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When Agents Disagree: Bayesian Backward Reasoning as a Label-Free Anchor for Multi-Agent Collective Decision-Making

arxiv.org · 8,967 words · saved by 1 readers

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

Ken Chen Affiliation: Department of Mechanical Engineering, The University of Melbourne, Melbourne, Australia Email: kenchen1@student.unimelb.edu.au Wei Wang Affiliation: Department of Mechanical Engineering, The University of Melbourne, Melbourne, Australia Sachith Seneviratne Affiliation: Department of Mechanical Engineering, The University of Melbourne, Melbourne, Australia Hansani Weeratunge Affiliation: Department of Mechanical Engineering, Sri Lanka Institute of Information Technology, Sri Lanka Saman Halgamuge Affiliation: Department of Mechanical Engineering, The University…

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