CS-WCP: Robust Conformal Sets for LLM-Judge Traffic Shifts with Uncertain Group Proportions

Prediction sets built from an LLM judge can undercover when deployment traffic changes the prevalence of task or policy groups. Weighted conformal prediction is exact under covariate shift when the density ratio is known, but group proportions must usually be estimated from finite unlabeled samples. We introduce confidence-set weighted conformal prediction (CS-WCP), which constructs simultaneous exact intervals for source and target group masses and returns the union of weighted conformal sets over every compatible ratio vector. For a fixed or independently learned finite partition, CS-WCP attains coverage at least 1-alpha-delta_w-tau_A-kappa, where tau_A measures within-cell covariate mismatch and kappa measures conditional shift. A linear endpoint rule computes the robust union in O(G|Y|) time. Across 336 constructed shared-support traffic shifts, CS-WCP reaches 0.973 mean coverage with 13 point failures, compared with 0.954 and 44 failures for source conformal prediction, at mean binary set sizes 1.74 and 1.65. On 336 natural cross-task transfers, coverage rises from 0.882 to 0.962, but mean set size reaches 1.87 and a size-matched group plug-in baseline is competitive. The method therefore supplies an auditable coverage safeguard under uncertain mixture weights; its value is conservative tail protection, not scalar probability calibration or uniformly smaller sets.