When ranking goes wrong: fixing spectral methods against biased comparisons

Ranking items from pairwise comparisons (like sports wins/losses) works well in theory when data is uniformly sampled, but breaks down when an adversary selectively amplifies certain matchups. This paper shows spectral algorithms are vulnerable to such bias, but proves you can recover near-optimal accuracy by reweighting edges to restore the graph's spectral properties. Results hold even against semi-random adversaries controlling which comparisons appear.