To encourage subjects to make responses on sensi- tive questions, the method of randomized response is often

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To encourage subjects to make responses on sensi- tive questions, the method of randomized response is often used. The subject is asked to flip a coin, in secret. If it is a bead, the subject tosses the coin once more and reports the outcome, head or tails. If, instead, the first flip is a tail, the subject reports instead the response to the sensitive question; for instance, reporting the response head if the true response is yes and reporting the response tail if the true response is no. Let w denote the true probabil- ity of the yes response on the sensitive question.

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