Robust measles vaccine allocation in US schools requires hedging against unmeasured introduction risk

The United States is on the verge of losing measles elimination status, and the doses that could prevent it are already committed; what is still open is which schools get them first. Allocation theory answers that by ordering schools on marginal herd-immunity return rather than lowest coverage, and across 36,031 US schools the theorem's binding case is the common one: two thirds to three quarters of susceptible kindergarteners attend schools where each added dose buys increasing herd immunity. That ordering returns 1.92 times the indirect protection of lowest-coverage-first, or 1.16 times the total protection. But it assumes every school is equally likely to see a case. Pre-outbreak records from the 2025-26 Upstate South Carolina outbreak are inconsistent with that premise: exposed schools are over-represented 5.0-fold in the top decile of susceptible headcount (95% CI 3.0 to 7.3), while enrollment, a negative control carrying school size but not susceptibility, shows none. An independent outbreak in Clark County, Washington reproduces the scaling, but only two US jurisdictions publish records permitting this test, so how steeply risk scales is unidentified nationally. Under that uncertainty the theoretically optimal rule is the least robust of seven we evaluate, losing 86% of attainable benefit in its worst case, and that fragility holds however the uncertainty set is drawn. A light hedge on measured risk holds roughly 90% at the primary budget, computed from the two columns states already publish. Wherever targeting is optimized on a well-measured variable while exposure risk goes unmeasured, the point-estimate optimum is the fragile choice.