# How Hard is it to Rig a Benchmark? A Social Choice Analysis of Leaderboard Robustness

arXiv: https://arxiv.org/abs/2605.23628 · HTML: https://mlsanity.com/paper/2605.23628/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 40 of its 67 references that are in the map.
- First posted on arXiv 22 May 2026.

## Builds on (most cited first, 30 of 40)

- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [GLUE: A Multi-Task Benchmark and Analysis Platform for Natural Language Understanding](https://mlsanity.com/paper/1804.07461/) (2018)
- [Beyond the Imitation Game: Quantifying and extrapolating the capabilities of language models](https://mlsanity.com/paper/2206.04615/) (2022)
- [Challenging BIG-Bench Tasks and Whether Chain-of-Thought Can Solve Them](https://mlsanity.com/paper/2210.09261/) (2022)
- [SuperGLUE: A Stickier Benchmark for General-Purpose Language Understanding Systems](https://mlsanity.com/paper/1905.00537/) (2019)
- [A Survey on Evaluation of Large Language Models](https://mlsanity.com/paper/2307.03109/) (2023)
- [Deep Reinforcement Learning at the Edge of the Statistical Precipice](https://mlsanity.com/paper/2108.13264/) (2021)
- [Dynabench: Rethinking Benchmarking in NLP](https://mlsanity.com/paper/2104.14337/) (2021)
- [NLP Evaluation in trouble: On the Need to Measure LLM Data Contamination for each Benchmark](https://mlsanity.com/paper/2310.18018/) (2023)
- [Strategic Classification](https://mlsanity.com/paper/1506.06980/) (2015)
- [Data Contamination: From Memorization to Exploitation](https://mlsanity.com/paper/2203.08242/) (2022)
- [Rethinking Benchmark and Contamination for Language Models with Rephrased Samples](https://mlsanity.com/paper/2311.04850/) (2023)
- [Investigating Data Contamination in Modern Benchmarks for Large Language Models](https://mlsanity.com/paper/2311.09783/) (2023)
- [The Benchmark Lottery](https://mlsanity.com/paper/2107.07002/) (2021)
- [Generalization or Memorization: Data Contamination and Trustworthy Evaluation for Large Language Models](https://mlsanity.com/paper/2402.15938/) (2024)
- [Investigating Data Contamination for Pre-training Language Models](https://mlsanity.com/paper/2401.06059/) (2024)
- [Generalization in Adaptive Data Analysis and Holdout Reuse](https://mlsanity.com/paper/1506.02629/) (2015)
- [The Ladder: A Reliable Leaderboard for Machine Learning Competitions](https://mlsanity.com/paper/1502.04585/) (2015)
- [Leakage and the Reproducibility Crisis in ML-based Science](https://mlsanity.com/paper/2207.07048/) (2022)
- [Data Contamination Through the Lens of Time](https://mlsanity.com/paper/2310.10628/) (2023)
- [A Survey on Large Language Model Benchmarks](https://mlsanity.com/paper/2508.15361/) (2025)
- [Training on the Test Task Confounds Evaluation and Emergence](https://mlsanity.com/paper/2407.07890/) (2024)
- [Better than Average: Paired Evaluation of NLP Systems](https://mlsanity.com/paper/2110.10746/) (2021)
- [JuStRank: Benchmarking LLM Judges for System Ranking](https://mlsanity.com/paper/2412.09569/) (2024)
- [Inherent Trade-Offs between Diversity and Stability in Multi-Task Benchmarks](https://mlsanity.com/paper/2405.01719/) (2024)
- [Training on the Benchmark Is Not All You Need](https://mlsanity.com/paper/2409.01790/) (2024)
- [How Robust are Model Rankings: A Leaderboard Customization Approach for Equitable Evaluation](https://mlsanity.com/paper/2106.05532/) (2021)
- [Vote'n'Rank: Revision of Benchmarking with Social Choice Theory](https://mlsanity.com/paper/2210.05769/) (2022)
- [Towards More Robust NLP System Evaluation: Handling Missing Scores in Benchmarks](https://mlsanity.com/paper/2305.10284/) (2023)
- [The Benchmarking Epistemology: Validity Theory for Evaluating Machine Learning Models](https://mlsanity.com/paper/2510.23191/) (2025)

## Built on by (most cited first, 1 of 1)

- [TARE: Weigh a Never-Poisoned Twin Before Reading Backdoor-Defense Costs](https://mlsanity.com/paper/2610.06994/) (2026)

## Abstract (arXiv)

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.