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smoofra comments on The Aumann's agreement theorem game (guess 2/3 of the average) - Less Wrong
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Comments (149)
I think it's entirely rational to submit a non-zero answer.
I would prefer to win outright, rather than tie, and I think it's safe to assume this is true of more people than just me.
If everyone does the "rational" thing of guessing 0, it will be a big tie.
If anyone guesses above 0, anyone guessing 0 will be beaten by someone with a guess between 0 and the average.
Therefore, a small non-zero guess would seem superior to a guess of zero, to those who value outright wins above ties (EDIT: and don't value a tie as being much better than a loss).
Perhaps I'll write a program to simulate what the best guess would be if everyone reasons as above and writes a program to simulate it...
if the average is less than 3/4 then the zeros will still win
It depends where in the range of 0-average the guess is.
But of course I see what you mean; I meant between 0 and (average * 3/4), sorry.
EDIT: (average * 3/4 + average * 3/8) is the upper bound, unless I forgot something or you're not allowed to go over.
EDIT 2: The point being, there's a lot more winning non-zero answers than zero answers.
Sure, but what are the odds of you getting the right one. If they're too low, then you could still better of with zero.
If I rank a tie and a loss the same, then I'm don't risk anything by guessing a non-0 value for the chance of winning outright.