  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.
