Surveys with negative questions for sensitive items

This paper proposes a strategy for administering a survey that is mindful of sensitive data and individual privacy. The survey seeks to estimate the population proportion of a sensitive variable and does not depend on anonymity, cryptography, or legal guarantees for its privacy preserving properties. Our technique presents interviewees with a question and t possible answers, and asks participants to eliminate one of the t-1 alternatives at random. We introduce a specific setup that requires just a single coin as randomizing device, and that limits the amount of information each respondent is exposed to by presenting to her/him only a subset of the question's alternatives. Finally we conduct a simulation study to provide evidence of the robustness against the response and the non-response bias of the suggested procedure.