Byzantine Spectral Ranking
This addresses the robustness of ranking systems in adversarial environments, such as online platforms, by providing a method resilient to malicious attacks, though it is incremental as it builds on existing spectral ranking techniques.
The paper tackles the problem of rank aggregation in an adversarial setting where malicious Byzantine voters aim to deteriorate rankings, showing that the popular Rank-Centrality algorithm fails with a small constant fraction of Byzantine voters, and introduces the Byzantine Spectral Ranking Algorithm that produces reliable rankings when good voters outnumber Byzantine ones, supported by theoretical and experimental results.
We study the problem of rank aggregation where the goal is to obtain a global ranking by aggregating pair-wise comparisons of voters over a set of items. We consider an adversarial setting where the voters are partitioned into two sets. The first set votes in a stochastic manner according to the popular score-based Bradley-Terry-Luce (BTL) model for pairwise comparisons. The second set comprises malicious Byzantine voters trying to deteriorate the ranking. We consider a strongly-adversarial scenario where the Byzantine voters know the BTL scores, the votes of the good voters, the algorithm, and can collude with each other. We first show that the popular spectral ranking based Rank-Centrality algorithm, though optimal for the BTL model, does not perform well even when a small constant fraction of the voters are Byzantine. We introduce the Byzantine Spectral Ranking Algorithm (and a faster variant of it), which produces a reliable ranking when the number of good voters exceeds the number of Byzantine voters. We show that no algorithm can produce a satisfactory ranking with probability > 1/2 for all BTL weights when there are more Byzantine voters than good voters, showing that our algorithm works for all possible population fractions. We support our theoretical results with experimental results on synthetic and real datasets to demonstrate the failure of the Rank-Centrality algorithm under several adversarial scenarios and how the proposed Byzantine Spectral Ranking algorithm is robust in obtaining good rankings.