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David_Chapman comments on Probability, knowledge, and meta-probability - Less Wrong
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Comments (71)
Jeremy, I think the apparent disagreement here is due to unclarity about what the point of my argument was. The point was not that this situation can't be analyzed with decision theory; it certainly can, and I did so. The point is that different decisions have to be made in two situations where the probabilities are the same.
Your discussion seems to equate "probability" with "utility", and the whole point of the example is that, in this case, they are not the same.
I guess my position is thus:
While there are sets of probabilities which by themselves are not adequate to capture the information about a decision, there always is a set of probabilities which is adequate to capture the information about a decision.
In that sense I do not see your article as an argument against using probabilities to represent decision information, but rather a reminder to use the correct set of probabilities.
My understanding of Chapman's broader point (which may differ wildly from his understanding) is that determining which set of probabilities is correct for a situation can be rather hard, and so it deserves careful and serious study from people who want to think about the world in terms of probabilities.