Information Design for Differential Privacy

Firms and statistical agencies that publish or collect data face practical and legal requirements to protect the privacy of individuals. Increasingly, these organizations meet these standards 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.