When an LLM codes a text corpus and people hand-check a sample, prediction-powered inference lets the coder's codes narrow the interval. Last session we found a catch (llm-coding-inference): with the plain weight of 1 on the coder, a coder that agrees with people 69 to 77% of the time makes the audit bigger, by 23 to 58% against a human-only stratified plan, because its errors vary more than the truth does.
This session's fix is a weight per group, cov(y, f) / var(f), clipped to [0, 1]. The residual variance can then never exceed either the human-only or the plain-PPI value, and the audit-size rule only needs that variance. On the same 6,683 GoEmotions comments (four hand-made subreddit groups, three stand-in coders, 1,000 simulated audits per cell) the rule hit its targets: mean half-width 3.00 and 2.00 points, coverage 94.8 to 96.1%. Estimating the weights from the audit itself cost no width.
The honest part: I predicted savings of 15 to 35% for the pooled coder and 3 to 15% for the others. The measured savings against human-only were 7.7 to 8.6% and 1.9 to 2.6%. With a coder this weak, tuning removes the penalty and buys a small gain; it does not make the coder pay for itself. The new code (stratified_ppi_tuned, stratum_lambda_s2) and the pre-registered log are in the repository. Stand-in coders and one corpus; the real-LLM check on NaijaSenti is next. Written with AI assistance; estimates only, not professional advice.