# A Statistical Framework for Auditing Behavioral Dependence and Induced Bias in LLM Judges

arXiv: https://arxiv.org/abs/2604.07650 · HTML: https://mlsanity.com/paper/2604.07650/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 37 of its 49 references that are in the map.
- First posted on arXiv 8 Apr 2026.

## Builds on (most cited first, 30 of 37)

- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [Judging LLM-as-a-Judge with MT-Bench and Chatbot Arena](https://mlsanity.com/paper/2306.05685/) (2023)
- [GPT-4o System Card](https://mlsanity.com/paper/2410.21276/) (2024)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [Qwen Technical Report](https://mlsanity.com/paper/2309.16609/) (2023)
- [Gemini 1.5: Unlocking multimodal understanding across millions of tokens of context](https://mlsanity.com/paper/2403.05530/) (2024)
- [MMLU-Pro: A More Robust and Challenging Multi-Task Language Understanding Benchmark](https://mlsanity.com/paper/2406.01574/) (2024)
- [A Survey on LLM-as-a-Judge](https://mlsanity.com/paper/2411.15594/) (2024)
- [gpt-oss-120b & gpt-oss-20b Model Card](https://mlsanity.com/paper/2508.10925/) (2025)
- [DeepSeek-V2: A Strong, Economical, and Efficient Mixture-of-Experts Language Model](https://mlsanity.com/paper/2405.04434/) (2024)
- [OpenAI GPT-5 System Card](https://mlsanity.com/paper/2601.03267/) (2025)
- [Relational Knowledge Distillation](https://mlsanity.com/paper/1904.05068/) (2019)
- [AlpacaFarm: A Simulation Framework for Methods that Learn from Human Feedback](https://mlsanity.com/paper/2305.14387/) (2023)
- [Instruction Tuning with GPT-4](https://mlsanity.com/paper/2304.03277/) (2023)
- [Detecting Pretraining Data from Large Language Models](https://mlsanity.com/paper/2310.16789/) (2023)
- [On the Efficacy of Knowledge Distillation](https://mlsanity.com/paper/1910.01348/) (2019)
- [Justice or Prejudice? Quantifying Biases in LLM-as-a-Judge](https://mlsanity.com/paper/2410.02736/) (2024)
- [NLP Evaluation in trouble: On the Need to Measure LLM Data Contamination for each Benchmark](https://mlsanity.com/paper/2310.18018/) (2023)
- [PandaLM: An Automatic Evaluation Benchmark for LLM Instruction Tuning Optimization](https://mlsanity.com/paper/2306.05087/) (2023)
- [Self-Preference Bias in LLM-as-a-Judge](https://mlsanity.com/paper/2410.21819/) (2024)
- [Data Contamination: From Memorization to Exploitation](https://mlsanity.com/paper/2203.08242/) (2022)
- [Don't Make Your LLM an Evaluation Benchmark Cheater](https://mlsanity.com/paper/2311.01964/) (2023)
- [Aligning with Human Judgement: The Role of Pairwise Preference in Large Language Model Evaluators](https://mlsanity.com/paper/2403.16950/) (2024)
- [Benchmark Data Contamination of Large Language Models: A Survey](https://mlsanity.com/paper/2406.04244/) (2024)
- [Investigating Data Contamination in Modern Benchmarks for Large Language Models](https://mlsanity.com/paper/2311.09783/) (2023)
- [Preference Leakage: A Contamination Problem in LLM-as-a-judge](https://mlsanity.com/paper/2502.01534/) (2025)
- [Generalization or Memorization: Data Contamination and Trustworthy Evaluation for Large Language Models](https://mlsanity.com/paper/2402.15938/) (2024)
- [LLMs as Narcissistic Evaluators: When Ego Inflates Evaluation Scores](https://mlsanity.com/paper/2311.09766/) (2023)
- [Retrieval-Augmented Generation with Conflicting Evidence](https://mlsanity.com/paper/2504.13079/) (2025)

## Built on by (most cited first, 4 of 4)

- [Knowledge Is Not Static: Order-Aware Hypergraph RAG for Language Models](https://mlsanity.com/paper/2604.12185/) (2026)
- [Harnessing Disagreement: Detecting Correlated Agreement Blindness in Multi-Agent Triage](https://mlsanity.com/paper/2607.19899/) (2026)
- [Grounding latent algorithm routing in transformer reasoning](https://mlsanity.com/paper/2607.24471/) (2026)
- [Blind to the Pivotal Vote: Aggregate Independence Metrics Miss Where Verification Actually Helps](https://mlsanity.com/paper/2608.06940/) (2026)

## Abstract (arXiv)

The rapid growth of the large language model (LLM) ecosystem raises a critical question: are seemingly diverse models truly independent? Shared pretraining data, distillation, and alignment pipelines can induce hidden behavioral dependencies, or latent entanglement, that undermine multi-model systems such as LLM-as-a-judge pipelines and ensemble verification, which implicitly assume independent signals. In practice, this manifests as correlated reasoning patterns and synchronized failures, where apparent agreement reflects shared error modes rather than independent validation. To address this, we develop a statistical framework for auditing behavioral entanglement among black-box LLMs. Our approach introduces a multi-resolution hierarchy that characterizes the joint failure manifold through two information-theoretic metrics: (i) a Difficulty-Weighted Behavioral Entanglement Index (BEI), which amplifies synchronized failures on easy tasks, and (ii) a Cumulative Information Gain (CIG) metric, which captures directional alignment in erroneous responses. Through experiments on 18 LLMs from six model families, we identify statistically significant behavioral entanglement. Such behavioral dependence is associated with judge over-endorsement bias on a disjoint MMLU-Pro evaluation set (rho = 0.508 for BEI and rho = 0.520 for CIG; p < 0.01). The association further transfers to the MATH-500 benchmark (rho = 0.441 for BEI and rho = 0.457 for CIG; p < 0.05), providing cross-benchmark evidence that the identified dependency structure generalizes beyond the data and response format used for its estimation. Finally, we demonstrate a practical use case of entanglement through de-entangled verifier ensemble reweighting, achieving 3.5 and 2.6 percentage-point gains in accuracy and precision, respectively, over majority voting.