Weighted Regression with Sybil Networks

In many online domains, Sybil networks -- or cases where a single user assumes multiple identities -- is a pervasive feature. This complicates experiments, as off-the-shelf regression estimators at least assume known network topologies (if not fully independent observations) when Sybil network topologies in practice are often unknown. The literature has exclusively focused on techniques to detect Sybil networks, leading many experimenters to subsequently exclude suspected networks entirely before estimating treatment effects. I present a more efficient solution in the presence of these suspected Sybil networks: a weighted regression framework that applies weights based on the probabilities that sets of observations are controlled by single actors. I show in the paper that the MSE-minimizing solution is to set the weight matrix equal to the inverse of the expected network topology. I demonstrate the methodology on simulated data, and then I apply the technique to a competition with suspected Sybil networks run on the Sui blockchain and show reductions in the standard error of the estimate by 6 - 24%.