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A Closed-Form Estimator and Diagnostic Battery for Anchor-Judge Error Correlation, Under a Single-Common-Factor Model

arXiv · AI, language, vision and robotics · article · Sep 8, 2026 · UTC

When an external reference set (an anchor) is used to decompose an LLM-judge panel's error into a quality signal and a shared common-mode error, standard practice assumes the anchor is uncontaminated: its error uncorrelated with the judges' shared error. We study when that assumption can be dropped and replaced by an estimate. Under a single-common-factor model, >=2 judges and >=2 anchors point-identify the quality variance, the common-mode variance, and each anchor's contamination correlation rho_k in closed form, with an exact per-anchor-pair failure boundary; a designated clean-anchor estim

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