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Alexei comments on Interlude for Behavioral Economics - Less Wrong
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I think you can apply TDT of sorts: if I was in the other person's position, I would want them to cooperate. Coupled with the fact that the roles were selected randomly, you could essentially make a precommitment: if another person and I are in this situation, I'll cooperate no matter what. I think that doesn't change your expected value, but it does reduce variance.
BTW, lots of LWers said they'd give money to Omega in the Counterfactual mugging.