Vladimir_Nesov comments on Rationality is Systematized Winning - Less Wrong
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Another variation, playing only on real/counterfactual, without motivating the real decision. Omega comes to you and offers $1, if and only if it predicts that you won't take it. What do you do? It looks neutral, since expected gain in both cases is zero. But the decision to take the $1 sounds rather bizarre: if you take the $1, then you don't exist!
Agents self-consistent under reflection are counterfactual zombies, indifferent to whether they are real or not.
Seems roughly as disturbing as Wikipedia's article on Gaussian adaptation: