An emerging literature examines the critical question of when and how prediction can be useful in allocating scarce societal resources. We examine a novel variant of this question: What happens when predictive uncertainty differs systematically across the population? This can occur in several situations; for example, when machine learning models have significantly different accuracies across different demographics. We show that this uncertainty has serious implications for resource allocation when coupled with commonly used binary measures of societal benefit from allocation. We formulate a novel mathematical model of scarce resource allocation that accounts for heterogeneous predictive uncertainties and analyze implications for both the allocation mechanism and the realized population-level benefits. We find that when resources are very scarce, maximum marginal benefit (MMB) prioritization favors individuals with lower predictive uncertainty even at the identical underlying initial state. However, we observe a flip in prioritization when resources are abundant, targeting higher-uncertainty individuals. We illustrate the implications of our results on the PISA educational testing dataset. Our findings have meaningful ramifications for the distributional outcomes of prioritization policies in many domains touched by the theory of local justice, including the allocation of public education resources, medical triage, and homelessness services. They also reveal a new moral dilemma in the ethics of scarce resource allocation - is it just to allocate a resource to one person over another solely based on predictive uncertainty about their futures? We also assess efficiency losses under both MMB and the vulnerability-first (VF) prioritization. Our model predicts efficiency losses across all resource levels, but particularly in low-resource settings.

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