ABSTRACT
In their research book, Chaudhuri and Mukerjee (1988) gave an account of how one may calculate the posterior probability of a person given an RR to bear the characteristic A as, say, R which is “Yes” or the characteristic Ac on giving the response as “No.” If the “Yes” answer raises the probability of being perceived to bear A, a respondent would naturally dislike giving the “Yes” answer fearing the possibility of disclosure of the sensitive feature consequent on the specific RR and revelation of the secrecy. They covered details available in the relevant works of Lanke (1975b, 1976), Leysieffer (1975), Leysieffer and Warner (1976), and Anderson (1975a,b,c)—all related to SRSWR method of sample selection. Privacy may be protected if a given RR does not enhance the posterior probability beyond the prior proba bility θ that the person may bear the sensitive attribute A. A thoroughly undesirable aspect of the situation is that “the closer these two probabilities the greater turns out the variance of an unbiased estimator for θ” that is yielded by the specific RR device. After Chaudhuri and Mukerjee’s (1988) publication, the only noteworthy work in print on this subject is due to Nayak (1994), which is also related to SRSWR for which on each draw the prior probability of a person’s bearing A continues to remain as θ. The first publication in the context covering general probability designs is credited to Chaudhuri and Saha (2004). This is followed by the detailed publication by Chaudhuri, Christofides, and Saha (2009). Some details with illustrations are recorded in this chapter under “Illustrations.”
