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 ...
It's NP-hard. Here's a reduction from the complement problem of 3SAT: let's say you have n clauses of the form (p and not-q and r), i.e., conjunctions of 3 positive or negated atoms. Offer bets on each clause that cost 1 and pay n+1. The whole book is Dutch iff the disjunction of all the clauses is a propositional tautology.
I've written some speculations about what this might mean. The tentative title is "Against the possibility of a formal account of rationality":
http://cs.stanford.edu/people/slingamn/philosophy/against_rationality/against_ratio...
Oh, thanks, you're completely right.
To unify all the language and make things explicit: if you have n atoms, then there are 2^n possible states of the world (truth assignments to the atoms). Then, if you have a personal probability for each of the 2^n states ("complete joint distribution", "complete table"), you can check consistency by summing them and seeing that you get 1. This is O(n) in the size of the table.
The question at stake seems to be something like this: does the agent legitimately have access to her (exponentially large) c... (read more)