Weighted Regression with Sybil Networks

TL;DR

This paper introduces a weighted regression method that accounts for suspected Sybil networks by assigning weights based on the probability of observations being controlled by the same user, improving estimation accuracy.

Contribution

It proposes a novel weighted regression framework that incorporates probabilistic weights to handle unknown Sybil network topologies, enhancing treatment effect estimation.

Findings

Reduces standard error by 6-24% in simulated and real blockchain data.

Derives the optimal weight matrix as the inverse of expected network topology.

Demonstrates improved estimation accuracy in the presence of Sybil networks.

Abstract

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%.