  Rank aggregation with pairwise comparisons is widely encountered in
sociology, politics, economics, psychology, sports, etc . Given the enormous
social impact and the consequent incentives, the potential adversary has a
strong motivation to manipulate the ranking list. However, the ideal attack
opportunity and the excessive adversarial capability cause the existing methods
to be impractical. To fully explore the potential risks, we leverage an online
attack on the vulnerable data collection process. Since it is independent of
rank aggregation and lacks effective protection mechanisms, we disrupt the data
collection process by fabricating pairwise comparisons without knowledge of the
future data or the true distribution. From the game-theoretic perspective, the
confrontation scenario between the online manipulator and the ranker who takes
control of the original data source is formulated as a distributionally robust
game that deals with the uncertainty of knowledge. Then we demonstrate that the
equilibrium in the above game is potentially favorable to the adversary by
analyzing the vulnerability of the sampling algorithms such as Bernoulli and
reservoir methods. According to the above theoretical analysis, different
sequential manipulation policies are proposed under a Bayesian decision
framework and a large class of parametric pairwise comparison models. For
attackers with complete knowledge, we establish the asymptotic optimality of
the proposed policies. To increase the success rate of the sequential
manipulation with incomplete knowledge, a distributionally robust estimator,
which replaces the maximum likelihood estimation in a saddle point problem,
provides a conservative data generation solution. Finally, the corroborating
empirical evidence shows that the proposed method manipulates the results of
rank aggregation methods in a sequential manner.
