# Bayesian Calibration of Win Rate Estimation with LLM Evaluators

arXiv: https://arxiv.org/abs/2411.04424 · HTML: https://mlsanity.com/paper/2411.04424/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 51 references that are in the map.
- First posted on arXiv 7 Nov 2024.

## Builds on (most cited first, 24 of 24)

- [BERTScore: Evaluating Text Generation with BERT](https://mlsanity.com/paper/1904.09675/) (2019)
- [G-Eval: NLG Evaluation using GPT-4 with Better Human Alignment](https://mlsanity.com/paper/2303.16634/) (2023)
- [Hierarchical Neural Story Generation](https://mlsanity.com/paper/1805.04833/) (2018)
- [Large Language Models are not Fair Evaluators](https://mlsanity.com/paper/2305.17926/) (2023)
- [Teaching Machines to Read and Comprehend](https://mlsanity.com/paper/1506.03340/) (2015)
- [AlpacaFarm: A Simulation Framework for Methods that Learn from Human Feedback](https://mlsanity.com/paper/2305.14387/) (2023)
- [ChatEval: Towards Better LLM-based Evaluators through Multi-Agent Debate](https://mlsanity.com/paper/2308.07201/) (2023)
- [Can Large Language Models Be an Alternative to Human Evaluations?](https://mlsanity.com/paper/2305.01937/) (2023)
- [SummEval: Re-evaluating Summarization Evaluation](https://mlsanity.com/paper/2007.12626/) (2020)
- [Prometheus: Inducing Fine-grained Evaluation Capability in Language Models](https://mlsanity.com/paper/2310.08491/) (2023)
- [MAUVE: Measuring the Gap Between Neural Text and Human Text using Divergence Frontiers](https://mlsanity.com/paper/2102.01454/) (2021)
- [Is ChatGPT a Good NLG Evaluator? A Preliminary Study](https://mlsanity.com/paper/2303.04048/) (2023)
- [PandaLM: An Automatic Evaluation Benchmark for LLM Instruction Tuning Optimization](https://mlsanity.com/paper/2306.05087/) (2023)
- [Evaluating Large Language Models at Evaluating Instruction Following](https://mlsanity.com/paper/2310.07641/) (2023)
- [AlignScore: Evaluating Factual Consistency with a Unified Alignment Function](https://mlsanity.com/paper/2305.16739/) (2023)
- [QAFactEval: Improved QA-Based Factual Consistency Evaluation for Summarization](https://mlsanity.com/paper/2112.08542/) (2021)
- [Judging the Judges: Evaluating Alignment and Vulnerabilities in LLMs-as-Judges](https://mlsanity.com/paper/2406.12624/) (2024)
- [PRD: Peer Rank and Discussion Improve Large Language Model based Evaluations](https://mlsanity.com/paper/2307.02762/) (2023)
- [Wider and Deeper LLM Networks are Fairer LLM Evaluators](https://mlsanity.com/paper/2308.01862/) (2023)
- [Of Human Criteria and Automatic Metrics: A Benchmark of the Evaluation of Story Generation](https://mlsanity.com/paper/2208.11646/) (2022)
- [LLM Comparative Assessment: Zero-shot NLG Evaluation through Pairwise Comparisons using Large Language Models](https://mlsanity.com/paper/2307.07889/) (2023)
- [Spectral Methods meet EM: A Provably Optimal Algorithm for Crowdsourcing](https://mlsanity.com/paper/1406.3824/) (2014)
- [OpenMEVA: A Benchmark for Evaluating Open-ended Story Generation Metrics](https://mlsanity.com/paper/2105.08920/) (2021)
- [LLM-Ensemble: Optimal Large Language Model Ensemble Method for E-commerce Product Attribute Value Extraction](https://mlsanity.com/paper/2403.00863/) (2024)

## Built on by (most cited first, 16 of 16)

- [From Generation to Judgment: Opportunities and Challenges of LLM-as-a-judge](https://mlsanity.com/paper/2411.16594/) (2024)
- [LLMs-as-Judges: A Comprehensive Survey on LLM-based Evaluation Methods](https://mlsanity.com/paper/2412.05579/) (2024)
- [Harnessing Multiple Large Language Models: A Survey on LLM Ensemble](https://mlsanity.com/paper/2502.18036/) (2025)
- [Toward Generalizable Evaluation in the LLM Era: A Survey Beyond Benchmarks](https://mlsanity.com/paper/2504.18838/) (2025)
- [When LLM Judge Scores Look Good but Best-of-N Decisions Fail](https://mlsanity.com/paper/2603.12520/) (2026)
- [From Rubrics to Reliable Scores: Evidence-Grounded Text Evaluation with LLM Judges](https://mlsanity.com/paper/2601.08654/) (2026)
- [STABLEVAL: Disagreement-Aware and Stable Evaluation of AI Systems](https://mlsanity.com/paper/2605.02122/) (2026)
- [The Superalignment of Superhuman Intelligence with Large Language Models](https://mlsanity.com/paper/2412.11145/) (2024)
- [LLMPopcorn: Exploring LLMs as Assistants for Popular Micro-video Generation](https://mlsanity.com/paper/2502.12945/) (2025)
- [Learning Explainable Dense Reward Shapes via Bayesian Optimization](https://mlsanity.com/paper/2504.16272/) (2025)
- [PETS: A Principled Framework Towards Optimal Trajectory Allocation for Efficient Test-Time Self-Consistency](https://mlsanity.com/paper/2602.16745/) (2026)
- [Sequential Bayesian Evaluation of Large Language Model Behavior](https://mlsanity.com/paper/2511.10661/) (2025)
- [BenchBrowser: Retrieving Evidence for Evaluating Benchmark Validity](https://mlsanity.com/paper/2603.18019/) (2026)
- [Which Metrics Save the Most Human Annotation? Prediction-Powered Evaluation and Meta-Evaluation](https://mlsanity.com/paper/2608.26638/) (2026)
- [From Static Personal Values to Contextualized Personalization: Bayesian Personalized Value Alignment for LLMs](https://mlsanity.com/paper/2609.28942/) (2026)
- [Can We Trust This Evaluation? Instance-Level Reliability of LLM-as-a-Judge](https://mlsanity.com/paper/2610.14029/) (2026)

## Abstract (arXiv)

Recent advances in large language models (LLMs) show the potential of using LLMs as evaluators for assessing the quality of text generations from LLMs. However, applying LLM evaluators naively to compare or judge between different systems can lead to unreliable results due to the intrinsic win rate estimation bias of LLM evaluators. In order to mitigate this problem, we propose two calibration methods, Bayesian Win Rate Sampling (BWRS) and Bayesian Dawid-Skene, both of which leverage Bayesian inference to more accurately infer the true win rate of generative language models. We empirically validate our methods on six datasets covering story generation, summarization, and instruction following tasks. We show that both our methods are effective in improving the accuracy of win rate estimation using LLMs as evaluators, offering a promising direction for reliable automatic text quality evaluation.