HCP-MAD:Heterogeneous Consensus-Progressive Reasoning for Efficient Multi-Agent Debate

Multi-agent debate (MAD) systems leverage collective intelligence to enhance reasoning capabilities, yet existing approaches struggle to simultaneously optimize accuracy, consensus formation, and computational efficiency. Static topology methods lack adaptability to task complexity variations, while external LLM-based coordination risks introducing privileged knowledge that compromises debate neutrality. This work presents RUMAD (Reinforcement-Unifying Multi-Agent Debate), a novel framework that formulates dynamic communication topology control in MAD as a reinforcement learning (RL) problem. RUMAD employs a content-agnostic observation scheme that captures high-level debate dynamics avoiding access to raw agent reasoning content. RUMAD uses a multi-objective reward to model solution quality, cohesion and efficiency. A PPO-trained controller dynamically adjusts edge weights in the communication graph, while a dual-threshold mechanism enables fine-grained control over both agent activation and information visibility. Experimental evaluation across MMLU, GSM8K, and GPQA benchmarks demonstrates that RUMAD achieves substantial efficiency gains, reducing token costs by over 80%, while still improving reasoning accuracy compared to single LLM model and multiple MAD baselines. Notably, RUMAD trained exclusively on MMLU exhibits robust zero-shot generalization to out-of-domain (OOD) tasks, indicating that the learned communication strategies capture task-independent principles of effective multi-agent coordination. These results establish RUMAD as a efficient and robust approach for deploying multi-agent reasoning application with practical resource constraints.

Multi-agent debate (MAD) was proposed as a promising approach for ensembling the wisdom of multiple large language models (LLMs) to improve reasoning and provide effective supervision to superhuman LLMs. However, increasing empirical evidence suggests that MAD may not outperform or even significantly underperform single-agent approaches (SA), raising doubts about the benefits of MAD. In this work, we investigate this issue by analyzing the incentive structures of popular MAD paradigms: (i) competitive MAD (CopMAD) where agents compete by holding opposing positions; (ii) consensus-seeking MAD (CosMAD) where agents are driven to seek consensus. We show that both paradigms suffer from debate hacking: CopMAD reduces to a cheap-talk game, where agents produce misleading messages to win the game, while CosMAD filters out informative disagreements for premature consensus. Consequently, agents in both CopMAD and CosMAD fail to jointly resolve the ambiguity and seek the truth. To this end, we introduce ColMAD, a collaborative protocol that reframes MAD as a non-zero-sum game to encourage agents to provide informative while truthful messages. Through extensive benchmarking on challenging tasks such as error detection, we show that ColMAD significantly outperforms previous MAD protocols up to 10 percentage points. Under the same budgets, ColMAD effectively brings non-trivial improvements over SA methods, implying that the protocol design is critical to realizing the potential of MAD.

Multi-agent debate (MAD) improves the reasoning capabilities of large language models by having multiple agents iteratively refine their responses through discussion. However, MAD suffers from a critical vulnerability known as shared misconception: when a majority of agents initially converge on an incorrect answer, the debate process tends to amplify rather than correct the error. Existing methods primarily address peer skew but leave the agents' inherently biased concept priors unaddressed. To mitigate this systematic weakness, we propose R$^2$-MAD (Remember and Reweight for Multi-Agent Debate), a framework that equips agents with an experience memory accumulated from past debates. R$^2$-MAD intervenes on both failure modes through two complementary mechanisms: A debate-state-aware retrieval policy dynamically calibrates the concept prior by retrieving relevant historical evidence based on the current consensus level. Then these retrieved experiences provide a basis for estimating per-agent reliability, yielding confidence weights to modulate peer influence. Experiments on various benchmarks show that R$^2$-MAD achieves consistent improvements over existing single-agent and MAD baselines.