When Agents Disagree: Bayesian Backward Reasoning as a Label-Free Anchor for Multi-Agent Collective Decision-Making
Ken Chen, Saman Halgamuge and colleagues (University of Melbourne) resolve disagreement between LLM agents by comparing each agent's forward answer with a posterior computed by Bayesian backward reasoning, which is less likely to share the same errors.
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Problem: Voting, electoral rules and LLM judges all aggregate forward evidence-to-label reasoning, so they can inherit errors that are correlated across agents.
Reverse posterior: For each instance a posterior is built by reasoning backward from an explicit likelihood, which factorizes the problem differently from forward reasoning.
Three aggregation strategies: Agents are ranked by Jensen-Shannon divergence between forward and reverse paths, then used for hard selection (MinJS), soft reweighting (FwdJS) or log-linear fusion (LogLin).
Results: On DDXPlus with five LLM backbones, LogLin performs best, with its largest gains where agents disagree. The reverse posterior is weaker on its own but is the more useful anchor.
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.