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Vladimir_Nesov comments on Timeless Decision Theory: Problems I Can't Solve - Less Wrong
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What you just described is group selection, and thus highly unlikely.
It's to your individual benefit to be more (unconsciously) selfish and calculating in these situations, whether the other people in your group have a fairness drive or not.
Not if you are punished for selfishness. I'm not sure how reasonable the following analysis it (since I didn't study this kind of thing at all); it suggests that fairness is a stable strategy, and given some constraints a more feasible one than selfishness:
M. A. Nowak, et al. (2000). `Fairness versus reason in the ultimatum game.'. Science 289(5485):1773-1775. (PDF)
See reply to Tim Tyler.