Finite Audits of Model Updating: Coverage and Resolution of Paired Disparity Comparisons

arXiv:2609.09788v2 Announce Type: replace Abstract: Finite audits can become more precise and decisive without reliably covering the change in subgroup disparity. We study the updating-minus-frozen difference in absolute subgroup gaps, averaged over a fixed history, for true-positive and false-positive rates separately. Controlled paired-count experiments and independent audits of retained model histories distinguish interval coverage, erroneous conclusions and decision resolution. With a zero frozen gap and a five-percentage-point updating gap, bootstrap coverage is 12.0%; a numerical-delta alternative improves coverage to 52.9%, still far below the nominal 95%, with 500 smaller-group and 2,000 other-group observations of the specified outcome per window over ten windows. Unequal absolute-gap biases explain point-estimate displacement, and gap direction changes pairing's variance contribution. Prior strength materially affects sparse, off-centre comparisons. In the retained panel, relatively high mean coverage coexists with substantial undercoverage for individual histories, while larger audits can considerably improve resolution. Conservative projection provides conditional coverage under the sampling assumptions but often leaves comparisons unresolved. These findings show why interval width and conclusive margin decisions cannot, by themselves, establish the reliability of an estimated disparity change.