Byzantine Spectral Ranking

TL;DR

This paper introduces a robust spectral ranking algorithm designed to accurately aggregate pairwise comparisons in the presence of malicious Byzantine voters, outperforming existing methods under adversarial conditions.

Contribution

The paper proposes the Byzantine Spectral Ranking Algorithm, which remains reliable when the number of good voters exceeds Byzantine voters, addressing a key vulnerability in existing spectral ranking methods.

Findings

The Rank-Centrality algorithm fails under adversarial Byzantine attacks.

The Byzantine Spectral Ranking Algorithm is robust when good voters outnumber Byzantine voters.

Experimental results confirm the algorithm's effectiveness on synthetic and real data.

Abstract

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.