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jsalvatier comments on Solve Psy-Kosh's non-anthropic problem - Less Wrong
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If the decision of a group decider is "1/9th as important", then what's the correct way to calculate the expected benefit of saying "yea" in the second case? Do you have in mind something like 0.9*1000/9 + 0.1*100/1 = 110? This doesn't look right :-(
This kind of answer seems like on the right track, but I do not know of a good decision theory when you are not 100% "important". I have an intuitive sense of what this means, but I don't have a technical understanding of what it means to be merely part of a decision and not the full decision maker.
Can the Shapely value and its generalizations help us here? They deal with "how important was this part of the coalition to the final result?".