Playing against sufficiently rational agents the correct guess is zero. But assuming that not every other player is completely rational, applies sufficient recursion etc, you have to take into account their irrationality. If some non negligible proportion answer anything other than zero, and at least one participant guesses a very small non-zero number, every player choosing zero is guaranteed to miss. I don’t know how much I trust the NPR readership to take recursion to the limit.
I asked a friend just now. She (immediately) answered 5.
Sounds like the Less Wrong readership may overestimate the rationality of the average participant.
If some non negligible proportion answer anything other than zero, the rational players choosing zero will get it wrong.
Will they, though? The object is to choose the number closest to half the average. If ten people pick zero, five pick twelve and five pick twenty-five, the average will be 9.25, half of which is 4.625, which is closer to zero than twelve.
(I mean, the people choosing zero will get it wrong, but it’s because at least one person—me—thought that far ahead and picked 1. fiddlemath picked 2, presumably due to a different estimate of the ratio of LWers/NPRers in the poll.)
I have a feeling the half-average “should” be in the interval between 0 and 1.
I will be very surprised if the half-average is zero.
I’m guessing there is both literature and mathematical models for this interesting problem,
but I’m not going to go ahead and Google it. Not knowing is way more fun.
Playing against sufficiently rational agents the correct guess is zero. But assuming that not every other player is completely rational, applies sufficient recursion etc, you have to take into account their irrationality. If some non negligible proportion answer anything other than zero, and at least one participant guesses a very small non-zero number, every player choosing zero is guaranteed to miss. I don’t know how much I trust the NPR readership to take recursion to the limit.
I asked a friend just now. She (immediately) answered 5.
Sounds like the Less Wrong readership may overestimate the rationality of the average participant.
Will they, though? The object is to choose the number closest to half the average. If ten people pick zero, five pick twelve and five pick twenty-five, the average will be 9.25, half of which is 4.625, which is closer to zero than twelve.
(I mean, the people choosing zero will get it wrong, but it’s because at least one person—me—thought that far ahead and picked 1. fiddlemath picked 2, presumably due to a different estimate of the ratio of LWers/NPRers in the poll.)
I have a feeling the half-average “should” be in the interval between 0 and 1.
I will be very surprised if the half-average is zero.
I’m guessing there is both literature and mathematical models for this interesting problem, but I’m not going to go ahead and Google it. Not knowing is way more fun.