Oops. That's completely wrong. It's the case where every honest answer is yes!

I think this is indeterminate. You have to know the ratio of total yesses to total participants.

The real world use-case I was recalling is simpler: flip a coin and answer honestly if it's heads and "yes" if it's tails. Any individual response is non-incriminating, but if N is large enough where you can assume N/2 got heads, you can know the number of "honest cheaters."