  Algorithmic predictions are emerging as a promising solution concept for
efficiently allocating societal resources. Fueling their use is an underlying
assumption that such systems are necessary to identify individuals for
interventions. We propose a principled framework for assessing this assumption:
Using a simple mathematical model, we evaluate the efficacy of prediction-based
allocations in settings where individuals belong to larger units such as
hospitals, neighborhoods, or schools. We find that prediction-based allocations
outperform baseline methods using aggregate unit-level statistics only when
between-unit inequality is low and the intervention budget is high. Our results
hold for a wide range of settings for the price of prediction, treatment effect
heterogeneity, and unit-level statistics' learnability. Combined, we highlight
the potential limits to improving the efficacy of interventions through
prediction.
