Ranking agents by cross-path consistency between forward and backward reasoning beats voting and LLM judges when agents disagree

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arXiv 2609.11709 (submitted 2026-09-10) argues that voting, electoral rules and LLM judges all aggregate forward evidence-to-label reasoning and therefore inherit correlated errors from a shared factorization. It builds a reverse posterior per instance via Bayesian backward reasoning from an explicit likelihood, then ranks agents by Jensen-Shannon divergence between the two posteriors, yielding three strategies: hard selection, soft reweighting, and log-linear fusion. On DDXPlus across five backbones the log-linear fusion performs best, with its largest gains precisely on the subset where the agents disagree, even though the reverse posterior alone is the weaker standalone predictor.