SVR-MAD: A Bayesian-Inspired Framework for Posterior-Guided Multi-Agent Debate
Authors: Weifan Jiang, Rana Shahout, Minghao Li, Zhenting Qi, Yilun Du, Michael Mitzenmacher, Minlan Yu
Organizations: Harvard University
Abstract
Multi-Agent Debate (MAD) improves LLM-agent accuracy but suffers from rapid context growth, limiting scalability in larger multi-agent settings. Existing methods prune low-utility communications using prior signals, such as token-level log-likelihoods or LLM self-reported confidence. However, these signals become unreliable under hallucination, degrading the accuracy of MAD methods that rely on them. We propose SVR-MAD, a Bayesian-inspired MAD framework that treats pre-debate signals as priors and debate outcomes as posterior-style evidence for estimating agent correctness. SVR-MAD uses this evidence to incrementally construct the communication graph, prioritizing agents whose answers survive peer challenges. Experiments across multiple LLMs and benchmarks show that SVR-MAD reduces token cost by up to 61% while matching or improving accuracy relative to the most accurate competing MAD baseline.
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 R2-MAD (Remember and Reweight for Multi-Agent Debate), a framework that equips agents with an experience memory accumulated from past debates. R2-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 R2-MAD achieves consistent improvements over existing single-agent and MAD baselines.
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) can improve large language model reasoning, but fixed debate pipelines often waste computation and can amplify correlated errors among similar agents. We propose ARMOR-MAD, a training-free heterogeneous MAD framework that treats debate as conditional computation. ARMOR-MAD combines three components: Pre-debate Agreement Routing (PAR) decides whether independently generated Round-0 answers require debate; Early Agreement Stopping Evaluator (EASE) stops debate after convergence; and Semantic Outlier Detection (SOD) down-weights abnormal final answers during aggregation. Across MATH Level 5, GSM8K, MMLU, and MMLU-Pro, ARMOR-MAD consistently improves over fixed-round heterogeneous debate with the same model pool, reaching 65.5%, 96.5%, 90.0%, and 81.5% accuracy, respectively. The results suggest that genuine model heterogeneity and agreement-based control are both important for making MAD more accurate and efficient.