# The Geometry of LLM-as-Judge: Why Inter-LLM Consensus Is Not Human Alignment

arXiv: https://arxiv.org/abs/2606.03043 · HTML: https://mlsanity.com/paper/2606.03043/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 56 references that are in the map.
- First posted on arXiv 2 Jun 2026.

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

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [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)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [G-Eval: NLG Evaluation using GPT-4 with Better Human Alignment](https://mlsanity.com/paper/2303.16634/) (2023)
- [Large Language Models are not Fair Evaluators](https://mlsanity.com/paper/2305.17926/) (2023)
- [ChatGPT Outperforms Crowd-Workers for Text-Annotation Tasks](https://mlsanity.com/paper/2303.15056/) (2023)
- [The State and Fate of Linguistic Diversity and Inclusion in the NLP World](https://mlsanity.com/paper/2004.09095/) (2020)
- [AlpacaFarm: A Simulation Framework for Methods that Learn from Human Feedback](https://mlsanity.com/paper/2305.14387/) (2023)
- [Can Large Language Models Be an Alternative to Human Evaluations?](https://mlsanity.com/paper/2305.01937/) (2023)
- [Are Emergent Abilities of Large Language Models a Mirage?](https://mlsanity.com/paper/2304.15004/) (2023)
- [Large Language Models Are State-of-the-Art Evaluators of Translation Quality](https://mlsanity.com/paper/2302.14520/) (2023)
- [Estimating the intrinsic dimension of datasets by a minimal neighborhood information](https://mlsanity.com/paper/1803.06992/) (2018)
- [Challenges and Strategies in Cross-Cultural NLP](https://mlsanity.com/paper/2203.10020/) (2022)
- [Linear Algebraic Structure of Word Senses, with Applications to Polysemy](https://mlsanity.com/paper/1601.03764/) (2016)
- [Aya Expanse: Combining Research Breakthroughs for a New Multilingual Frontier](https://mlsanity.com/paper/2412.04261/) (2024)
- [Are Large Language Model-based Evaluators the Solution to Scaling Up Multilingual Evaluation?](https://mlsanity.com/paper/2309.07462/) (2023)
- [The Alternative Annotator Test for LLM-as-a-Judge: How to Statistically Justify Replacing Human Annotators with LLMs](https://mlsanity.com/paper/2501.10970/) (2025)
- [PARIKSHA: A Large-Scale Investigation of Human-LLM Evaluator Agreement on Multilingual and Multi-Cultural Data](https://mlsanity.com/paper/2406.15053/) (2024)
- [Building Benchmarks from the Ground Up: Community-Centered Evaluation of LLMs in Healthcare Chatbot Settings](https://mlsanity.com/paper/2509.24506/) (2025)

## Built on by (most cited first, 3 of 3)

- [Opening LLM Judges: Recovering Preference Signals Beyond the Final Verdict](https://mlsanity.com/paper/2609.32407/) (2026)
- [Agreement Without Alignment: Label-Free Rubric Clarification Increases LLM-Judge Consensus but Not Agreement with Humans](https://mlsanity.com/paper/2610.13303/) (2026)
- [PRISM: Calibrating Black-Box Judges with Counterfactual Probes](https://mlsanity.com/paper/2610.18389/) (2026)

## Abstract (arXiv)

LLM judges now score most open-ended NLP output, and their mutual agreement is routinely read as evidence that the scores can be trusted. That reading is unsafe: judges may agree because they capture quality, or because they share the same blind spots, and agreement statistics alone cannot tell these apart. We develop a geometric test that can. Treating each judge's scores as a vector, we measure spread, effective rank, the angle to human scores, and the judge-judge, judge-human, and human-human agreement triple for 42 judges on two community-built Indic benchmarks covering four domains and eight languages. Every comparison is reference-matched: a judge and a held-out rater are scored against the same two-rater mean, since an averaged reference otherwise flatters judges by several degrees. On subjective rubrics, judges agree with one another as much as humans do yet reach only 58-66% of human agreement and often concentrate on an axis humans do not weight. On the one rubric with a verifiable answer, most of that gap closes. Ensembles converge on the judges' shared axis rather than the human one, and training widens scores without rotating them. Inter-judge agreement is evidence of human alignment only after this check passes.