It may be a good idea to recall a few aspects of the literature concerning the problem of the estimation of Y yN i= ∑1 and of the variance or mean square error (MSE) of the estimator of Y when direct response (DR) survey data (s, yi|i ∈ s) are available straightaway. Recognizing that yis in the present context are not directly available but themselves are amenable to unbiased estimation in terms of randomized responses (RR) to be ingeniously procurable by appropriate means that fresh procedures are to be established for the estimation of Y and also of the measures of error of the requisite RR databased estimators for Y. There is of course a parallelism in the analogous problem in estimation by dint of multistage sampling when yi is treated as the first-stage unit totals to be estimated through sampling of units in subsequent stages when they are not directly ascertainable. However, there is crucial difference as we shall recount in greater detail in due course. Let us attempt at a review in the next section in quest of a right way to place the reader on the center of the situation in a well-equipped frame, to explore further developments in the right and ever-increasing directions.