On the Optimality of Randomization in Experimental Design: How to Randomize for Minimax Variance and Design-Based Inference

Abstract I study the minimax-optimal design for a two-arm controlled experiment where conditional mean outcomes vary in given set and objective is effect-estimation precision. When this permutation symmetric, optimal shown to be complete randomization. Notably, even when has structure (i.e., not symmetric), being precision still requires randomization beyond single partition of units, that is, randomizing identity treatment. A means are linear. Since only targets precision, it may nonetheless ensure sufficient uniformity design-based randomization) inference. therefore propose inference-constrained mixed-strategy as among designs subject sufficient-uniformity constraints.