Making Use of “Benford’s Law†for the Randomized Response Technique

In this article, “Benford’s law†is applied to the “randomized response technique†(RRT) to increase the validity of answers to sensitive questions. Using the Newcomb–Benford distribution as a randomizing device has several advantages. It is easy to explain and follow the procedure, as no physical device such as a coin or a dice is necessary and the method guarantees full anonymity. As is well known, the price for the anonymity of the RRT is a decrease in the efficiency of the estimator. However, because of the subjective overestimation of certain numbers (Benford illusion), the conflict between the variance of the estimates and the degree of anonymity is less pronounced compared to other RRT methods. The suggested RRT variant has the potential to improve the efficiency of the estimator. Moreover, the assumption is that this method works well with self-administered questionnaires.