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CarlShulman comments on Outlawing Anthropics: An Updateless Dilemma - Less Wrong
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"Hence if you wake up in a green room and you're asked to steal from the red rooms and give to the green rooms, you either commit a group of 2 of you to a loss of 52 or commit a group of 18 of you to a gain of 12."
In the example you care equally about the red room and green room dwellers.
Hence if there are 2 instances of your decision algorithm in Green rooms, there are 2 runs of your decision algorithm, and if they vote to steal there is a loss of 3 from each red and gain 1 for each green, for a total gain of 12-318 = - 52.
If there are 18 instances in Green rooms, there are 18 runs of your decision algorithm, and if they vote to steal there is a loss of 3 from each red and a gain of 1for each green, for a total gain of 118-23 = 12
The "committal of a group of" is noting that there are 2 or 18 runs of your decision algorithm that are logically forced by the decision made this specific instance of the decision algorithm in a green room.