Buying Private Data without Verification

Arpita Ghosh, Katrina Ligett, Aaron Roth, Grant Schoenebeck


We design a differentially private peer-prediction mechanism that supports accurate estimation of the population statistic as a Bayes-Nash equilibrium in settings where agents have explicit preferences for privacy. The mechanism requires knowledge of the marginal prior distribution on bits, but does not need full knowledge of the marginal distribution on the costs, instead requiring only an approximate upper bound. Our mechanism guarantees differential privacy to each agent against any adversary who can observe the statistical estimate output by the mechanism, as well as the payments made to the n-1 other agents. Finally, we show that with slightly more structured assumptions on the privacy cost functions of each agent, the cost of running the survey goes to 0 as the number of agents diverges.