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utilitymonster comments on What a reduction of "probability" probably looks like - Less Wrong
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tl;dr Philsophers have been writing about what probabilities reduce to for a while. As far as I know, the only major reductionist view is David Lewis's "best system" account of laws (of nature) and chances. You can look for "best system" in this article for an intro. Barry Loewer has developed this view in this paper.
From what I understand of Lewis's view, it's not a "reduction" in my sense of the word which (I think) also coincides with common LW usage. I generally try to reduce phenomena to programs that can be implemented on computers; the first two scenarios in the post are of this kind, and the third one can probably be implemented as well, once I understand it a little better.