Efficiency comparison of unrelated question models based on same privacy protection degree

In this study, the problem of estimating the proportion π _A of people bearing a sensitive attribute A is considered. Three dichotomous unrelated question mechanisms which are alternative to the well-known Simmons’ model are discussed and their performance is evaluated taking into account both efficiency and respondent privacy protection. The variance of the estimators of π _A is compared under equal levels of confidentiality measures introduced by Lanke (1976) and Leysieffer and Warner (1976).