  Post-processing immunity is a fundamental property of differential privacy:
it enables the application of arbitrary data-independent transformations to the
results of differentially private outputs without affecting their privacy
guarantees. When query outputs must satisfy domain constraints, post-processing
can be used to project the privacy-preserving outputs onto the feasible region.
Moreover, when the feasible region is convex, a widely adopted class of
post-processing steps is also guaranteed to improve accuracy. Post-processing
has been applied successfully in many applications including census
data-release, energy systems, and mobility. However, its effects on the noise
distribution is poorly understood: It is often argued that post-processing may
introduce bias and increase variance. This paper takes a first step towards
understanding the properties of post-processing. It considers the release of
census data and examines, both theoretically and empirically, the behavior of a
widely adopted class of post-processing functions.
