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Randomized response technique protects respondents by introducing random noise.
What is randomized response technique?
For example, from Blair, Imai and Zhou (2015).
"For this question, I want you to answer yes or no. But I want you to consider the number of your dice throw. If 1 shows on the dice, tell me no. If 6 shows, tell me yes. But if another number, like 2 or 3 or 4 or 5 shows, tell me your own opinion about the question that I will ask you after you throw the dice. [TURN AWAY FROM THE RESPONDENT] Now you throw the dice so that I cannot see what comes out. Please do not forget the number that comes out. [ WAIT TO TURN AROUND UNTIL RESPONDENT SAYS YES TO: ] Have you thrown the dice? Have you picked it up?"
Thus, when the respondent rolls a one, they are forced to respond “no” to the question; when respondents roll a six, they are forced to respond “yes.” Finally, when respondents roll two,
three, four, or five, they are instructed to truthfully answer the following sensitive questions.
"Now, during the height of the conflict in 2007 and 2008, did you know any militants, like a family member, a friend, or someone you talked to on a regular basis. Please, before you answer, take note of the number you rolled on the dice."
See Blair, Imai and Zhou (2015) for additional examples and applications, e.g. mirrored question design, disguised response design, and unrelated question design.
When should I use randomized response technique?
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This article is part of the topic Questionnaire Design
- Blair, Graeme, Kosuke Imai, and Yang-Yang Zhou. 2015. “Design And Analysis of the Randomized Response Technique.” Journal of the American Statistical Association 110(511): 1304–19. 
Abstract: About a half century ago, in 1965, Warner proposed the randomized response method as a survey technique to reduce potential bias due to nonresponse and social desirability when asking questions about sensitive behaviors and beliefs. This method asks respondents to use a randomization device, such as a coin flip, whose outcome is unobserved by the interviewer. By introducing random noise, the method conceals individual responses and protects respondent privacy. While numerous methodological advances have been made, we find surprisingly few applications of this promising survey technique. In this article, we address this gap by (1) reviewing standard designs available to applied researchers, (2) developing various multivariate regression techniques for substantive analyses, (3) proposing power analyses to help improve research designs, (4) presenting new robust designs that are based on less stringent assumptions than those of the standard designs, and (5) making all described methods available through open-source software. We illustrate some of these methods with
an original survey about militant groups in Nigeria.
- Kraay, Aart, and Peter Murrell. "Misunderestimating corruption." Review of Economics and Statistics 98.3 (2016): 455-466. 
Abstract: Estimates of the extent of corruption rely largely on self-reports of individuals, business managers, and government officials. Yet it is well known that survey respondents are reticent to tell the truth about activities to which social and legal stigma are attached, implying a downward bias in survey-based estimates of corruption. This paper develops a method to estimate the prevalence of reticent behavior, in order to isolate rates of corruption that fully reflect respondent reticence in answering sensitive questions. The method is based on a statistical model of how respondents behave when answering a combination of conventional and random-response survey questions. The responses to these different types of questions reflect three probabilities—that the respondent has done the sensitive act in question, that the respondent exhibits reticence in answering sensitive questions, and that a reticent respondent is not candid in answering any specific sensitive question. These probabilities can be estimated using a method-of-moments estimator. Evidence from the 2010 World Bank Enterprise survey in Peru suggests reticence-adjusted estimates of corruption that are roughly twice as large as indicated by responses to standard questions. Reticence-adjusted estimates of corruption are also substantially higher in a set of ten Asian countries covered in the Gallup World Poll.