Firms and statistical agencies must protect the privacy of the individuals whose data they collect, analyze, and publish. Increasingly, these organizations do so by using publication mechanisms that satisfy differential privacy. We consider the problem of choosing such a mechanism so as to maximize the value of its output to end users. We show that this is a constrained information design problem, and characterize its solution. When the underlying database is drawn from a symmetric distribution -- for instance, if individuals' data are i.i.d. -- we show that the problem's dimensionality can be reduced, and that its solution belongs to a simpler class of mechanisms. When, in addition, data users have supermodular payoffs, we show that the simple geometric mechanism is always optimal by using a novel comparative static that ranks information structures according to their usefulness in supermodular decision problems.
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