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.

中文翻译：

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隐私保护机制的前瞻理论分析

我们研究了隐私保护机制设计的问题。数据收集器希望从个人获取数据以执行一些计算。为了减轻对贡献者的隐私威胁，数据收集器采用了一种隐私保护机制，即在计算结果中添加随机噪声，但会降低准确性。面对隐私问题，个人决定是否提供数据。由于隐私保护的内在不确定性，我们使用前景理论对个人与隐私相关的决策进行建模。这种理论比传统的预期效用理论更准确地模拟了不确定性下的个人行为，后者的预测总是偏离实际的人类行为。我们表明，数据收集器的效用最大化问题涉及高阶和分数阶多项式，其根源很难进行分析计算。我们通过考虑较大的人口近似值来解决此问题，并获得一个很好地逼近精确解的闭式解。我们发现，与基于预期效用理论建模的案例相比，考虑更现实的基于前景理论的个人决策建模的数据收集器将采用更为保守的隐私保护机制。我们还研究了前景理论参数的影响，并得出结论，更多的规避损失或寻求风险的个人将触发更为保守的机制。当个体具有不同的前景理论参数时，模拟表明，隐私保护会随着异质性从低值到高值的增加而先增强然后减弱。