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.
This paper studies how to enforce differential privacy by using the randomized response in the data collection scenario. Given a client’s value, the randomized algorithm executed by the client reports to the untrusted server a perturbed value. The use of randomized response in surveys enables easy estimations of accurate population statistics while preserving the privacy of the individual respondents. We compare the randomized response with the standard Laplace mechanism which is based on query-output independent adding of Laplace noise. Our research starts from the simple case with one single binary attribute and extends to the general case with multiple polychotomous attributes. We measure utility preservation in terms of the mean squared error of the estimate for various calculations including individual value estimate, proportion estimate, and various derived statistics. We theoretically derive the explicit formula of the mean squared error of various derived statistics based on the randomized response theory and prove the randomized response outperforms the Laplace mechanism. We evaluate our algorithms on YesiWell database including sensitive biomarker data and social network relationships of patients. Empirical evaluation results show effectiveness of our proposed techniques. Especially the use of the randomized response for collecting data incurs fewer utility loss than the output perturbation when the sensitivity of functions is high.