Abstract
We consider the problem of estimation of a finite population proportion (P) related to a sensitive character under the randomized response plans due to Warner (1965) and Eriksson (1973) and prove that for a given probability sampling design, given any linear unbiased estimator (LUE) of P based on Warner’s (1965) plan with any given value of the plan parameter there exists an LUE of P based on Eriksson’s (1973) plan with a uniformly smaller variance for suitable choices of the plan parameters. The same is also shown to be true when the plan parameters for the two plans are so chosen so that both offer the same level of privacy.
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