🔎 The Problem Addressed

Matching is a straightforward way to make groups comparable on observed characteristics, but standard matching methods struggle when study designs are complex or samples are very large. A motivating example is a voter mobilization experiment run in Michigan in 2006: scaling the experiment up to the full population of registered voters (6,762,701 observations) with six treatment arms is beyond the capacity of existing matching approaches.

🧭 What the Paper Introduces

A generalization of full matching that handles any number of treatment conditions and complex compositional constraints. Key capabilities include:

• Support for multiple treatment arms (e.g., six or more).

• Accommodation of complex constraints on group composition.

• Practical application to samples of several million units.

⚙️ Performance and Theoretical Guarantees

• The associated algorithm produces near-optimal matchings.

• Worst-case guarantee: the maximum within-group dissimilarity is at most four times the optimal solution.

• Empirical simulations show the algorithm typically comes considerably closer to optimal than the worst-case bound.

• Computational efficiency: terminates in linearithmic time (n log n) while using linear space, keeping memory demands low and runtime fast.

📌 Why This Matters

This method makes it feasible to construct well-performing matchings for large, complex studies—turning problems that were previously intractable into analyses that can be completed in minutes. The approach thus opens the door to causal comparisons in massive experiments (such as the scaled Michigan voter mobilization example) that conventional matching techniques cannot handle.