Perturbation Sensitivity of Maximum-Likelihood Pairwise Ranking in Computational Decision Systems

Evaluation leaderboards such as LMArena play a central role in benchmarking large language models by aggregating pairwise human preferences into model rankings, yet the robustness of these rankings remains poorly understood. We present a unified perturbation framework for analyzing Bradley-Terry leaderboards under structured data modifications using influence-based approximations. Our framework studies three match-level perturbations -- Drop, Add, and Flip -- together with player removal, and evaluates their effects on top-k membership, global ranking consistency via Kendall's tau, and confidence-interval-based uncertainty. Across Chatbot Arena and six additional pairwise-comparison datasets, we show that modern leaderboards are non-robust across all three objectives: sub-1% targeted perturbations can change the top-ranked model, degrade Kendall's tau, and alter confidence intervals. Beyond robustness auditing, we show that the same influence scores enable efficient targeted perturbations, promoting or demoting specific models and reducing target-model uncertainty with fewer actions than previous manipulation and active-sampling baselines. By summarizing these effects with normalized dataset-level robustness scores, our framework provides a practical and helpful tool for auditing leaderboard stability and motivating more robust evaluation protocols.

Multi-task benchmarks have become a central pillar of machine learning research, yet their growing influence has incentivised benchmark gaming -- strategic actions taken to improve the leaderboard rank of a specific model. Treating datasets as voters and models as candidates, we consider benchmark-specific training -- the inclusion of benchmark data in training -- as a form of election manipulation. For any ordinal benchmark, the problem of choosing datasets to train on so that a target model becomes top-ranked corresponds to shift bribery, a class of manipulation problems from computational social choice. Leveraging this identification, we show that the benchmark-specific training problem is NP-hard under Borda count and mean win rate. Complementing this worst-case perspective, we introduce the instance-level robustness, the minimum number of datasets a model developer must include in training to top a given leaderboard, and derive expressions for it under arithmetic mean, median, mean win rate and pairwise majority. We evaluate these expressions on MMLU under HELM and on BIG-Bench Hard (BBH) under the Open LLM Leaderboard. Across both suites, mean win rate is hardest to manipulate: this gap is clear on BBH (24 tasks, 4507 models), where its median robustness is 22 tasks (92%), compared with 13 (54%) under arithmetic mean and 12 (50%) under median and pairwise majority.

Neural Ranking Models (NRMs) are central to modern information retrieval but remain highly vulnerable to adversarial manipulation. Existing attacks often rely on heuristics or surrogate models, limiting effectiveness and transferability. We propose CRAFT, a supervised framework for black-box adversarial rank attacks powered by large language models (LLMs). CRAFT operates in three stages: adversarial dataset generation via retrieval-augmented generation and self-refinement, supervised fine-tuning on curated adversarial examples, and preference-guided optimization to align generations with rank-promotion objectives. Extensive experiments on the MS MARCO passage dataset, TREC Deep Learning 2019, and TREC Deep Learning 2020 benchmarks show that CRAFT significantly outperforms state-of-the-art baselines, achieving higher promotion rates and rank boosts while preserving fluency and semantic fidelity. Moreover, CRAFT transfers effectively across diverse ranking architectures, including cross-encoder, embedding-based, and LLM-based rankers, underscoring vulnerabilities in real-world retrieval systems. This work provides a principled framework for studying adversarial threats in NRMs, underscores the risks of generative AI in rank manipulation, and provides a foundation for developing more robust retrieval systems. To support reproducibility, we publicly release our source code, trained models, and prompt templates.