Effects of Privacy-Inducing Noise on Welfare and Influence of Referendum Systems

TL;DR

This paper investigates how increasing privacy guarantees through noise affects social welfare and influence in referendum systems, revealing an inverse relationship between privacy levels and both welfare and influence.

Contribution

It provides a theoretical analysis of the trade-offs between differential privacy, influence, and welfare in referendum settings using the randomized response mechanism.

Findings

Welfare decreases as privacy increases

Influence diminishes with higher privacy levels

Inverse proportionality between privacy and both welfare and influence

Abstract

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.