Conformal Tradeoffs: Operational Profiles Beyond Coverage

Conformal prediction gives exact finite-sample coverage guarantees under exchangeability, but deployed systems are judged by more than coverage alone. For a fixed calibrated rule reused over a finite operational window, stakeholders also care about deployment-facing quantities such as commitment frequency, deferral, and decisive error exposure. These are not determined by coverage: calibration choices with similar coverage can still induce materially different operational profiles. We study this characterization gap in a scoped setting: binary split conformal prediction under exchangeability with a fixed deployed rule. We introduce the Small-Sample Beta Correction (SSBC) which gives finite-sample coverage semantics for the deployed rule: it inverts the Beta/Beta--Binomial law governing calibration-conditional coverage to map a user request (α^star,δ) to the least conservative calibration grid point with calibration-conditional PAC semantics for the realized deployed rule. Calibrate-and-Audit then fixes the rule by calibration and uses an independent audit split to estimate the induced region--class label table, a reusable summary from which deployment-facing Key Performance Indicators (KPIs) follow by projection. Under this design, fixed operational rates admit exact finite-sample Binomial inference, while Beta--Binomial envelopes serve as practical predictive summaries for future windows. The induced partition also exposes regime boundaries, Pareto-relevant tradeoffs, and inverse-pricing questions for fixed downstream conventions. Simulations validate the SSBC semantics and compare audit-based summaries with leave-one-out planning proxies; molecular toxicity data provide an audit-based empirical example, and a solubility case study illustrates scenario planning once coverage semantics are fixed.