It is often the case that enhancing individual privacy entails increased cost. In this puzzle, anyone who answers based on coin flips is essentially wasted as far as the poll is concerned. For example, if everyone who flips a coin twice and ends with two heads must say candidate A and everyone who ends with two heads must say candidate B, then the pollster learns nothing from roughly half the respondents. Suppose that the pollee doesn’t trust the pollster but might trust five friends. Could some spokesperson for the five friends respond to a pollster with a statement like this: “Among us 5, x of us express support for A and 5-x for B, but two of us flipped coins twice which perhaps determined their votes. The other three express their true preferences.” What kind of privacy guarantee could one get?