Earlier, I was told that after a month or so, if a question does not have a BA selected, then the moderators will select it. This was told to me in my Auto-BA suggestion. There are questions without BA such as:
These are the oldest ones without BA. Why do they not have BA? ____ These were asked over a month ago:
I can list more if this isn't proof enough.
Moderators can select best answer if a long time has passed (at least a month) and the question has a clear answer that is better.
So for example, on #299 both answers were given 5 votes. And on #686 honestly the answer is pretty awful (terrible English and not a definite answer). It shouldn't have 3 upvotes let along BA.