# When Debate Helps: Proposal Supply and Verification-Aware Readout in Multi-Agent Reasoning

arXiv: https://arxiv.org/abs/2610.04686 · HTML: https://mlsanity.com/paper/2610.04686/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Social simulation and multi-agent debate, one of 16 directions in LLM agents and tool use.
- Builds on 23 of its 33 references that are in the map.
- First posted on arXiv 3 Oct 2026.

## Placed in

- LLM agents and tool use / [Social simulation and multi-agent debate](https://mlsanity.com/agents/social-simulation-and-multi-agent-debate/)

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

- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Self-Refine: Iterative Refinement with Self-Feedback](https://mlsanity.com/paper/2303.17651/) (2023)
- [GPQA: A Graduate-Level Google-Proof Q&A Benchmark](https://mlsanity.com/paper/2311.12022/) (2023)
- [Improving Factuality and Reasoning in Language Models through Multiagent Debate](https://mlsanity.com/paper/2305.14325/) (2023)
- [ChatEval: Towards Better LLM-based Evaluators through Multi-Agent Debate](https://mlsanity.com/paper/2308.07201/) (2023)
- [JudgeBench: A Benchmark for Evaluating LLM-based Judges](https://mlsanity.com/paper/2410.12784/) (2024)
- [ReConcile: Round-Table Conference Improves Reasoning via Consensus among Diverse LLMs](https://mlsanity.com/paper/2309.13007/) (2023)
- [Making Large Language Models Better Reasoners with Step-Aware Verifier](https://mlsanity.com/paper/2206.02336/) (2022)
- [Are We Done with MMLU?](https://mlsanity.com/paper/2406.04127/) (2024)
- [Rethinking the Bounds of LLM Reasoning: Are Multi-Agent Discussions the Key?](https://mlsanity.com/paper/2402.18272/) (2024)
- [Should we be going MAD? A Look at Multi-Agent Debate Strategies for LLMs](https://mlsanity.com/paper/2311.17371/) (2023)
- [Examining Inter-Consistency of Large Language Models Collaboration: An In-depth Analysis via Debate](https://mlsanity.com/paper/2305.11595/) (2023)
- [Debate or Vote: Which Yields Better Decisions in Multi-Agent Large Language Models?](https://mlsanity.com/paper/2508.17536/) (2025)
- [Voting or Consensus? Decision-Making in Multi-Agent Debate](https://mlsanity.com/paper/2502.19130/) (2025)
- [Towards Bayesian Deep Learning: A Framework and Some Existing Methods](https://mlsanity.com/paper/1608.06884/) (2016)
- [Stop Overvaluing Multi-Agent Debate -- We Must Rethink Evaluation and Embrace Model Heterogeneity](https://mlsanity.com/paper/2502.08788/) (2025)
- [Natural-Parameter Networks: A Class of Probabilistic Neural Networks](https://mlsanity.com/paper/1611.00448/) (2016)
- [Neural Thickets: Diverse Task Experts Are Dense Around Pretrained Weights](https://mlsanity.com/paper/2603.12228/) (2026)
- [Domain-Indexing Variational Bayes: Interpretable Domain Index for Domain Adaptation](https://mlsanity.com/paper/2302.02561/) (2023)
- [Training-Free Bayesianization for Low-Rank Adapters of Large Language Models](https://mlsanity.com/paper/2412.05723/) (2024)

## Abstract (arXiv)

Multi-agent debate can improve reasoning, yet often fails to beat simple majority voting. We argue that successful debate requires two distinct mechanisms: proposal supply must surface a correct answer, and readout must identify that answer when voting misses it. We formalize the first requirement through recoverable headroom, which measures cases where a correct proposal is available but the majority answer is wrong. For the second, we develop Latent Verification Debate (LVD), an accounting model in which candidate proposals receive answer-specific verification evidence before final generation. Controlled fixed-proposal interventions estimate this latent effect in equivalent peer-support units and show that correct evidence changes answer probabilities and generated decisions while proposal supply remains fixed. To improve proposal supply, we construct societies from neural-thicket agents using labeled and label-free coverage objectives. Across two backbones and matched-budget reasoning benchmarks, coverage-selected societies increase complementary proposal supply and improve aggregate accuracy in repeated stochastic evaluations. Round-level controls further show that interaction provides gains beyond applying the same finalizer directly to the initial proposals. These results identify proposal coverage and truth-sensitive evidence use as complementary conditions for debate to outperform voting. Code is available at https://github.com/Wang-ML-Lab/when-debate-helps.