Pairwise ranking systems based on Maximum Likelihood Estimation (MLE), such as the Bradley-Terry model, are widely used to aggregate preferences from pairwise comparisons. However, their robustness under strategic data manipulation remains insufficiently understood. In this paper, we study the vulnerability of MLE-based ranking systems to adversarial perturbations. We formulate the manipulation task as a constrained combinatorial optimization problem and propose an Adaptive Subset Selection Attack (ASSA) to efficiently identify high-impact perturbations. Experimental results on both synthetic data and real-world election datasets show that MLE-based rankings exhibit a sharp phase-transition behavior: beyond a small perturbation budget, a limited number of strategic voters can significantly alter the global ranking. In particular, our method consistently outperforms random and greedy baselines under constrained budgets. These findings reveal a fundamental sensitivity of MLE-based ranking mechanisms to structured perturbations and highlight the need for more robust aggregation methods in collective decision-making systems.

翻译：基于极大似然估计（MLE）的成对排名系统（如Bradley-Terry模型）被广泛用于从成对比较中聚合偏好。然而，这些系统在策略性数据操纵下的鲁棒性尚未得到充分理解。本文研究了基于MLE的排名系统对抗性扰动的脆弱性。我们将操纵任务建模为带约束的组合优化问题，并提出一种自适应子集选择攻击（ASSA）方法，以高效识别高影响力的扰动。在合成数据和真实选举数据集上的实验结果表明，基于MLE的排名呈现尖锐的相变行为：当扰动预算超过临界值时，少量策略性投票者即可显著改变全局排名。值得注意的是，在有限预算约束下，我们的方法始终优于随机和贪婪基线方法。这些发现揭示了基于MLE的排名机制对结构化扰动存在根本敏感性，凸显了在集体决策系统中开发更鲁棒聚合方法的必要性。