Optimal Privacy-Preserving Data Collection: A Prospect Theory Perspective

We study a mechanism design problem of privacy- preserving data collection with privacy protection uncertainty. A data collector wants to collect enough data to perform a certain computation that benefits the individuals who contribute the data, with the possibility of individual privacy leakage. The data collector adopts a privacy-preserving mechanism by adding some random noise to the computation result, which reduces the accuracy of the computation. Individuals decide whether to contribute data based on the potential benefit and the possible privacy cost induced by the mechanism. Due to the intrinsic uncertainty involved in privacy protection, we model individuals' privacy-aware participation using the prospect theory, which more accurately models individuals' behavior under uncertainty than the traditional expected utility theory. We show that the data collector's utility maximization problem involves a polynomial of high and fractional order, which is difficult to solve analytically. We get around this issue by proposing an approximation method, which allows us to obtain a closed form unique solution of the data collector's decision problem. We numerically show that the approximation error is small when the number of individuals is large. By comparing with the results under the expected utility theory, we conclude that a data collector who considers the more realistic prospect theory modeling should adopt a stricter privacy-preserving mechanism to boost her utility.