We'll never get an accurate answer to this - who would admit it??
I once read that the US government wanted to know what percentage of US soldiers did drugs while serving in Viet Nam. (but they knew they wouldn't get an accurate answer from a poll).
So - They put three questions in a box:
a) is 1+1 = 2?
b) is 1+1 = 3?
c) Did you do drugs while serving in Viet Nam?
Soldiers were shown the 3 questions, drew one out randomly, and could answer honestly, since the 'questioner' had no way of knowing what they drew.
The questioners figured 1/3 of the, say, 3000 soldiers asked picked a) and answered 'yes', and 1/3 of the soldiers picked b) and answered 'no'.
They then removed 1000 yes answers, and 1000 no answers. What they were left with was a (fairly) accurate poll of 1000 soldiers answering the question they were actually interested in.
Whew - long story. Essentially, that's the kind of exercise you'd have to do - because I'd rather tell the US gov't I smoked up in 'Nam than admit to you guys I'd read Loeb's hulk!