Effects of Privacy-Inducing Noise on Welfare and Influence of Referendum Systems
This work addresses the trade-off between privacy and social choice outcomes for referendum systems, but it is incremental as it focuses on a specific mechanism and setting.
The paper investigates how differential privacy noise affects welfare and influence in two-candidate referendum systems using randomized response, finding an inversely proportional relationship between both welfare and privacy, and influence and privacy.
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.