When Agents Disagree: Bayesian Backward Reasoning as a Label-Free Anchor for Multi-Agent Collective Decision-Making
Authors: Ken Chen, Wei Wang, Sachith Seneviratne, Hansani Weeratunge, Saman Halgamuge
Abstract
When multiple LLM agents yield conflicting answers, the decision-making process dictates whether agent diversity improves performance or merely compounds shared errors. Existing collective decision-making methods, including voting, electoral rules, and LLM judges, rely on forward reasoning: they map evidence to labels in one direction. Although these methods can combine diverse forward traces, they still aggregate estimates that share this evidence-to-label factorization and can inherit correlated errors within the forward pool. We therefore construct a reverse posterior for each instance through Bayesian backward reasoning from an explicit likelihood. The forward and reverse posteriors provide differently factorized approximations of the underlying posterior. Because estimates from different factorizations may tend to share the same error less often, we use Jensen-Shannon divergence to rank agents by cross-path consistency. This cross-path consistency signal underlies three strategies: hard selection (MinJS), soft reweighting (FwdJS), and log-linear fusion (LogLin). Evaluated on DDXPlus across five LLM backbones, our proposed strategies show consistent improvements: MinJS outperforms random selection across all backbones, FwdJS generally improves over the strongest baseline, and LogLin achieves the best performance among the evaluated methods, with its largest gains on the subset where the agents disagree. Despite its weaker standalone accuracy, the reverse posterior serves as a more useful anchor than forward-only alternatives, providing complementary information for collective decision-making. When labeled data are available, a lightweight two-stage calibration can further refine the reverse anchor and improve aggregation performance.
The rapid development of large language models (LLMs) has motivated research on decision-making in multi-agent systems, where multiple agents collaborate to achieve shared objectives. Existing aggregation approaches, such as voting and debate, are largely ad-hoc and lack formal guarantees regarding the informativeness of the resulting decisions. In this paper, we provide a principled approach to analyse decisions made in the multi-LLM setting using Blackwell's informativeness framework. Within the Blackwell information-structure abstraction, we show that voting and debate induce information structures that are no more informative than the pooled private information of all agents. This result identifies Bayesian pooled posterior maximisation as an information-theoretic upper-bound decision rule under the Blackwell ordering. Motivated by this theoretical analysis, we introduce a practical method for LLM-based question-answering (QA) tasks that estimates each agent's posterior and approximates the pooled posterior using a product-of-posteriors estimator. Extensive experiments on six QA benchmarks demonstrate that our approach outperforms state-of-the-art multi-LLM debate and voting methods.
Multi-agent systems (MAS) can substantially extend the reasoning capacity of large language models (LLMs). Most MAS frameworks aggregate agent outputs via simple majority voting, discarding the evidential structure of reasoning traces. Majority voting is brittle under confabulation consensus, where agents share correlated biases and converge on the same incorrect rationale. We introduce AgentAuditor, which moves beyond frequency-based aggregation by organizing agent traces into a Reasoning Tree that explicitly represents agreements and divergences in their reasoning. AgentAuditor resolves conflicts by comparing branch-level evidence at critical divergence points, turning global adjudication into efficient, localized verification. We further propose Anti-Consensus Preference Optimization (ACPO), which trains the adjudicator with evidence-verified preference supervision to reduce conformity to misleading majority cues. Across four MAS frameworks and multiple reasoning benchmarks, AgentAuditor consistently improves aggregation performance over majority voting, with gains of up to 5% absolute accuracy while remaining token-efficient.
Multi-agent debate (MAD) is a promising strategy for improving LLM reasoning, but when agents converge on a shared answer, it is unclear whether that convergence reflects genuine deliberation or social compliance. We show that the conventional answer flip rate conflates three distinct mechanisms: spontaneous instability, stance-induced conformity, and reasoning-induced persuasion. Our three-source decomposition framework isolates each through controlled counterfactual conditions. In the primary MMLU-Pro setting, 37% of agent-question observations change under self-reflection alone, while robustness tests show substantial model-dependent instability across GPQA-Diamond and three model families; strict conformity is 29% in the primary setting and remains predominantly harmful across model replications (57-77% correct-to-wrong). A controlled information-gradient experiment reveals that even vacuous reasoning is associated with 20-39% error adoption among resistant agents, with reasoning-like presentation carrying substantial persuasive weight. Harmful conformity can be predicted from Round 0 features (AUC = 0.79), and risk-targeted intervention reduces it by 13.6 percentage points (p < 0.001). However, without correctness labels or self-reflection controls, reducing peer adoption does not improve accuracy, because harmful and beneficial influence cannot be distinguished.