Who's lying?

Once I heard a puzzle that went like this - a missionary was in an area where he knew there were two tribes. One tribe always told the truth and the other always lied. The two tribes knew this of each other and were otherwise indistinguishable.

The missionary is traveling to Oogabooga when reaches a fork in the road and doesn't know which way to go. He sees a native coming by and wants to ask him which road to take to OogaBooga - it's fair to expect the natives to know the right answer. What question can he ask of the native to make sure he can know the right way to go?

While you're thinking about that, I'll note a recent study that suggests that perhaps women lie about sex more than men do:

"Women are sensitive to social expectations for their sexual behaviour and may be less than totally honest when asked about their behaviour in some survey conditions," said Fisher. "Women appear to feel pressure to adhere to sex role expectations that indicate women should be more relationship-oriented and should avoid being seen as promiscuous."

"Before the study, we thought men would generally over-report their sexual behaviour and women would under-report it under certain testing conditions. However, we found that women were more likely than men to have different answers depending on conditions when they were surveyed."

Maybe the trick is to ask them not what they do themselves, but what their friends do.

Pollsters grapple with bias in questions all the time. I recall one poll I heard of on the radio once that noted how much difference some phrasing made. In broad outline, when a question was phrased as "would you deny X welfare payments", people were more likely to vote against, but if it was phrased as "would you not give X welfare payments" people were less likely to oppose. I guess the distinction was essentially "I wouldn't deny them as long as I don't have to chip in myself". Anyway, I'm sure somebody like Jane Galt has better examples of polling perversities.

So have you figured out what question to ask the native? Here it comes: "if I asked someone from the other tribe which of these two roads went to OogaBooga, what way would he tell me to go?" Then take the other road. Proof is left as an exercise....