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JGWeissman comments on Outlawing Anthropics: An Updateless Dilemma - Less Wrong
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In this case the chosen copy in the green room should update on the anthropic evidence of being chosen to make the choice. That copy had a 1/18 probability of being chosen if the coin flip came up heads, and a 1/2 probability of being chosen if the coin flip came up tails, so the odds of heads:tails should be updated from 9:1 to 1:1. This exactly canceled the anthropic evidence of being in a green room.