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steven0461 comments on Value of Information: Four Examples - Less Wrong
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This is not quite correct.
Suppose you know that difference in utility has a uniform distribution between 10 and 20. Then you already known which of the alternatives is better. So you shouldn't pay the standard deviation's worth (which is 2.88675).
The mean of the difference matters much more than the standard deviation. Math will follow.
I said "it's a mistake to pay more than one standard deviation's worth", not "one should pay exactly a standard deviation's worth".