A Unified Approach to Measures of Privacy in Randomized Response Models: A Utilitarian Perspective

Randomized response survey techniques are used for collecting data on sensitive issues while trying to protect the respondents' privacy. The degree of confidentiality will clearly determine whether or not respondents choose to cooperate. This has motivated a search for an appropriate measure of privacy. This article shows that most of the proposed measures of privacy are inconsistent with the underlying rationale for the randomized response procedure. That is, respondents are thought to feel discomfort from being perceived as belonging to the sensitive group, but they prefer to answer questions truthfully than to lie, unless it is too revealing. Instead of guessing another privacy measure, this article derives the correct one from the stated rationale and the assumption that respondents maximize their well-being; that is, the utilitarian approach. It is shown how a respondent's decision to answer truthfully or to lie depends on a relative welfare comparison. Thus the correct measure of privacy involves both conditional probabilities of being perceived as belonging to the sensitive group, pr(A | yes) and Pr(A | no). A practical implication is that uncertainty about the respondents' demand for privacy should be handled by choosing these conditional probabilities sufficiently close to each other. The utilitarian approach also provides the fundamental framework for evaluating all previous and future measures of privacy. For example, Lanke's recommendation of only focusing on the most jeopardizing answer is shown to be inconsistent with rational behavior of the respondents.