Privacy, Prediction, and Allocation

Ben Jacobsen, Nitin Kohli

Abstract:

Algorithmic predictions are increasingly used to inform the allocation of scarce resources.
The promise of these methods is that, through machine learning, they can better identify
the people who would benefit most from interventions. Recently, however, several works
have called this assumption into question by demonstrating the existence of settings where
simple, unit-level allocation strategies can meet or even exceed the performance of those
based on individual-level targeting. Separately, other works have objected to individual-
level targeting on privacy grounds, leading to an unusual situation where a single solution,
unit-level targeting, is recommended for reasons of both privacy and utility. Motivated
by the desire to fully understand the interplay of privacy and targeting levels, we initiate
the study of aid allocation systems that satisfy differential privacy, synthesizing existing
works on private optimization with the economic models of aid allocation used in the non-
private literature. To this end, we investigate private variants of both individual and unit-
level allocation strategies in both stochastic and distribution-free settings under a range
of constraints on data availability. Through this analysis, we provide clean, interpretable
bounds characterizing the tradeoffs between privacy, efficiency, and targeting precision in
allocation.