# Do We Need Complex Topology Control? Distinct-Peer Random Routing Improves Cost-Efficiency in Sparse Multi-Agent Debate

arXiv: https://arxiv.org/abs/2609.27150 · HTML: https://mlsanity.com/paper/2609.27150/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Reasoning for agents, planning and code, one of 17 directions in LLM reasoning.
- Builds on 33 of its 35 references that are in the map.
- First posted on arXiv 22 Sep 2026.

## Placed in

- LLM reasoning / [Reasoning for agents, planning and code](https://mlsanity.com/lr/reasoning-for-agents-planning-and-code/)
- LLM agents and tool use / [General LLM agent frameworks and benchmarks](https://mlsanity.com/agents/general-llm-agent-frameworks-and-benchmarks/)

## Builds on (most cited first, 30 of 33)

- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [GPQA: A Graduate-Level Google-Proof Q&A Benchmark](https://mlsanity.com/paper/2311.12022/) (2023)
- [Learn to Explain: Multimodal Reasoning via Thought Chains for Science Question Answering](https://mlsanity.com/paper/2209.09513/) (2022)
- [MMLU-Pro: A More Robust and Challenging Multi-Task Language Understanding Benchmark](https://mlsanity.com/paper/2406.01574/) (2024)
- [Improving Factuality and Reasoning in Language Models through Multiagent Debate](https://mlsanity.com/paper/2305.14325/) (2023)
- [Encouraging Divergent Thinking in Large Language Models through Multi-Agent Debate](https://mlsanity.com/paper/2305.19118/) (2023)
- [ReConcile: Round-Table Conference Improves Reasoning via Consensus among Diverse LLMs](https://mlsanity.com/paper/2309.13007/) (2023)
- [Debating with More Persuasive LLMs Leads to More Truthful Answers](https://mlsanity.com/paper/2402.06782/) (2024)
- [Scaling Large Language Model-based Multi-Agent Collaboration](https://mlsanity.com/paper/2406.07155/) (2024)
- [Cut the Crap: An Economical Communication Pipeline for LLM-based Multi-Agent Systems](https://mlsanity.com/paper/2410.02506/) (2024)
- [G-Designer: Architecting Multi-agent Communication Topologies via Graph Neural Networks](https://mlsanity.com/paper/2410.11782/) (2024)
- [Should we be going MAD? A Look at Multi-Agent Debate Strategies for LLMs](https://mlsanity.com/paper/2311.17371/) (2023)
- [Improving Multi-Agent Debate with Sparse Communication Topology](https://mlsanity.com/paper/2406.11776/) (2024)
- [Assemble Your Crew: Automatic Multi-agent Communication Topology Design via Autoregressive Graph Generation](https://mlsanity.com/paper/2507.18224/) (2025)
- [Understanding the Information Propagation Effects of Communication Topologies in LLM-based Multi-Agent Systems](https://mlsanity.com/paper/2505.23352/) (2025)
- [Adaptive Graph Pruning for Multi-Agent Communication](https://mlsanity.com/paper/2506.02951/) (2025)
- [Free-MAD: Consensus-Free Multi-Agent Debate](https://mlsanity.com/paper/2509.11035/) (2025)
- [S2-MAD: Breaking the Token Barrier to Enhance Multi-Agent Debate Efficiency](https://mlsanity.com/paper/2502.04790/) (2025)
- [Demystifying Multi-Agent Debate: The Role of Confidence and Diversity](https://mlsanity.com/paper/2601.19921/) (2026)
- [AMAS: Adaptively Determining Communication Topology for LLM-based Multi-Agent System](https://mlsanity.com/paper/2510.01617/) (2025)
- [Dynamic Generation of Multi-LLM Agents Communication Topologies with Graph Diffusion Models](https://mlsanity.com/paper/2510.07799/) (2025)
- [CortexDebate: Debating Sparsely and Equally for Multi-Agent Debate](https://mlsanity.com/paper/2507.03928/) (2025)
- [Chain-of-Thought as a Lens: Evaluating Structured Reasoning Alignment between Human Preferences and Large Language Models](https://mlsanity.com/paper/2511.06168/) (2025)
- [Graph-GRPO: Stabilizing Multi-Agent Topology Learning via Group Relative Policy Optimization](https://mlsanity.com/paper/2603.02701/) (2026)
- [Jailbreaking Vision-Language Models Through the Visual Modality](https://mlsanity.com/paper/2605.00583/) (2026)
- [PathMark: Protecting Intellectual Property of Mixture-of-Expert LLMs via Path Watermarks](https://mlsanity.com/paper/2607.03688/) (2026)
- [Do System Prompts Leave Behavioral Fingerprints? A Large-Scale Empirical Study of Clone Detection via Output Similarity](https://mlsanity.com/paper/2608.24461/) (2026)
- [FragileFlow: Spectral Control of Correct-but-Fragile Predictions for Foundation Model Robustness](https://mlsanity.com/paper/2605.08896/) (2026)
- [Decentralised and Cooperative Control of Multi-Robot Systems through Distributed Optimisation](https://mlsanity.com/paper/2302.01728/) (2023)

## Abstract (arXiv)

Multi-agent debate (MAD) has emerged as a promising paradigm for improving the reasoning accuracy of large language models (LLMs) through iterative peer interaction. Communication topology plays a central role in this process, motivating increasingly sophisticated mechanisms that learn, adapt, or dynamically reconfigure agent interactions to improve accuracy or reasoning reliability. Meanwhile, prior studies suggest that much simpler sparse communication can already achieve competitive performance at substantially lower cost. In this work, we take a closer look at sparse MAD and ask whether complex topology control is actually necessary to improve collective reasoning. We find that a simple random-without-replacement routing policy, which lets each agent debate with two distinct and newly sampled peers at every round, provides a surprisingly strong baseline and consistently improves the accuracy-cost trade-off of sparse MAD. Building on this observation, we further study deliberation stopping and show that lightweight stopping can substantially reduce inference cost while preserving competitive accuracy. Our results suggest that sophisticated topology control such as learned topology adaption should be evaluated against strong simple routing and stopping baselines before its additional complexity is justified.