Odds Law

Theory of partially correlated verifier cascades in LLM harnesses: concave log-odds and reliability ceilings

A new arXiv preprint provides a formal theory of serial verification gates in LLM harnesses when verifiers are partially correlated, closing an open problem noted in the recent Odds Law paper (arXiv:2606.15712). Using a de Finetti latent-variable model for per-instance false-accept rates, the authors derive that cascade reliability grows only polynomially (not exponentially) under correlation, that blind-spot atoms impose hard ceilings on extractable evidence, and that adding more gates can sometimes actively harm reliability. Synthetic experiments show independence-based extrapolation underestimates failure by 20x at k=5 and ~3000x at k=10, with the practical implication that decorrelation (changing model family, modality, or evidence source) is the correct lever, not adding more gates.