Making eigenvector-based reputation systems robust to collusion

Eigenvector based methods in general, and Google's PageRank algorithm for rating web pages in particular, have become an important component of information retrieval on the Web. In this paper, we study the efficacy of, and countermeasures for, collusions designed to improve user rating in such systems. We define a metric, called the amplification factor, which captures the amount of PageRank-inflation obtained by a group due to collusions. We prove that the amplification factor can be at most 1/epsilon, where epsilon is the reset probability of the PageRank random walk. We show that colluding nodes (e.g., web-pages) can achieve this amplification and increase their rank significantly in realistic settings; further, several natural schemes to address this problem are demonstrably inadequate. We propose a relatively simple modification to PageRank which renders the algorithm insensitive to such collusion attempts. Our scheme is based on the observation that nodes which cheat do so by "stalling" the random walk in a small portion of the web graph and, hence, their PageRank must be especially sensitive to the reset probability epsilon. We perform exhaustive simulations on the Web graph to demonstrate that our scheme successfully prevents colluding nodes from improving their rank, yielding an algorithm that is robust to gaming.