If choice A is vastly better than choice B, you don't need much information to determine that. So if, after gathering lots of information, you still can't determine which is better, don't stress too much about choosing the best one.
A professor of mine pointed this out to me when I was stressing about which grad school to go to. He then pointed out that at my age, his life choices were CUNY (math dept) or West Point - that was a decision that would have had a far larger effect on his life than my choice of Rutgers vs Brown vs Austin.
But I imagine that if I did view democracy as a meaningful decision procedure, then I suspect I would view close votes as a belief that both outcomes are almost equally good. Both decisions are not similar, but the utility attached to each decision is.