Privacy Preserving Signals

54 Pages Posted: 5 Jun 2023 Last revised: 26 Feb 2024

See all articles by Philipp Strack

Philipp Strack

Yale, Department of Economics

Kai Hao Yang

Yale School of Management

Date Written: February 25, 2024


A signal is privacy-preserving with respect to a collection of privacy sets, if the posterior probability assigned to every privacy set remains unchanged conditional on any signal realization. We characterize the privacy-preserving signals for arbitrary state space and arbitrary privacy sets. A signal is privacy-preserving if and only if it is a garbling of a reordered quantile signal. These signals are equivalent to couplings, which in turn lead to a characterization of optimal privacy-preserving signals as solutions to an optimal transport problem. We discuss the economic implications of our characterization for statistical discrimination, the revelation of sensitive information in auctions, monopoly pricing, and price discrimination.

Keywords: Privacy-preserving signal, privacy sets, independence, reordered quantile signal, protected characteristics.

JEL Classification: C11, D63, D42, D83

Suggested Citation

Strack, Philipp and Yang, Kai Hao, Privacy Preserving Signals (February 25, 2024). Available at SSRN: or

Philipp Strack (Contact Author)

Yale, Department of Economics ( email )

28 Hillhouse Ave
New Haven, CT 06520-8268
United States

Kai Hao Yang

Yale School of Management ( email )

165 Whitney Ave
New Haven, CT 06511

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