Imagine you want to run a survey to determine how many people have had an extramarital affair. There are obvious problems just asking people "Have you had an a

Imagine you want to run a survey to determine how many people have had an extramarital affair. There are obvious problems just asking people "Have you had an affair?" on a survey, especially a live one. So instead, you ask the person taking the survey to secretly flip a coin and privately look at the result. Then, you word the question as "If the coin came up heads, OR if you've had an affair, check this box". When you look at overall survey data, and you see 51% of people checked the box, then it's reasonable to infer that 2% of them had an affair. But even if I de-anonymized the survey and saw you checked the box, I don't really have good evidence that you had an affair.