# Buying Private Data without Verification

arXiv: https://arxiv.org/abs/1404.6003 · HTML: https://mlsanity.com/paper/1404.6003/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Apr 2014.

## Built on by (most cited first, 8 of 8)

- [Optimal and Differentially Private Data Acquisition: Central and Local Mechanisms](https://mlsanity.com/paper/2201.03968/) (2022)
- [FL-Market: Trading Private Models in Federated Learning](https://mlsanity.com/paper/2106.04384/) (2021)
- [A Survey of Data Pricing for Data Marketplaces](https://mlsanity.com/paper/2303.04810/) (2023)
- [Optimal Scoring Rule Design under Partial Knowledge](https://mlsanity.com/paper/2107.07420/) (2021)
- [Collaborative Mean Estimation Among Heterogeneous Strategic Agents: Individual Rationality, Fairness, and Truthful Contribution](https://mlsanity.com/paper/2407.15881/) (2024)
- [Striking a Balance: An Optimal Mechanism Design for Heterogenous Differentially Private Data Acquisition for Logistic Regression](https://mlsanity.com/paper/2309.10340/) (2023)
- [Truthful Generalized Linear Models](https://mlsanity.com/paper/2209.07815/) (2022)
- [A Cram'er-von Mises Approach to Incentivizing Truthful Data Sharing](https://mlsanity.com/paper/2506.07272/) (2025)

## Abstract (arXiv)

We consider the problem of designing a survey to aggregate non-verifiable information from a privacy-sensitive population: an analyst wants to compute some aggregate statistic from the private bits held by each member of a population, but cannot verify the correctness of the bits reported by participants in his survey. Individuals in the population are strategic agents with a cost for privacy, ie, they not only account for the payments they expect to receive from the mechanism, but also their privacy costs from any information revealed about them by the mechanism's outcome---the computed statistic as well as the payments---to determine their utilities. How can the analyst design payments to obtain an accurate estimate of the population statistic when individuals strategically decide both whether to participate and whether to truthfully report their sensitive information? 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 bi, but does not need full knowledge of the marginal distribution on the costs ci, instead requiring only an approximate upper bound. Our mechanism guarantees ε-differential privacy to each agent i 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 jneq i. 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.