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Lumifer comments on Top-Down and Bottom-Up Logical Probabilities - Less Wrong Discussion
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Comments (4)
Badly in need of tl;dr
tl;dr Some methods of assigning logical probability seem to be convergent. That's neat.
I disagree strongly, but here is a prototype of one anyways.
There are top-down and bottom-up approaches to logical probabilities. Top-down approaches typically involve distributions selected to fit certain properties, and, while being elegant and easy to apply math to, are often quite uncomputable. Bottom-up approaches take an agent with some information, and ask what they should do to assign probabilities/find out more, leading to a more "hacky" probability distribution, but they also tend to be easier to compute. Interestingly enough, given limited computing resources, these two sorts of distributions have distinct similarities. They both involve a starting probability distribution modified by iterated consistency checks.
Did I get it mostly right?
This part is a bit misleading because there's nothing special about having a starting distribution and updating it (thought that's definitely a bottom-up trait). It's also okay to create the logical probability function all at once, or through Monte Carlo sampling, or other weird stuff we haven't thought up yet.