  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.
