# Precise but Uncoupled: Reviewer Precision Does Not Guarantee Critique Uptake in Multi-Agent Math Reasoning

arXiv: https://arxiv.org/abs/2607.15388 · HTML: https://mlsanity.com/paper/2607.15388/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in Reasoning for agents, planning and code, one of 17 directions in LLM reasoning.
- Builds on 31 of its 38 references that are in the map.
- First posted on arXiv 16 Jul 2026.

## Placed in

- LLM reasoning / [Reasoning for agents, planning and code](https://mlsanity.com/lr/reasoning-for-agents-planning-and-code/)

## Builds on (most cited first, 30 of 31)

- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Reflexion: Language Agents with Verbal Reinforcement Learning](https://mlsanity.com/paper/2303.11366/) (2023)
- [Self-Refine: Iterative Refinement with Self-Feedback](https://mlsanity.com/paper/2303.17651/) (2023)
- [Tree of Thoughts: Deliberate Problem Solving with Large Language Models](https://mlsanity.com/paper/2305.10601/) (2023)
- [AutoGen: Enabling Next-Gen LLM Applications via Multi-Agent Conversation](https://mlsanity.com/paper/2308.08155/) (2023)
- [Improving Factuality and Reasoning in Language Models through Multiagent Debate](https://mlsanity.com/paper/2305.14325/) (2023)
- [CAMEL: Communicative Agents for "Mind" Exploration of Large Language Model Society](https://mlsanity.com/paper/2303.17760/) (2023)
- [AgentBench: Evaluating LLMs as Agents](https://mlsanity.com/paper/2308.03688/) (2023)
- [Large Language Models Cannot Self-Correct Reasoning Yet](https://mlsanity.com/paper/2310.01798/) (2023)
- [Why Do Multi-Agent LLM Systems Fail?](https://mlsanity.com/paper/2503.13657/) (2025)
- [Multi-Agent Collaboration Mechanisms: A Survey of LLMs](https://mlsanity.com/paper/2501.06322/) (2025)
- [Omni-MATH: A Universal Olympiad Level Mathematic Benchmark For Large Language Models](https://mlsanity.com/paper/2410.07985/) (2024)
- [A Survey on Test-Time Scaling in Large Language Models: What, How, Where, and How Well?](https://mlsanity.com/paper/2503.24235/) (2025)
- [AI Agents That Matter](https://mlsanity.com/paper/2407.01502/) (2024)
- [Survey on Evaluation of LLM-based Agents](https://mlsanity.com/paper/2503.16416/) (2025)
- [Towards a Science of Scaling Agent Systems](https://mlsanity.com/paper/2512.08296/) (2025)
- [Establishing Best Practices for Building Rigorous Agentic Benchmarks](https://mlsanity.com/paper/2507.02825/) (2025)
- [On scalable oversight with weak LLMs judging strong LLMs](https://mlsanity.com/paper/2407.04622/) (2024)
- [Towards Scientific Intelligence: A Survey of LLM-based Scientific Agents](https://mlsanity.com/paper/2503.24047/) (2025)
- [MALT: Improving Reasoning with Multi-Agent LLM Training](https://mlsanity.com/paper/2412.01928/) (2024)
- [xVerify: Efficient Answer Verifier for Reasoning Model Evaluations](https://mlsanity.com/paper/2504.10481/) (2025)
- [Evaluating Judges as Evaluators: The JETTS Benchmark of LLM-as-Judges as Test-Time Scaling Evaluators](https://mlsanity.com/paper/2504.15253/) (2025)
- [Confidence v.s. Critique: A Decomposition of Self-Correction Capability for LLMs](https://mlsanity.com/paper/2412.19513/) (2024)
- [Can LLM Agents Really Debate? A Controlled Study of Multi-Agent Debate in Logical Reasoning](https://mlsanity.com/paper/2511.07784/) (2025)
- [Reinforce LLM Reasoning through Multi-Agent Reflection](https://mlsanity.com/paper/2506.08379/) (2025)
- [Can LLMs Correct Themselves? A Benchmark of Self-Correction in LLMs](https://mlsanity.com/paper/2510.16062/) (2025)
- [Benchmarks Saturate When The Model Gets Smarter Than The Judge](https://mlsanity.com/paper/2601.19532/) (2026)
- [On Evaluating the Integration of Reasoning and Action in LLM Agents with Database Question Answering](https://mlsanity.com/paper/2311.09721/) (2023)
- [Decomposing LLM Self-Correction: The Accuracy-Correction Paradox and Error Depth Hypothesis](https://mlsanity.com/paper/2601.00828/) (2025)

## Built on by (most cited first, 2 of 2)

- [Reviewer Capability Governs Rejection Targeting, Not Repair Skill: Evidence from LLM Execute-Review-Revise Pipelines](https://mlsanity.com/paper/2609.04270/) (2026)
- [Review Rarely Beats the Stronger Model: Separating Verification from Capability Transfer in LLM Pipelines](https://mlsanity.com/paper/2610.15897/) (2026)

## Abstract (arXiv)

Many math- and science-oriented agent systems use hierarchical designs with specialized reviewer roles, assuming that a dedicated review stage should help turn wrong candidates into correct ones. We test this assumption on 4,181 verifier-grounded Omni-MATH problems using matched gpt-oss-120b actors. Collaboration adds little on the easiest tiers, but from tier 4 onward the gains open sharply; in this harder regime, broadcast-style peer discussion reaches higher final accuracy than a planner-executor-reviewer pipeline (PER). We ask whether this gap is explained by reviewer quality or by whether critique changes the next answer the protocol carries forward. It is not explained by reviewer precision alone: PER's reviewer is more precise than broadcast's (0.861 vs. 0.644), yet evaluator-verified useful critique is much less likely to change the next candidate and produces lower reviewer-guided repair. These results show that reviewer detection quality and critique uptake are empirically separable. Within matched PER interventions, forcing explicit acknowledgment lowers final accuracy, while embedding reviewer guidance directly in the solver's working context partially improves follow-through without closing the gap. Overall, reviewer-centric evaluation can overstate system quality: a protocol may spot errors well yet still fail to solve more problems if it does not act on those critiques.