  Post-processing immunity is a fundamental property of differential privacy:
it enables arbitrary data-independent transformations to differentially private
outputs without affecting their privacy guarantees. Post-processing is
routinely applied in data-release applications, including census data, which
are then used to make allocations with substantial societal impacts. This paper
shows that post-processing causes disparate impacts on individuals or groups
and analyzes two critical settings: the release of differentially private
datasets and the use of such private datasets for downstream decisions, such as
the allocation of funds informed by US Census data. In the first setting, the
paper proposes tight bounds on the unfairness of traditional post-processing
mechanisms, giving a unique tool to decision-makers to quantify the disparate
impacts introduced by their release. In the second setting, this paper proposes
a novel post-processing mechanism that is (approximately) optimal under
different fairness metrics, either reducing fairness issues substantially or
reducing the cost of privacy. The theoretical analysis is complemented with
numerical simulations on Census data.
