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

精确却脱节：在多智能体数学推理中，评审者的精确度并不能保证对批评意见的采纳

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. 许多面向数学和科学的智能体系统采用了具有专门评审角色的分层设计，假设专门的评审阶段有助于将错误的候选答案转化为正确的答案。

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). 我们使用匹配的 gpt-oss-120b 智能体，在 4,181 个基于验证器的 Omni-MATH 问题上测试了这一假设。在最简单的层级上，协作带来的提升微乎其微，但从第 4 层开始，收益显著增加；在这种更困难的场景下，广播式的同行讨论比“规划者-执行者-评审者”（PER）流程能达到更高的最终准确率。

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. 我们探讨了这种差距是由评审质量决定的，还是由批评意见是否改变了协议后续采纳的答案所决定的。仅靠评审者的精确度无法解释这一现象：PER 的评审者比广播式的评审者更精确（0.861 对 0.644），但经评估验证的有效批评意见却不太可能改变下一个候选答案，且产生的评审引导修复效果更差。

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. 这些结果表明，评审者的检测质量与对批评意见的采纳在经验上是可分离的。在匹配的 PER 干预措施中，强制要求明确确认反而降低了最终准确率，而将评审者的指导直接嵌入到求解器的工作上下文中，虽然在一定程度上改善了后续执行，但仍未能消除差距。

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. 总的来说，以评审者为中心的评估可能会高估系统质量：一个协议可能很擅长发现错误，但如果它不能根据这些批评意见采取行动，依然无法解决更多的问题。