# BACON: Budgeted Human Calibration for Modeling and Evaluation with Multiple AI Judges

arXiv: https://arxiv.org/abs/2607.16239 · HTML: https://mlsanity.com/paper/2607.16239/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 23 of its 34 references that are in the map.
- First posted on arXiv 26 Jun 2026.

## Builds on (most cited first, 23 of 23)

- [Judging LLM-as-a-Judge with MT-Bench and Chatbot Arena](https://mlsanity.com/paper/2306.05685/) (2023)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Sigmoid Loss for Language Image Pre-Training](https://mlsanity.com/paper/2303.15343/) (2023)
- [G-Eval: NLG Evaluation using GPT-4 with Better Human Alignment](https://mlsanity.com/paper/2303.16634/) (2023)
- [Improving Factuality and Reasoning in Language Models through Multiagent Debate](https://mlsanity.com/paper/2305.14325/) (2023)
- [A Survey on LLM-as-a-Judge](https://mlsanity.com/paper/2411.15594/) (2024)
- [Large Language Models are not Fair Evaluators](https://mlsanity.com/paper/2305.17926/) (2023)
- [Encouraging Divergent Thinking in Large Language Models through Multi-Agent Debate](https://mlsanity.com/paper/2305.19118/) (2023)
- [Prometheus: Inducing Fine-grained Evaluation Capability in Language Models](https://mlsanity.com/paper/2310.08491/) (2023)
- [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)
- [Experts, Errors, and Context: A Large-Scale Study of Human Evaluation for Machine Translation](https://mlsanity.com/paper/2104.14478/) (2021)
- [Replacing Judges with Juries: Evaluating LLM Generations with a Panel of Diverse Models](https://mlsanity.com/paper/2404.18796/) (2024)
- [PandaLM: An Automatic Evaluation Benchmark for LLM Instruction Tuning Optimization](https://mlsanity.com/paper/2306.05087/) (2023)
- [Prediction-Powered Inference](https://mlsanity.com/paper/2301.09633/) (2023)
- [Generative Judge for Evaluating Alignment](https://mlsanity.com/paper/2310.05470/) (2023)
- [PPI++: Efficient Prediction-Powered Inference](https://mlsanity.com/paper/2311.01453/) (2023)
- [An Empirical Study of LLM-as-a-Judge for LLM Evaluation: Fine-tuned Judge Model is not a General Substitute for GPT-4](https://mlsanity.com/paper/2403.02839/) (2024)
- [Cross-Prediction-Powered Inference](https://mlsanity.com/paper/2309.16598/) (2023)
- [Semi-supervised Inference: General Theory and Estimation of Means](https://mlsanity.com/paper/1606.07268/) (2016)
- [Robust Sampling for Active Statistical Inference](https://mlsanity.com/paper/2511.08991/) (2025)
- [Active Measurement: Efficient Estimation at Scale](https://mlsanity.com/paper/2507.01372/) (2025)
- [More power to you: Using machine learning to augment human coding for more efficient inference in text-based randomized trials](https://mlsanity.com/paper/2309.13666/) (2023)

## Abstract (arXiv)

AI judges offer a scalable, low-cost alternative to human evaluation, but their outputs can be biased relative to human preferences and highly item-dependent, varying across judges, tasks, and domains. When uncalibrated AI evaluations are used for model ranking, item scoring, or population-level quality reporting, these biases can directly distort downstream decisions. We propose BACON, a four-stage pipeline that combines budgeted human calibration with multiple AI-judge outputs to produce more accurate annotations. BACON constructs full-coverage auxiliary features for every item, including multi-judge scores, token-level uncertainty statistics, and contextual embeddings. It then collects human labels for a small sampled subset and trains a cross-fitted outcome model to generate calibrated item-level surrogate predictions. These predictions support two use cases: population-level estimation of summary metrics, such as means or quantiles, using an augmented estimating-equation estimator with valid confidence intervals; and individual-level surrogate scoring for item ranking and annotation. BACON treats AI judges as auxiliary measurements rather than ground truth: human labels provide the calibration anchor, while AI-derived signals improve efficiency. Across diverse tasks, domains, and labeling budgets, BACON improves predictive accuracy and ranking consistency, and reduces bias and variance relative to raw AI outputs and purely human-label-based methods. These results show that BACON offers a practical, statistically grounded framework for scalable evaluation with limited human annotation.