.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Bradley, Richard C and Tone, Cristina (2017) A central limit theorem for non-stationary strongly mixing random fields | 0.928 | 4 | 3 | 100% |
| 2 | Bojinov, Iavor and Simchi-Levi, David and Zhao, Jinglong (2023) Design and analysis of switchback experiments | 0.811 | 4 | 2 | 100% |
| 3 | Chen, Hongyu and Simchi-Levi, David (2025) Efficient switchback experiments with surrogate variables: Estimation and experimental design | 0.737 | 3 | 2 | 100% |
| 4 | Rio, Emmanuel and others (2017) Asymptotic theory of weakly dependent random processes | 0.737 | 3 | 2 | 100% |
| 5 | Billingsley, Patrick (2013) Convergence of probability measures | 0.644 | 2 | 2 | 100% |
| 6 | Feller, William (1991) An introduction to probability theory and its applications, Volume 2 | 0.644 | 2 | 2 | 100% |
| 7 | Ni, Tu and Bojinov, Iavor (2025) Enhancing Efficiency and Robustness for Switchback Experiments: A Practical Model-assisted Framework | 0.644 | 2 | 2 | 100% |
| 8 | Tang, Yanhan and Li, Andrew and Scheller-Wolf, Alan and Tayur, Sridhar (2025) Multi-armed bandits with endogenous learning curves: an application to split liver transplantation | 0.644 | 2 | 2 | 100% |
| 9 | D. Paulin (2012) Concentration inequalities for Markov chains by Marton couplings and spectral methods | 0.511 | 2 | 1 | 100% |
| 10 | de la Peña, Victor and Giné, Evarist (1999) Decoupling: From Dependence to Independence | 0.511 | 2 | 1 | 100% |
Showing the top 10 of 68 scored citations.