The paper proposes a Bayesian backward-reasoning method for aggregating decisions from multiple LLM agents, constructing reverse posteriors via explicit likelihood calculations rather than relying only on forward, evidence-to-label reasoning. It uses Jensen-Shannon divergence to measure cross-path consistency between forward and reverse estimates, yielding three aggregation strategies: MinJS (hard selection), FwdJS (soft reweighting), and LogLin (log-linear fusion). On medical decision-making tasks, all three consistently outperform baseline aggregation methods, with LogLin showing the largest gains when agents disagree.
