Prospect Theoretic Analysis of Privacy-Preserving Mechanism

TL;DR

This paper models individuals' privacy-related decisions using Prospect Theory to analyze how a data collector can design privacy-preserving mechanisms, revealing more conservative strategies under realistic behavioral assumptions and the effects of individual heterogeneity.

Contribution

It introduces Prospect Theory into privacy mechanism design, providing a closed-form solution and analyzing the impact of behavioral parameters on privacy strategies.

Findings

Prospect Theory leads to more conservative privacy mechanisms.

Risk attitudes influence the level of privacy protection.

Heterogeneity in individuals' preferences affects privacy outcomes.

Abstract

We study a problem of privacy-preserving mechanism design. A data collector wants to obtain data from individuals to perform some computations. To relieve the privacy threat to the contributors, the data collector adopts a privacy-preserving mechanism by adding random noise to the computation result, at the cost of reduced accuracy. Individuals decide whether to contribute data when faced with the privacy issue. Due to the intrinsic uncertainty in privacy protection, we model individuals' privacy-related decision using Prospect Theory. Such a theory more accurately models individuals' behavior under uncertainty than the traditional expected utility theory, whose prediction always deviates from practical human behavior. We show that the data collector's utility maximization problem involves a polynomial of high and fractional order, the root of which is difficult to compute analytically. We get around this issue by considering a large population approximation, and obtain a closed-form solution that well approximates the precise solution. We discover that the data collector who considers the more realistic Prospect Theory based individual decision modeling would adopt a more conservative privacy-preserving mechanism, compared with the case based on the expected utility theory modeling. We also study the impact of Prospect Theory parameters, and concludes that more loss-averse or risk-seeking individuals will trigger a more conservative mechanism. When individuals have different Prospect Theory parameters, simulations demonstrate that the privacy protection first becomes stronger and then becomes weaker as the heterogeneity increases from a low value to a high one.