Causal Judge Evaluation: Calibrated Surrogate Metrics for LLM Systems

arXiv:2512.11150v3 Announce Type: replace-cross
Abstract: Measuring long-run LLM outcomes (user satisfaction, expert judgment, downstream KPIs) is expensive. Teams default to cheap LLM judges, but uncalibrated proxies can invert rankings entirely. Causal Judge Evaluation (CJE) makes it affordable to aim at the right target: calibrate cheap scores against a small oracle slice, then evaluate at scale with valid uncertainty. We treat surrogate validity as auditable: for each policy or deployment context, a small oracle audit tests whether the learned calibration remains mean-unbiased, turning an uncheckable identification condition into a falsifiable diagnostic. On 4,961 Chatbot Arena prompts comparing five policies with a 16x oracle/judge cost ratio, at a 5% oracle fraction CJE achieves 99% pairwise ranking accuracy at 14x lower cost; across all configurations (5-50% oracle, varying n), accuracy averages 94%. An adversarial policy fails the transport audit and is correctly flagged; in such cases CJE refuses level claims rather than reporting biased estimates. Key findings: naive confidence intervals on raw judge scores achieve 0% coverage (CJE: ~95%); importance-weighted estimators fail despite >90% effective sample size; and the Coverage-Limited Efficiency (CLE) bound and its TTC diagnostic explain why.