  This paper considers the estimation of treatment effects in randomized
experiments with complex experimental designs, including cases with
interference between units. We develop a design-based estimation theory for
arbitrary experimental designs. Our theory facilitates the analysis of many
design-estimator pairs that researchers commonly employ in practice and provide
procedures to consistently estimate asymptotic variance bounds. We propose new
classes of estimators with favorable asymptotic properties from a design-based
point of view. In addition, we propose a scalar measure of experimental
complexity which can be linked to the design-based variance of the estimators.
We demonstrate the performance of our estimators using simulated datasets based
on an actual network experiment studying the effect of social networks on
insurance adoptions.
