# The Coin Flip Judge? Reliability and Bias in LLM-as-a-Judge Evaluation

arXiv: https://arxiv.org/abs/2606.13685 · HTML: https://mlsanity.com/paper/2606.13685/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Placed in Human values and AI feedback alignment, one of 10 directions in LLM alignment / RLHF / preference optimisation.
- Builds on 11 of its 16 references that are in the map.
- First posted on arXiv 23 Apr 2026.

## Placed in

- LLM alignment / RLHF / preference optimisation / [Human values and AI feedback alignment](https://mlsanity.com/alignment/human-values-and-ai-feedback-alignment/)

## Builds on (most cited first, 11 of 11)

- [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)
- [Constitutional AI: Harmlessness from AI Feedback](https://mlsanity.com/paper/2212.08073/) (2022)
- [G-Eval: NLG Evaluation using GPT-4 with Better Human Alignment](https://mlsanity.com/paper/2303.16634/) (2023)
- [Chatbot Arena: An Open Platform for Evaluating LLMs by Human Preference](https://mlsanity.com/paper/2403.04132/) (2024)
- [Large Language Models are not Fair Evaluators](https://mlsanity.com/paper/2305.17926/) (2023)
- [AlpacaFarm: A Simulation Framework for Methods that Learn from Human Feedback](https://mlsanity.com/paper/2305.14387/) (2023)
- [JudgeLM: Fine-tuned Large Language Models are Scalable Judges](https://mlsanity.com/paper/2310.17631/) (2023)
- [All That's 'Human' Is Not Gold: Evaluating Human Evaluation of Generated Text](https://mlsanity.com/paper/2107.00061/) (2021)
- [Large Language Models are Inconsistent and Biased Evaluators](https://mlsanity.com/paper/2405.01724/) (2024)
- [Who Validates the Validators? Aligning LLM-Assisted Evaluation of LLM Outputs with Human Preferences](https://mlsanity.com/paper/2404.12272/) (2024)

## Built on by (most cited first, 7 of 7)

- [JudgeSense: A Benchmark for Prompt Sensitivity in LLM-as-a-Judge Systems](https://mlsanity.com/paper/2604.23478/) (2026)
- [OmnilingualGAIA2: Evaluating the Multilingual Gap in Frontier AI Agents](https://mlsanity.com/paper/2608.08775/) (2026)
- [A Calibrated Instrument for Measuring How Inference Optimizations Affect Output Quality](https://mlsanity.com/paper/2609.18005/) (2026)
- [Ask Which, Not How Good: Sizing Benchmarks Scored by an LLM](https://mlsanity.com/paper/2609.27787/) (2026)
- [On Evaluating and Improving Conversational Agents in Production](https://mlsanity.com/paper/2609.32092/) (2026)
- [Asking for What Was Never Requested: Horizontal and Vertical Proactivity in Agents](https://mlsanity.com/paper/2609.37236/) (2026)
- [CompOrca: Corpus-Scale Compliance Labelling of Instruction-Tuning Data](https://mlsanity.com/paper/2609.37807/) (2026)

## Abstract (arXiv)

LLM-as-a-Judge is now widely used to rank model outputs, train reward models, and populate public leaderboards, but its run-to-run reliability remains under-characterized. We study repeated identical evaluations on 29 tasks spanning 10 categories using two OpenAI judge models (GPT-4o-mini and GPT-4.1-mini), with 50 pairwise trials and 50 pointwise trials per question, supplemented by temperature and prompt-sensitivity ablations. Across judges, pairwise preferences flip on average 13.6% of the time, with 28% of questions exceeding a 20% flip rate and one question reaching 56%. GPT-4o-mini also exhibits a significant first-position bias (72% A-majority, p = 0.024). At the same time, mean pointwise score gaps are small (0.19--0.36 on a 10-point scale) and not statistically significant in aggregate, producing a pairwise--pointwise gap: judges frequently choose a winner even when their own scalar scores provide little evidence of a meaningful quality difference. Beyond within-judge instability, cross-judge agreement is only 76% (kappa = 0.51), semantically equivalent prompt templates change majority outcomes in 25% of tested cases, and deterministic decoding reduces but does not eliminate inconsistency. A reliability curve analysis shows that, in our dataset, 11 repeated trials are needed for a majority vote to recover the 50-trial reference verdict with 95% probability on average, rising to 15 for high-variance questions. These findings suggest that single-trial LLM judging is often too noisy for high-stakes evaluation, and that multi-trial aggregation, position randomization, and explicit uncertainty reporting should be standard practice. Because both judges are from a single provider, cross-provider replication remains an important next step.