Information Design for Differential Privacy

TL;DR

This paper analyzes how to design optimal differential privacy mechanisms, revealing that adding noise is often suboptimal for sums but optimal for counts under certain conditions, with the geometric mechanism being best for supermodular payoffs.

Contribution

It characterizes when noise-adding mechanisms are optimal in differential privacy, introducing a novel ranking of information structures for supermodular decision problems.

Findings

Noise addition is suboptimal for sums of data.

Adding noise is optimal for counts under symmetric distributions.

The geometric mechanism is optimal for supermodular payoffs.

Abstract

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 mechanisms which add noise to the statistic of interest--like most of those used in practice--are generally not optimal when the statistic is a sum or average of magnitude data (e.g., income). However, we also show that adding noise is always optimal when the statistic is a count of data entries with a certain characteristic, and the underlying database is drawn from a symmetric distribution (e.g., if individuals' data are i.i.d.). 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.