Performative Privacy Shows Differential Privacy Can Maximize Utility

The conventional wisdom is that privacy-preserving learning builds trust and encourages user participation, ultimately enhancing long-term utility. However, this claim has largely lacked formalization. This paper bridges this gap by introducing "performative privacy," a novel framework that integrates the concept of performative learning, where a system's deployment influences the data it subsequently observes. In this framework, data leakage directly leads to a reduction in future user participation. The study models a scenario where agents contribute data for mean estimation but may withdraw if their data is compromised. Differential privacy mechanisms are employed to protect data, creating a trade-off between the noise introduced for privacy and the potential for sustained participation. Through theoretical analysis and numerical experiments, the research demonstrates that, under conditions where the feedback loop between data leakage and participation is sufficiently strong, implementing a finite differential privacy budget can actually lead to superior long-term utility compared to non-private estimation. This provides the first formal evidence that differential privacy can be optimal not just for protection, but also for maximizing utility over time.