Randomized Response and Estimation

In survey sampling, directly asking sensitive questions often leads to evasive answers or untruthful responses. The randomized response technique introduces a probabilistic privacy mechanism: a respondent answers truthfully with some probability r, and otherwise gives a random response (such as flipping a fair coin). This plausible deniability protects individual privacy while still allowing the aggregate prevalence to be estimated.

Experiment

Explore the trade-off between privacy and estimation variance:

1. Set Prevalence quarters to 1.
2. Set Truth quarters to 2.
3. Set Respondents to 8.
4. Adjust the Observed yes count and note how the Moment Estimate changes. Notice that it can exceed 1 or fall below 0, which is normal for this unbiased estimator.
5. Change Truth quarters to 0 to observe that the prevalence becomes unidentifiable and the estimator unavailable.

The experiment is available here.