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This approach is typically cheaper and faster than traditional screening procedures that directly observe the latent vulnerability status through physical verification. Yet, even access to the true conditional vulnerability probability cannot eliminate misallocation: aleatoric uncertainty over individual vulnerability status is irreducible, and probabilistic targeting inevitably misallocates some resources. In this work we study how screening and algorithmic targeting should be optimally combined in a two-stage allocation framework where a screening stage observes true outcomes for a subset of units before a final allocation stage assigns the resource under a fixed coverage budget. 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