Determine width ordering outside the sufficient dominance region

Determine whether the Joint mean/disagreement confidence interval has smaller expected width than exact pooled uniform inference for fixed cohorts whose mean disagreement lies outside the sufficient finite-cohort dominance region.

Background

The paper proves a sufficient condition under which the Joint interval, based on the sampled mean and within-task disagreement count, has no larger expected width than exact pooled uniform inference. The condition is expressed through the full-cohort positive-count total and the average probability of disagreement between two distinct paths within a task.

The sufficient condition is not claimed to be necessary. For cohorts outside this region, the theorem does not determine which design produces the narrower expected interval, leaving the finite-width comparison unresolved.

References

Outside the sufficient region, the width ordering remains an empirical question.

— Sharp Limits for Honest Uncertainty in Hard-Budget Repeated Evaluation  (2609.29140 - Cheng et al., 24 Sep 2026) in Section “Sharp certification laws,” subsection “Finite-regime boundary”