Private Private Information
For researchers in information theory and economics, this provides a formal framework for privacy-preserving information sharing, though the contribution is theoretical and incremental.
The paper introduces 'private private signals' that carry information about an unknown state but not about other signals, characterizing optimal signals that maximize informativeness under this privacy constraint. It discusses implications for recommendation systems, information design, causal inference, and mechanism design.
Private signals model noisy information about an unknown state. Although these signals are called "private," they may still carry information about each other. Our paper introduces the concept of private private signals, which contain information about the state but not about other signals. To achieve privacy, signal quality may need to be sacrificed. We study the informativeness of private private signals and characterize those that are optimal in the sense that they cannot be made more informative without violating privacy. We discuss implications for privacy in recommendation systems, information design, causal inference, and mechanism design.