# From Calculation to Adjudication: Examining LLM judges on Mathematical Reasoning Tasks

arXiv: https://arxiv.org/abs/2409.04168 · HTML: https://mlsanity.com/paper/2409.04168/

## Key facts

- Cited by 22 papers in the map (data through 14 Oct 2026).
- Placed in Reasoning benchmarks and evaluation, one of 17 directions in LLM reasoning.
- Builds on 18 of its 42 references that are in the map.
- First posted on arXiv 6 Sep 2024.

## Placed in

- LLM reasoning / [Reasoning benchmarks and evaluation](https://mlsanity.com/lr/reasoning-benchmarks-and-evaluation/)

## Builds on (most cited first, 18 of 18)

- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Mistral 7B](https://mlsanity.com/paper/2310.06825/) (2023)
- [Constitutional AI: Harmlessness from AI Feedback](https://mlsanity.com/paper/2212.08073/) (2022)
- [Qwen2 Technical Report](https://mlsanity.com/paper/2407.10671/) (2024)
- [Mixtral of Experts](https://mlsanity.com/paper/2401.04088/) (2024)
- [Gemma: Open Models Based on Gemini Research and Technology](https://mlsanity.com/paper/2403.08295/) (2024)
- [Yi: Open Foundation Models by 01.AI](https://mlsanity.com/paper/2403.04652/) (2024)
- [LLM Evaluators Recognize and Favor Their Own Generations](https://mlsanity.com/paper/2404.13076/) (2024)
- [Self-Rewarding Language Models](https://mlsanity.com/paper/2401.10020/) (2024)
- [LLMs instead of Human Judges? A Large Scale Empirical Study across 20 NLP Evaluation Tasks](https://mlsanity.com/paper/2406.18403/) (2024)
- [HelpSteer2: Open-source dataset for training top-performing reward models](https://mlsanity.com/paper/2406.08673/) (2024)
- [Large Language Models for Data Annotation and Synthesis: A Survey](https://mlsanity.com/paper/2402.13446/) (2024)
- [Meta-Rewarding Language Models: Self-Improving Alignment with LLM-as-a-Meta-Judge](https://mlsanity.com/paper/2407.19594/) (2024)
- [Benchmarking Cognitive Biases in Large Language Models as Evaluators](https://mlsanity.com/paper/2309.17012/) (2023)
- [Is LLM-as-a-Judge Robust? Investigating Universal Adversarial Attacks on Zero-shot LLM Assessment](https://mlsanity.com/paper/2402.14016/) (2024)
- [Pride and Prejudice: LLM Amplifies Self-Bias in Self-Refinement](https://mlsanity.com/paper/2402.11436/) (2024)
- [The BiGGen Bench: A Principled Benchmark for Fine-grained Evaluation of Language Models with Language Models](https://mlsanity.com/paper/2406.05761/) (2024)
- [LLMs as Narcissistic Evaluators: When Ego Inflates Evaluation Scores](https://mlsanity.com/paper/2311.09766/) (2023)

## Built on by (most cited first, 22 of 22)

- [LLMs-as-Judges: A Comprehensive Survey on LLM-based Evaluation Methods](https://mlsanity.com/paper/2412.05579/) (2024)
- [U-MATH: A University-Level Benchmark for Evaluating Mathematical Skills in LLMs](https://mlsanity.com/paper/2412.03205/) (2024)
- [Brains vs. Bytes: Evaluating LLM Proficiency in Olympiad Mathematics](https://mlsanity.com/paper/2504.01995/) (2025)
- [A Systematic Assessment of OpenAI o1-Preview for Higher Order Thinking in Education](https://mlsanity.com/paper/2410.21287/) (2024)
- [Theorem Prover as a Judge for Synthetic Data Generation](https://mlsanity.com/paper/2502.13137/) (2025)
- [DualVLA: Building a Generalizable Embodied Agent via Partial Decoupling of Reasoning and Action](https://mlsanity.com/paper/2511.22134/) (2025)
- [Improving Preference Extraction In LLMs By Identifying Latent Knowledge Through Classifying Probes](https://mlsanity.com/paper/2503.17755/) (2025)
- [Can You Trick the Grader? Adversarial Persuasion of LLM Judges](https://mlsanity.com/paper/2508.07805/) (2025)
- [Who Endorsed It? Measuring Authority Bias Across Expertise Levels in Language Models](https://mlsanity.com/paper/2601.13433/) (2026)
- [UPME: An Unsupervised Peer Review Framework for Multimodal Large Language Model Evaluation](https://mlsanity.com/paper/2503.14941/) (2025)
- [EarthSE: A Benchmark for Evaluating Earth Scientific Exploration Capability of LLMs](https://mlsanity.com/paper/2505.17139/) (2025)
- [Judging Against the Reference: Uncovering Knowledge-Driven Failures in LLM-Judges on QA Evaluation](https://mlsanity.com/paper/2601.07506/) (2026)
- [RefGrader: Automated Grading of Mathematical Competition Proofs using Agentic Workflows](https://mlsanity.com/paper/2510.09021/) (2025)
- [A Matter of Interest: Understanding Interestingness of Math Problems in Humans and Language Models](https://mlsanity.com/paper/2511.08548/) (2025)
- [LLM Judges Can Be Too Generous When There Is No Reference Answer](https://mlsanity.com/paper/2607.12885/) (2026)
- [Reject, Resample, Repeat: Understanding Parallel Reasoning in Language Model Inference](https://mlsanity.com/paper/2603.07887/) (2026)
- [Rethinking Math Reasoning Evaluation: A Robust LLM-as-a-Judge Framework Beyond Symbolic Rigidity](https://mlsanity.com/paper/2604.22597/) (2026)
- [Right Answer, Wrong Method: Shortcut Hacking Misleads the Evaluation of LLM Reasoning on Frontier Science Benchmarks](https://mlsanity.com/paper/2608.02442/) (2026)
- [Improving Multilingual Math Reasoning for African Languages](https://mlsanity.com/paper/2505.19848/) (2025)
- [Evaluating Implicit Biases in LLM Reasoning through Logic Grid Puzzles](https://mlsanity.com/paper/2511.06160/) (2025)
- [TAMTRL: Teacher-Aligned Reward Reshaping for Multi-Turn Reinforcement Learning in Long-Context Compression](https://mlsanity.com/paper/2603.21663/) (2026)
- [How Hypocritical Is Your LLM judge? Listener-Speaker Asymmetries in the Pragmatic Competence of Large Language Models](https://mlsanity.com/paper/2604.15873/) (2026)

## Abstract (arXiv)

To reduce the need for human annotations, large language models (LLMs) have been proposed as judges of the quality of other candidate models. The performance of LLM judges is typically evaluated by measuring the correlation with human judgments on generative tasks such as summarization or machine translation. In contrast, we study LLM judges on mathematical reasoning tasks. These tasks require multi-step reasoning, and the correctness of their solutions is verifiable, enabling a more objective evaluation. We perform a detailed performance analysis and find that easy samples are easy to judge, and difficult samples are difficult to judge. Our analysis uncovers a strong correlation between judgment performance and the candidate model task performance, indicating that judges tend to favor higher-quality models even if their answer is incorrect. As a consequence, we test whether we can predict the behavior of LLM judges using simple features such as part-of-speech tags and find that we can correctly predict 70%-75% of judgments. We conclude this study by analyzing practical use cases, showing that LLM judges consistently detect the on-average better model but largely fail if we use them to improve task performance.