Title: Robust Federated Learning with Majority Adversaries via Projection-based Re-weighting. Abstract: Most robust aggregators for distributed or federated learning assume that adversarial clients are the minority in the system. In contrast, this paper considers the majority adversary setting. We first show that a filtering method using a few trusted clients can defend against many standard attacks. However, a new attack called Mimic-Shift can circumvent simple filtering. To this end, we develop a re-weighting strategy that identifies and down-weights the potential adversaries under the majority adversary regime. We show that our aggregator converges to a neighborhood around the optimum under the Mimic-Shift attack. Empirical results further show that our aggregator achieves negligible accuracy loss with a majority of adversarial clients, outperforming strong baselines.