Removable Defects: The Economics and Limits of Deliberate Deficiency

Abstract

A specialist tolerates blind spots that a generalist does not. Usually this is treated as a cost to be minimized. We treat it as a design variable: a deficiency can be kept because it pays and removed on demand in the rare situation where it would be fatal, by routing to a compensation channel. We give three results. First, an advantage condition under which keeping the deficiency is a computable economic position; structurally it is the Ehrlich-Becker market-vs-self-insurance margin applied to a competence gap, with the detector as a Townsend costly-state-verification technology. Second, a two-sided characterization of removability. A coupling lemma shows that when the deficiency is a coarsening of perception, no switch can separate benefit from harm, yielding a converse (a confounded detector earns zero premium, and any within-defect policy insisting on positive premium is driven, under multiplicative dynamics, to negative long-run growth) and an achievability result (a detector outside the deficiency earns a positive premium). Together, over structured uncertainty classes with severity capped or miss rate O(1/L): a defect is profitably removable iff the detector-relevant distinction survives the restriction and the advantage condition holds; the premium is the support function of the class's ROC set at an economic price vector. Third, observation defects and capacity defects differ exactly on whether access to the deployment distribution rescues them; the gap decomposes as cross-leak plus a closure deficit, and per-task randomization buys back the latter, never the former. The detector can be learned from declared fatal categories at a training bill linear in loss severity (up to a log factor). The results synthesize Chow's reject option, Kelly growth under ruin, and selective prediction.