Privacy Preserving Signals

Kai Hao Yang and Philipp Strack
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Kai Hao Yang: Yale University
Philipp Strack: Yale University

No 2379, Cowles Foundation Discussion Papers from Cowles Foundation for Research in Economics, Yale University

Abstract: 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 for a decision-maker. We demonstrate the applications of this characterization in the contexts of algorithmic fairness, price discrimination, and information design.

Pages: 45 pages
Date: 2023-07-03
New Economics Papers: this item is included in nep-gth and nep-mic
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