The Privacy Paradox and Optimal Bias-Variance Trade-offs in Data Acquisition

Whereas users claim to be concerned about privacy, often they do little to protect their privacy in their online actions. One prominent explanation for this privacy paradox is that, when an individual shares data, it is not just the individual's privacy that is compromised; the privacy of other individuals with correlated data is also compromised. This information leakage encourages oversharing of data and significantly impacts the incentives of individuals in online platforms. In this paper, we study the design of mechanisms for data acquisition in settings with information leakage and verifiable data. We design an incentive-compatible mechanism that optimizes the worst case trade-off between bias and variance of the estimation subject to a budget constraint, with which the worst case is over the unknown correlation between costs and data. Additionally, we characterize the structure of the optimal mechanism in closed form and study monotonicity and nonmonotonicity properties of the marketplace.