Reweighting Correlated Voters Does Not Repair Agreement Confidence: Structural Inertness and a Recalibration Control

Agreement among voters — a model with itself, or a panel with each other — is the default confidence signal in LLM systems, and it is documented to be an unreliable one. The standard remedy for correlated voters is to reweight them toward fewer effective votes. This note asks whether that remedy transfers from the decision to the confidence, and finds that it does not. Reanalysing a cached panel of ten real LLM writers (four models, three vendors; 80 items, 57 answerable) at zero API cost, agreement confidence is overconfident by 15.3 points: mean confidence 74.9% against 59.6% accuracy. Three weighting schemes — a free provenance-by-model rule, learned independence weights, and an oracle fitted on all items — leave that at 14.9, 15.3 and 13.6 points respectively, and no interval on any calibration delta excludes zero. Across 3,000 realistically composed panels per size, weighting removes 3.4–12.2% of the overconfidence and enlarges it on 14–36% of panels. We give the structural reason it cannot do better: when a panel's model multiplicities are balanced, provenance weights are uniform and the weighted confidence is bit-identical to the naive one. That case includes self-consistency, the most common ensemble and the worst-calibrated composition measured here at 31.6 points. An out-of-fold monotone recalibration removes 14.0 of the 15.3 points, but yields no Brier improvement and cannot improve ranking. Decision repair and calibration repair act on different terms, and the discrimination residual is moved by neither.