Ah, ok. For EU you care about the actual difference in probability, whereas for strength of evidence you care about the amount of information you would have to receive in order to change your credence that much, and this is compressed near the ends of the probability range.
Edit: What was your question again? At first I thought that you did not understand what you were talking about, and thought that your answer re the context would be a link or quote where somebody else brought it up. But what you gave me is almost a set of proofs, and the explanation is clear from your use of dB in the evidence/information case.
I was aware of the difference (what you note in your first paragraph), but could not articulate a good explanation of why there is a difference. I found this comment by vi21maobk9vp to be a good explanation, though I feel it could be more clear and concise. I’m not actually sure I could have given you the answer in the grandparent in so few words before reading vi21maobk9vp’s comment.
Anyone?
What is the context of these claims? I don’t really see why either of them would be necessary.
They are necessary.
For expected utility,
.51v-.50v ==.01 v == .81v-.80v
When evaluating the strength of evidence,
50%
is0dB
,51%
is0.17dB
(diff0.17dB
),80%
is6.02dB
, and81%
is6.30dB
(diff0.28dB
).Please offer a correction if I’ve made a mistake there.
Ah, ok. For EU you care about the actual difference in probability, whereas for strength of evidence you care about the amount of information you would have to receive in order to change your credence that much, and this is compressed near the ends of the probability range.
Edit: What was your question again? At first I thought that you did not understand what you were talking about, and thought that your answer re the context would be a link or quote where somebody else brought it up. But what you gave me is almost a set of proofs, and the explanation is clear from your use of dB in the evidence/information case.
I was aware of the difference (what you note in your first paragraph), but could not articulate a good explanation of why there is a difference. I found this comment by vi21maobk9vp to be a good explanation, though I feel it could be more clear and concise. I’m not actually sure I could have given you the answer in the grandparent in so few words before reading vi21maobk9vp’s comment.