Comment on Approaching Logical Probability

Thu, 27 Feb 2014 18:23:11 GMT

I agree that if the outcome depends on our strategy or programming, then P(outcome | do(action)) has no proper place in our agent's decision-making. Savages theorem requires us to use probabilities for the things that determine the outcome; if our action does not determine the outcome, its probability isn't given by Savage's theorem.

I think you'd agree that there are more-abstract objects like P(outcome | strategy) that do obey Savage's theorem in these problems (I'd claim always, you'd maybe just say usually?). In the absent-minded driver problem, we can work the problem and get the right answer by using P(outcome | strategy). The strategy used determines the outcome, and so Savage's theorem works on it.

And I do think that simultaneously, we can use Cox's theorem to show that the absent-minded driver has some probability P(state | information). It's just not integrated with decision-making in the usual way - we want to obey Savage's theorem for that.

Also, Wei Dai made a comment similar to yours here.

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