Certified Decisions
Isaiah Andrews, Jiafeng Chen
TL;DR
This work develops a theory of certified decisions by attaching high-probability loss bounds, or P-certificates, to recommended actions and analyzes how ambiguity-averse downstream decision-makers use these certificates to control risk. It shows that, under mild assumptions, the optimal adoption rule is a simple threshold on the certificate, and that any P-certified decision can be represented by as-if optimization against a confidence set, establishing an essentially complete class. The paper further extends the framework to E-certificates based on e-values, proving analogous dominance results and robust guarantees even with unbounded losses. Collectively, these results connect classical frequentist inference with decision-making in a way that yields practical, implementable guidance for risk-controlled adoption of data-driven recommendations, and link to conformal inference and related approaches.
Abstract
Hypothesis tests and confidence intervals are ubiquitous in empirical research, yet their connection to subsequent decision-making is often unclear. We develop a theory of certified decisions that pairs recommended decisions with inferential guarantees. Specifically, we attach P-certificates -- upper bounds on loss that hold with probability at least $1-α$ -- to recommended actions. We show that such certificates allow "safe," risk-controlling adoption decisions for ambiguity-averse downstream decision-makers. We further prove that it is without loss to limit attention to P-certificates arising as minimax decisions over confidence sets, or what Manski (2021) terms "as-if decisions with a set estimate." A parallel argument applies to E-certified decisions obtained from e-values in settings with unbounded loss.