r/Fitness does a weekly "Moronic Monday", a judgment-free thread where people can ask questions that they would ordinarily feel embarrassed for not knowing the answer to. I thought this seemed like a useful thing to have here - after all, the concepts discussed on LessWrong are probably at least a little harder to grasp than those of weightlifting. Plus, I have a few stupid questions of my own, so it doesn't seem unreasonable that other people might as well.
That value doesn't directly lead to having a belief system where individual beliefs can be used to make accurate predictions. For most practical purposes the forward–backward algorithm produces better models of the world than Viterbi. Viterbi optimizes for overall consitstency while the forward–backward algorithm looks at local states.
If you have uncertainity in the data about which you reason, the world view with the most consistency is likely flawed.
One example is heat development in some forms of meditation. The fact that our body can develop heat through thermogenin without any shivering is a relatively new biochemical discovery. There were plenty of self professed rationalists who didn't believe in any heat development in meditation because the people in the meditation don't shiver. The search for consistency leads in examples like that to denying important empirical evidence.
It takes a certain humility to accept that there heat development during meditation without knowing a mechanism that can account for the development of heat.
People who want to signal socially that they know-it-all don't have the epistemic humility that allows for the insight that there are important things that they just don't understand.
To quote Nassim Taleb: "It takes extraordinary wisdom and self control to accept that many things have a logic we do not understand that is smarter than our own."
For the record, I'm not a member of any religion.
I'm pretty humble about what I know. That said, it sometimes pays to not undersell (when others are confidently wrong, and there's no time to explain why, for example).
Interesting analogy between "best path / MAP (viterbi)" :: "integral over all paths / expectation" as "consistent" :: "some other type of thinking/ not consistent?" I don't see what "integral over many possibilities" has to do with consistency, except that it's sometimes the correct (but more expensive) thing to do.