A potential solution to this is the following: suppose that 'YES' is the embarrassing or socially shameful answer; give the people you are polling the following instructions: flip a coin privately, and if it comes up heads answer honestly, but if it comes up tails answer 'YES' regardless of what the truth is. This gives people plausible deniability about why they answered yes, if pressed. Again, let py be the fraction of people who said 'YES'. Let p be the probability that a randomly selected person says 'yes'; let q be the probability that a person's true answer is 'yes'. Note again, we have that the expected value of px is p, but we are actually interested in measuring q. 7) What is the relationship between q and p? 8) Construct an estimator ĝN from px so that the expected value of qy is q. 9) If I want my estimate to be accurate, I want the error on qy to be small. How many people should I poll to guarantee that the expected squared error on qy is less than e, when I don't know the value of q? How does this compare to the answer in the previous section? 10) How many people should I poll to guarantee the actual error on qy is less than e, with 90% confidence, if I don't know q? 11) What is the additional 'cost' of accurate polling if I want to preserve people's privacy in this way?

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