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conchis comments on The Aumann's agreement theorem game (guess 2/3 of the average) - Less Wrong
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Comments (149)
Whether or not it's boring is a matter of taste. But the point was to test a hypothesis, not to be interesting. Have you just subverted the point entirely; or does your claim to have sent a guess of 100 actually serve a purpose?
The "guess 2/3 of the average" game is quite well-studied and has been played many times in controlled environments and on the Internet. No point in running yet another simulation.
My claim serves a purpose of providing some simple mathematical exercises to all involved.
Except to potentially gain information specific to this community, which is what I assumed the point was.
(This is not to suggest that your modification is not interesting. It is. I just think it's kind of poor form to hijack someone else's post like this. If you wanted to play a different game, with a different point, I think the best course would have been to start your own separate game, with you taking the entries, and to have left Warrigal's game as it was. There's no reason we couldn't have done both.)
Now that you said it, I see how my comment has made the community worse off. I somehow didn't see it then. I'm sorry.
Edit: please don't upvote this.
If it's any consolation, I'd assign high probability that some other merry prankster is going to intentionally screw with the results by not trying to win at all. Any future study of group rationality on LW would be advised, based on past experience, to throw out some outliers on principle.
Assuming you have actually entered a guess of 100, you may change it. If we didn't let people change their entries, they might as well wait until the last second and then enter.
On the bright side, I suppose, you certainly have helped meet the goal of gaining information specific to this community.
I believe the "correct" answer a is now given by the equation:
a = 2/3 * (100 + ((n-1) * a)) / n
where n is the total number of players, including cousin-it.
Except this doesn't take into account people who didn't see or ignored cousin-it 's post. But if cousin-it's guess was stated at the outset, I think the "correct" answer would be as above.
Edit: Richard Kennaway points out that this simplifies to a = 200 / (n+2)