# Improving LLM-as-a-Judge Inference with the Judgment Distribution

arXiv: https://arxiv.org/abs/2503.03064 · HTML: https://mlsanity.com/paper/2503.03064/

## Key facts

- Cited by 37 papers in the map (data through 14 Oct 2026).
- Builds on 57 of its 100 references that are in the map.
- First posted on arXiv 4 Mar 2025.

## Builds on (most cited first, 30 of 57)

- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Judging LLM-as-a-Judge with MT-Bench and Chatbot Arena](https://mlsanity.com/paper/2306.05685/) (2023)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [Training a Helpful and Harmless Assistant with Reinforcement Learning from Human Feedback](https://mlsanity.com/paper/2204.05862/) (2022)
- [G-Eval: NLG Evaluation using GPT-4 with Better Human Alignment](https://mlsanity.com/paper/2303.16634/) (2023)
- [Length-Controlled AlpacaEval: A Simple Way to Debias Automatic Evaluators](https://mlsanity.com/paper/2404.04475/) (2024)
- [ChatEval: Towards Better LLM-based Evaluators through Multi-Agent Debate](https://mlsanity.com/paper/2308.07201/) (2023)
- [RLAIF vs. RLHF: Scaling Reinforcement Learning from Human Feedback with AI Feedback](https://mlsanity.com/paper/2309.00267/) (2023)
- [From Crowdsourced Data to High-Quality Benchmarks: Arena-Hard and BenchBuilder Pipeline](https://mlsanity.com/paper/2406.11939/) (2024)
- [Generative Verifiers: Reward Modeling as Next-Token Prediction](https://mlsanity.com/paper/2408.15240/) (2024)
- [Prometheus 2: An Open Source Language Model Specialized in Evaluating Other Language Models](https://mlsanity.com/paper/2405.01535/) (2024)
- [JudgeLM: Fine-tuned Large Language Models are Scalable Judges](https://mlsanity.com/paper/2310.17631/) (2023)
- [JudgeBench: A Benchmark for Evaluating LLM-based Judges](https://mlsanity.com/paper/2410.12784/) (2024)
- [Large Language Models are Effective Text Rankers with Pairwise Ranking Prompting](https://mlsanity.com/paper/2306.17563/) (2023)
- [Evaluating Large Language Models at Evaluating Instruction Following](https://mlsanity.com/paper/2310.07641/) (2023)
- [To CoT or not to CoT? Chain-of-thought helps mainly on math and symbolic reasoning](https://mlsanity.com/paper/2409.12183/) (2024)
- [HelpSteer2: Open-source dataset for training top-performing reward models](https://mlsanity.com/paper/2406.08673/) (2024)
- [WildBench: Benchmarking LLMs with Challenging Tasks from Real Users in the Wild](https://mlsanity.com/paper/2406.04770/) (2024)
- [Chain-of-Thought Reasoning Without Prompting](https://mlsanity.com/paper/2402.10200/) (2024)
- [FLASK: Fine-grained Language Model Evaluation based on Alignment Skill Sets](https://mlsanity.com/paper/2307.10928/) (2023)
- [Do-Not-Answer: A Dataset for Evaluating Safeguards in LLMs](https://mlsanity.com/paper/2308.13387/) (2023)
- [RM-Bench: Benchmarking Reward Models of Language Models with Subtlety and Style](https://mlsanity.com/paper/2410.16184/) (2024)
- [Personalizing Reinforcement Learning from Human Feedback with Variational Preference Learning](https://mlsanity.com/paper/2408.10075/) (2024)
- [Large Language Models are Inconsistent and Biased Evaluators](https://mlsanity.com/paper/2405.01724/) (2024)
- [Aligning with Human Judgement: The Role of Pairwise Preference in Large Language Model Evaluators](https://mlsanity.com/paper/2403.16950/) (2024)
- [Distributional Preference Learning: Understanding and Accounting for Hidden Context in RLHF](https://mlsanity.com/paper/2312.08358/) (2023)
- [HelpSteer2-Preference: Complementing Ratings with Preferences](https://mlsanity.com/paper/2410.01257/) (2024)
- [Is LLM-as-a-Judge Robust? Investigating Universal Adversarial Attacks on Zero-shot LLM Assessment](https://mlsanity.com/paper/2402.14016/) (2024)
- [Mind Your Step (by Step): Chain-of-Thought can Reduce Performance on Tasks where Thinking Makes Humans Worse](https://mlsanity.com/paper/2410.21333/) (2024)

## Built on by (most cited first, 30 of 37)

- [AbstentionBench: Reasoning LLMs Fail on Unanswerable Questions](https://mlsanity.com/paper/2506.09038/) (2025)
- [Checklists Are Better Than Reward Models For Aligning Language Models](https://mlsanity.com/paper/2507.18624/) (2025)
- [Reliability without Validity: A Systematic, Large-Scale Evaluation of LLM-as-a-Judge Models Across Agreement, Consistency, and Bias](https://mlsanity.com/paper/2606.19544/) (2026)
- [Analyzing Uncertainty of LLM-as-a-Judge: Interval Evaluations with Conformal Prediction](https://mlsanity.com/paper/2509.18658/) (2025)
- [TrustJudge: Inconsistencies of LLM-as-a-Judge and How to Alleviate Them](https://mlsanity.com/paper/2509.21117/) (2025)
- [NarraBench: A Comprehensive Framework for Narrative Benchmarking](https://mlsanity.com/paper/2510.09869/) (2025)
- [CARE: Confounder-Aware Aggregation for Reliable LLM Evaluation](https://mlsanity.com/paper/2603.00039/) (2026)
- [Measuring Scalar Constructs in Social Science with LLMs](https://mlsanity.com/paper/2509.03116/) (2025)
- [Generate, Filter, Control, Replay: A Comprehensive Survey of Rollout Strategies for LLM Reinforcement Learning](https://mlsanity.com/paper/2605.02913/) (2026)
- [ChartEditBench: Evaluating Grounded Multi-Turn Chart Editing in Multimodal Language Models](https://mlsanity.com/paper/2602.15758/) (2026)
- [Measuring LLM Novelty As The Frontier Of Original And High-Quality Output](https://mlsanity.com/paper/2504.09389/) (2025)
- [Beyond Single-Point Judgment: Distribution Alignment for LLM-as-a-Judge](https://mlsanity.com/paper/2505.12301/) (2025)
- [ToolGrad: Efficient Tool-use Dataset Generation with Textual "Gradients"](https://mlsanity.com/paper/2508.04086/) (2025)
- [Scoring, Reasoning, and Selecting the Best! Ensembling Large Language Models via a Peer-Review Process](https://mlsanity.com/paper/2512.23213/) (2025)
- [PEDANTIC: A Dataset for the Automatic Examination of Definiteness in Patent Claims](https://mlsanity.com/paper/2505.21342/) (2025)
- [ProxAnn: Use-Oriented Evaluations of Topic Models and Document Clustering](https://mlsanity.com/paper/2507.00828/) (2025)
- [MENLO: From Preferences to Proficiency -- Evaluating and Modeling Native-like Quality Across 47 Languages](https://mlsanity.com/paper/2509.26601/) (2025)
- [Subliminal Signals in Preference Labels](https://mlsanity.com/paper/2603.01204/) (2026)
- [PsychePass: Calibrating LLM Therapeutic Competence via Trajectory-Anchored Tournaments](https://mlsanity.com/paper/2601.20330/) (2026)
- [RELISH: LLM REgression with a Latent Iterative State Head](https://mlsanity.com/paper/2604.01206/) (2026)
- [When Languages Disagree: Self-Evolving Multilingual LLM Judges](https://mlsanity.com/paper/2606.08092/) (2026)
- [From Uncertain Judgments to Calibrated Rankings: Conformal Elo Estimation for LLM Evaluation](https://mlsanity.com/paper/2606.13221/) (2026)
- [When Knowledge Changes: Metamorphic Testing of RAG Systems with Mutations](https://mlsanity.com/paper/2607.26843/) (2026)
- [Quantitative Introspection in Language Models: Tracking Emotive States Across Conversation](https://mlsanity.com/paper/2603.18893/) (2026)
- [Permutation-Consensus Listwise Judging for Robust Factuality Evaluation](https://mlsanity.com/paper/2603.20562/) (2026)
- [StanceBench: A Benchmark for Audio LLM-Based Interpersonal Stance Evaluation from Speech](https://mlsanity.com/paper/2607.22658/) (2026)
- [Spillover-Aware Multi-Value Steering for Pluralistic LLM Alignment](https://mlsanity.com/paper/2609.05800/) (2026)
- [Rethinking Verbalized Confidence for LLM-as-a-Judge: A Compatibility Shift on Post-2025 Proprietary Models](https://mlsanity.com/paper/2609.10996/) (2026)
- [MixAssist: An Audio-Language Dataset for Co-Creative AI Assistance in Music Mixing](https://mlsanity.com/paper/2507.06329/) (2025)
- [Approximating Human Preferences Using a Multi-Judge Learned System](https://mlsanity.com/paper/2510.25884/) (2025)

## Abstract (arXiv)

Using language models to scalably approximate human preferences on text quality (LLM-as-a-judge) has become a standard practice applicable to many tasks. A judgment is often extracted from the judge's textual output alone, typically with greedy decoding. However, LLM judges naturally provide distributions over judgment tokens, inviting a breadth of inference methods for extracting fine-grained preferences. We find that taking the mean of the judgment distribution consistently outperforms taking the mode (i.e. greedy decoding) in all evaluation settings (i.e. pointwise, pairwise, and listwise). We further explore novel methods of deriving preferences from judgment distributions, and find that methods incorporating risk aversion often improve performance. Lastly, we analyze LLM-as-a-judge paired with chain-of-thought (CoT) prompting, showing that CoT can collapse the spread of the judgment distribution, often harming performance. Our findings show that leveraging distributional output improves LLM-as-a-judge, as opposed to using the text interface alone.