  When the Stable Unit Treatment Value Assumption (SUTVA) is violated and there
is interference among units, there is not a uniquely defined Average Treatment
Effect (ATE), and alternative estimands may be of interest, among them average
unit-level differences in outcomes under different homogeneous treatment
policies. We term this target the Homogeneous Assignment Average Treatment
Effect (HAATE). We consider approaches to experimental design with multiple
treatment conditions under partial interference and, given the estimand of
interest, we show that difference-in-means estimators may perform better than
correctly specified regression models in finite samples on root mean squared
error (RMSE). With errors correlated at the cluster level, we demonstrate that
two-stage randomization procedures with intra-cluster correlation of treatment
strictly between zero and one may dominate one-stage randomization designs on
the same metric. Simulations demonstrate performance of this approach; an
application to online experiments at Facebook is discussed.
