Designing Multi-Arm Experiments for Global Average Treatment Effects Under Partial Interference
When interference is present, a unit's outcome depends on others' assignments and there is generally no single, design-free average treatment effect. We study settings where the decision problem is to choose among several alternative uniform policies---e.g., rolling out one platform configuration to all users, or one policy to all constituents---so the estimand of interest is the Global Average Treatment Effect (GATE), the average outcome difference under two uniform (global) policies. Under partial interference with clusters, cluster-level randomization identifies the GATE but can be statistically inefficient, while unit-level randomization can be highly precise yet biased for the GATE. We propose a continuum of implementable two-stage randomization designs that smoothly interpolate between these extremes by tuning within-cluster treatment correlation. For multi-arm experiments, we operationalize this continuum via a Dirichlet--multinomial design and give a pilot- and model-assisted procedure for selecting the design parameter using estimated finite-sample RMSE for the GATE. We also show that, even under a correctly specified linear interference model, difference-in-means estimators can have lower RMSE than least squares regression for GATE targets.Simulations and a large-scale Facebook video-player configuration experiment (43 million user sessions) illustrate the practical trade-off: intermediate designs can substantially reduce RMSE for estimating global rollout effects while remaining straightforward to deploy at scale.