Selling Privacy at Auction (1011.1375v4)

Abstract: We initiate the study of markets for private data, though the lens of differential privacy. Although the purchase and sale of private data has already begun on a large scale, a theory of privacy as a commodity is missing. In this paper, we propose to build such a theory. Specifically, we consider a setting in which a data analyst wishes to buy information from a population from which he can estimate some statistic. The analyst wishes to obtain an accurate estimate cheaply. On the other hand, the owners of the private data experience some cost for their loss of privacy, and must be compensated for this loss. Agents are selfish, and wish to maximize their profit, so our goal is to design truthful mechanisms. Our main result is that such auctions can naturally be viewed and optimally solved as variants of multi-unit procurement auctions. Based on this result, we derive auctions for two natural settings which are optimal up to small constant factors: 1. In the setting in which the data analyst has a fixed accuracy goal, we show that an application of the classic Vickrey auction achieves the analyst's accuracy goal while minimizing his total payment. 2. In the setting in which the data analyst has a fixed budget, we give a mechanism which maximizes the accuracy of the resulting estimate while guaranteeing that the resulting sum payments do not exceed the analysts budget. In both cases, our comparison class is the set of envy-free mechanisms, which correspond to the natural class of fixed-price mechanisms in our setting. In both of these results, we ignore the privacy cost due to possible correlations between an individuals private data and his valuation for privacy itself. We then show that generically, no individually rational mechanism can compensate individuals for the privacy loss incurred due to their reported valuations for privacy.

• The paper models the procurement of private data as an auction, quantifying privacy losses via differential privacy.
• The paper devises optimal auction designs that achieve fixed accuracy levels and budget-efficient data acquisition through VCG and truthful mechanisms.
• The paper proves that without bounded privacy valuations, no mechanism can ensure both individual rationality and non-trivial accuracy, highlighting inherent trade-offs.

An Overview of "Selling Privacy at Auction" by Arpita Ghosh and Aaron Roth

The paper "Selling Privacy at Auction," authored by Arpita Ghosh and Aaron Roth, explores the conceptualization and mathematical modeling of markets for private data using the framework of differential privacy. The authors approach this emerging problem by introducing and analyzing mechanisms for procuring private information while balancing two competing objectives: maintaining data privacy and achieving accurate estimations of underlying population metrics. This work effectively establishes the foundation for treating privacy as a quantifiable commodity that can be traded in an auction-based mechanism.

Key Contributions

1. Modeling Privacy Markets: The authors initiate the paper by framing the problem of procuring private data as a specialized multi-unit procurement auction. They consider a data analyst who seeks to buy empirical data to compute population statistics while the data owners incur costs proportional to their privacy losses. The auction is formulated under two scenarios: minimizing payment for a fixed accuracy level and maximizing accuracy subject to a budget constraint. The use of differential privacy provides a quantifiable measure for the privacy costs faced by individuals.
2. Optimal Auction Design: The paper offers optimal auctions, accurate up to small constant factors, for the scenarios described. When aiming for fixed accuracy, the VCG mechanism is shown to be practical within the class of envy-free mechanisms. For the budget-oriented scenario, a truthful mechanism is introduced that maximizes data accuracy in conjunction with a fixed budget, benchmarked against fixed-price mechanisms.
3. Impossibility of Stringent Privacy Guarantees: A significant theoretical finding is the authors’ demonstration of the limitations of ensuring strong privacy within certain models. They prove that no mechanism can be both individually rational and achieve non-trivial accuracy under more stringent privacy assumptions unless the valuations for privacy are bounded. This highlights the critical trade-offs in designing practical privacy-protecting mechanisms.

Theoretical and Practical Implications

The results present notable implications in both theoretical and practical dimensions. Theoretically, the paper deepens the understanding of privacy as a quantifiable resource within a formal economic structure. It also challenges the community to consider new models and techniques for ensuring privacy without sacrificing practical utility. Practically, the insights on auction-based data procurement offer a potential path forward for companies and institutions that seek to monetize or utilize sensitive data in a privacy-preserving manner, laying groundwork for future applications in data markets.

Future Directions

Several avenues for future investigation emerge from this work. A significant open question involves the development of mechanisms that can effectively incorporate the valuations individuals place on their data privacy in real-world applications. As digital ecosystems continue to grow and aggregate vast amounts of personal data, designing effective and equitable systems for data transaction will be critical. Moreover, exploring potential frameworks for multi-analyst scenarios, where multiple entities compete to procure private data, offers an intriguing direction that would add depth and applicability to this burgeoning field.

In conclusion, "Selling Privacy at Auction" represents a pivotal step in formalizing the economics of privacy and contributes foundational insights necessary for bridging the gap between theoretical privacy guarantees and practical data usage in the digital age. The ongoing discourse informed by this research will further enhance our understanding of privacy economics and guide the development of robust, privacy-aware data systems.