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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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Eh? Why would anyone take one for the team? If it's bad to tie, surely it's worse to lose for the purpose of helping someone else win.
I should have explicitly stated this (you've caused me to realize that it's necessary for my whole line of reasoning), but it's also the case that losing is not a worse outcome for me than tying.
Ah. OK. I think that's generally supposed to be excluded by the set up (though in this case it was admittedly ambiguous). But given that you have those preferences, I agree that your reasoning makes sense.
There's no prize offered, but in theory, these people could collaborate to share whatever prize makes winning better than tying. Since there's no prize except winning, losing to help someone else does seem like it would be bad.