To improve the performance of Simmons' randomized response model in the estimation of a sensitive proportion, two randomization devices, based on three outcomes, are introduced. The former acts as a dual method to that discussed in Singh et al. (2003)since it calls for a "yes" response when a blank card is drawn; the latter resorts to Simmons' device if a blank occurs. Under the two models, the estimators of the sensitive proportion are obtained in closed form and their efficiency is investigated by means of analytical and numerical comparisons. It is proved that the second device always works better than Simmons' one.
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