Information Design for Differential Privacy

Firms and statistical agencies that publish aggregate data face practical and legal requirements to protect the privacy of individuals. Increasingly, these organizations meet these standards by using publication mechanisms which 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 equivalent to a constrained information design problem, and characterize its solution. Moreover, we use a novel result on the comparison of information structures to show that the simple geometric mechanism is optimal whenever data users face supermodular decision problems