Photo: Björn Bechstein (Flickr)
Suppose a stranger knocks on your door and says she’s taking a poll about tax-law compliance. She asks you whether you’ve ever cheated on your taxes. Pretend for the sake of argument, that you have.
You’ll probably say no, especially if you have any suspicion that this poll-taker actually works for the IRS. But suppose the poll is legitimate, the pollsters don’t care about your taxes in particular, they actually want to find out what percentage of people cheat on their taxes. You, as a citizen, see value in finding this out, but you don’t want your privacy compromised.
Privacy Versus Honesty
One solution is this: the poll-taker gives you a spinner, like the ones that come with children’s board games. The circle on the spinner is divided into four equal parts. One of the parts is marked “yes.” The other three parts marked “no.”
The poll-taker asks, “Have you ever cheated on your taxes? Don’t tell me the answer,” she says. “Spin the spinner where I can’t see it, and just tell me whether the answer is right or wrong for you.”
Spin A Lie
From your answer “right” or “wrong,” the poll-taker cannot find out whether you personally cheated. But your answer, along with many others, allows her to calculate what percentage of people cheated on their taxes. For example: if everyone cheated, about one-fourth of the respondents would say the spinner was right; if no one cheated, about three-fourths would say it was right.
Spinners and other randomizing devices provide a way to get honest answers to personal questions without violating anyone’s privacy. Randomized surveys have been used to find out about drugs, abortion, and even shady practices in selling cars.
Sources And Further Reading:
- Gina Kolata, “How to Ask About Sex and Get Honest Answers,” Science 236:382 (April 24, 1987)
- Warner, Stanley L. “Randomized Response: A Survey Technique for Eliminating Evasive Answer Bias.” Journal of the American Statistical Association Vol. 60, Issue 309, 1965.