N the theory of randomized responses to two sensitive questions

This paper sets forth a stochastic model which can be applied to randomized response designs wherein more than one question is sensitive of stigmatizing. Using three specific designs applied to a pair of stigmatizing or sensitive traits leading to two by two contingency tables, it is proved that if the two traits are statistically independent then the responses are also and conversely. The converse statement gives the support we need for inference to be made on the traits based on the randomized responses.