= 27d567bc2d48d9f40e9ccc20ea370b15)
slingamn comments on Dutch Books and Decision Theory: An Introduction to a Long Conversation - Less Wrong
You are viewing a comment permalink. View the original post to see all comments and the full post content.
= 783df68a0f980790206b9ea87794c5b6)
Loading…= b715d02e85f7b3b4ae65ca3d3e450868)
Subscribe to RSS Feed
Powered by Reddit
= f037147d6e6c911a85753b9abdedda8d)
You are viewing a comment permalink. View the original post to see all comments and the full post content.
Comments (100)
Hm... if your probability assignments are conjunctions of that form, is it still true that finding a Dutch book is polynomial in the size of the probability table that would be required to store the entire joint probability distribution corresponding to every possible assignment of all atoms? I.e., NP-hard in the number of conjunctions, but polynomial in the size of the entire probability distribution?
Interesting. I'm actually not sure. The general result by Paris I cited is a little unclear. He proves CONSISTENCY (consistency of a set of personal probability statements) to be NP-complete. First he gets SAT \leq_P CONSISTENCY, but SAT is only O(2^n) in the number of atoms, not in the number of constraints. However, the corresponding positive result, that CONSISTENCY is in NP, is proven using an algorithm whose running time depends on the whole length of the input.
It could be that if you have the whole table in front of you, checking consistency is just checking that all the rows and columns sum to 1.
However, I don't think that looking at the complete joint distribution is the right formalization of the problem. For example, I have beliefs about 100 propositions, but it doesn't seem like I have 2^100 beliefs about the probabilities that they co-occur.