Social choice functions help aggregate individual preferences while differentially private mechanisms provide formal privacy guarantees to release answers of queries operating on sensitive data. However, preserving differential privacy requires introducing noise to the system, and therefore may lead to undesired byproducts. Does an increase in the level of differential privacy for releasing the outputs of social choice functions increase or decrease the level of influence and welfare, and at what rate? In this paper, we mainly address this question in more precise terms in a referendum setting with two candidates when the celebrated randomized response mechanism is used. We show that there is an inversely-proportional relation between welfare and privacy, and also influence and privacy.

翻译：社会选择函数有助于聚合个体偏好，而差分隐私机制为在敏感数据上运行查询的答案发布提供了形式化的隐私保障。然而，保护差分隐私需要向系统引入噪声，因此可能导致不良的副作用。在释放社会选择函数输出时提高差分隐私水平，是否会增加或降低影响力与福利水平？其变化速率如何？本文主要针对这一问题的更精确表述，聚焦于在两个候选人的全民公决场景中，采用著名的随机响应机制时进行探讨。我们证明，福利与隐私之间、以及影响力与隐私之间存在反比关系。