In the area of privacy-preserving data mining, a differentially private mechanism intuitively encourages people to share their data truthfully because they are at little risk of revealing their own information. However, we argue that this interpretation is incomplete because external incentives are necessary for people to participate in databases, and so data release mechanisms should not only be differentially private but also compatible with those incentives, otherwise the data collected may be false. We apply the notion of truthfulness from game theory. In certain settings, it turns out that existing differentially private mechanisms do not encourage participants to report their information truthfully. On the positive side, we exhibit a transformation that takes truthful mechanisms and transforms them into differentially private mechanisms that remain truthful. Our transformation applies to games where the type space is small and the goal is to optimize an insensitive quantity such as social welfare. Our transformation incurs only a small additive loss in optimality, and it is computationally efficient. Combined with the VCG mechanism, our transformation implies that there exists a differentially private, truthful, and approximately efficient mechanism for any social welfare game with small type space. We also study a model where an explicit numerical cost is assigned to the information leaked by a mechanism. We show that in this case, even differential privacy may not be strong enough of a notion to motivate people to participate truthfully. We show that mechanisms that release a perturbed histogram of the database may reveal too much information. We also show that, in general, any mechanism that outputs a synopsis that resembles the original database (such as the mechanism of Blum et al. (STOC ’08)) may reveal too much information. Of independent interest, one corollary of our techniques is a new lower bound on the sample complexity of differentially private non-interactive synopsis generators
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