Optimal Differentially Private Mechanisms for Randomised Response

TL;DR

This paper investigates optimal mechanisms for randomized response under differential privacy, providing closed-form solutions for both strict and relaxed privacy constraints, including the classic Warner technique.

Contribution

It introduces a unified framework for optimal randomized response mechanisms under differential privacy, extending classical methods with new optimal solutions.

Findings

Closed-form solutions for optimal mechanisms under strict and relaxed privacy.

Optimal mechanism for Warner's original randomized response.

Analysis of error bounds for statistical estimators.

Abstract

We examine a generalised Randomised Response (RR) technique in the context of differential privacy and examine the optimality of such mechanisms. Strict and relaxed differential privacy are considered for binary outputs. By examining the error of a statistical estimator, we present closed solutions for the optimal mechanism(s) in both cases. The optimal mechanism is also given for the specific case of the original RR technique as introduced by Warner in 1965.