# Agreement Overstates Evidence: Error Dependence in LLM Judge Consensus

arXiv: https://arxiv.org/abs/2609.22512 · HTML: https://mlsanity.com/paper/2609.22512/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 28 references that are in the map.
- First posted on arXiv 18 Sep 2026.

## Builds on (most cited first, 22 of 22)

- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [Judging LLM-as-a-Judge with MT-Bench and Chatbot Arena](https://mlsanity.com/paper/2306.05685/) (2023)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [Deep reinforcement learning from human preferences](https://mlsanity.com/paper/1706.03741/) (2017)
- [Large Language Models are not Fair Evaluators](https://mlsanity.com/paper/2305.17926/) (2023)
- [A General Theoretical Paradigm to Understand Learning from Human Preferences](https://mlsanity.com/paper/2310.12036/) (2023)
- [BeaverTails: Towards Improved Safety Alignment of LLM via a Human-Preference Dataset](https://mlsanity.com/paper/2307.04657/) (2023)
- [RewardBench: Evaluating Reward Models for Language Modeling](https://mlsanity.com/paper/2403.13787/) (2024)
- [UltraFeedback: Boosting Language Models with Scaled AI Feedback](https://mlsanity.com/paper/2310.01377/) (2023)
- [KTO: Model Alignment as Prospect Theoretic Optimization](https://mlsanity.com/paper/2402.01306/) (2024)
- [Large Language Models Sensitivity to The Order of Options in Multiple-Choice Questions](https://mlsanity.com/paper/2308.11483/) (2023)
- [PKU-SafeRLHF: Towards Multi-Level Safety Alignment for LLMs with Human Preference](https://mlsanity.com/paper/2406.15513/) (2024)
- [MiniCheck: Efficient Fact-Checking of LLMs on Grounding Documents](https://mlsanity.com/paper/2404.10774/) (2024)
- [Who Validates the Validators? Aligning LLM-Assisted Evaluation of LLM Outputs with Human Preferences](https://mlsanity.com/paper/2404.12272/) (2024)
- [An Empirical Study of LLM-as-a-Judge for LLM Evaluation: Fine-tuned Judge Model is not a General Substitute for GPT-4](https://mlsanity.com/paper/2403.02839/) (2024)
- [One Token to Fool LLM-as-a-Judge](https://mlsanity.com/paper/2507.08794/) (2025)
- [Great Models Think Alike and this Undermines AI Oversight](https://mlsanity.com/paper/2502.04313/) (2025)
- [Limits to scalable evaluation at the frontier: LLM as Judge won't beat twice the data](https://mlsanity.com/paper/2410.13341/) (2024)
- [Are LLM-Judges Robust to Expressions of Uncertainty? Investigating the effect of Epistemic Markers on LLM-based Evaluation](https://mlsanity.com/paper/2410.20774/) (2024)
- [Fairer Preferences Elicit Improved Human-Aligned Large Language Model Judgments](https://mlsanity.com/paper/2406.11370/) (2024)
- [BadJudge: Backdoor Vulnerabilities of LLM-as-a-Judge](https://mlsanity.com/paper/2503.00596/) (2025)

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

- [RAIM: Robust Aggregation of Inexpensive Models for Hallucination Detection](https://mlsanity.com/paper/2609.39229/) (2026)

## Abstract (arXiv)

Consensus among LLM judges is often taken as strong evidence that a decision is correct. This assumes that judges make their errors independently. In practice, LLM judges are often trained and evaluated in similar ways, so they can make the same mistakes. We study how this dependency affects the reliability of consensus. We find substantial error correlation across both open-weight and frontier LLM judges. In our main bank of ten judges, the average pairwise correlation between judge errors is 0.21. As a result, the ten judges only provide roughly as much statistical information as 3.5 independent judges. The dependency is even stronger among the high-accuracy frontier judges we evaluate, including judges from different providers. In up to 28% of our comparisons, ignoring shared errors leads to the conclusion that one system is significantly better, while accounting for them does not. We also find that the pattern of errors matters. Errors shared by most judges and errors concentrated among a smaller group affect consensus differently and favor different voting methods. Measuring the overall amount of correlation alone is therefore insufficient. Our results suggest a simple approach: use a small set of trusted examples to estimate judge accuracy and identify shared mistakes. These shared errors should then be considered when analyzing the results, and the voting method should be chosen using trusted examples before it is applied to new data.