Orthogonal Arrays are a powerful class of experimental designs that has been widely used to determine efficient arrangements of treatment factors in randomized controlled trials. Despite its popularity, the method is seldom used in social sciences. Social experiments must cope with randomization compromises such as noncompliance that often prevents the use of elaborate designs. We present a novel application of orthogonal designs that addresses the particular challenges arising in social experiments. We characterize the identification of counterfactual variables as a finite mixture problem in which choice incentives, rather than treatment factors, are randomly assigned. We show that the causal inference generated by an orthogonal array of incentives greatly outperforms a traditional design.