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Artificial intelligence, machine learning, and algorithmic techniques in general, provide two crucial abilities with the potential to improve decision-making in the context of allocation of scarce societal resources. They have the ability to flexibly and accurately model treatment response at the individual level, potentially allowing us to better match available resources to individuals. In addition, they have the ability to reason simultaneously about the effects of matching sets of scarce resources to populations of individuals. In this work, we leverage these abilities to study algorithmic allocation of scarce societal resources in the context of homelessness. In communities throughout the United States, there is constant demand for an array of homeless services intended to address different levels of need. Allocations of housing services must match households to appropriate services that continuously fluctuate in availability, while inefficiencies in allocation could “waste” scarce resources as households will remain in-need and re-enter the homeless system, increasing the overall demand for homeless services. This complex allocation problem introduces novel technical and ethical challenges. Using administrative data from a regional homeless system, we formulate the problem of “optimal” allocation of resources given data on households with need for homeless services. The optimization problem aims to allocate available resources such that predicted probabilities of household re-entry are minimized. The key element of this work is its use of a counterfactual prediction approach that predicts household probabilities of re-entry into homeless services if assigned to each service. Through these counterfactual predictions, we find that this approach has the potential to improve the efficiency of the homeless system by reducing re-entry, and, therefore, system-wide demand. However, efficiency comes with trade-offs - a significant fraction of households are assigned to services that increase probability of re-entry. To address this issue as well as the inherent fairness considerations present in any context where there are insufficient resources to meet demand, we discuss the efficiency, equity, and fairness issues that arise in our work and consider potential implications for homeless policies.