I see no value in it. It's an indicator of what people think of the post, but if I post something, I think it's worth posting, so the only disagreement I care about is if someone can refute the points I make in a clear and logical way. Receiving downvotes because people find it too hard to think critically about something for a few seconds only bothers me because people, again, have found it too hard to actually think about something for a few seconds. That speaks more to me about the people around me than about myself.
The majority of the downvotes I get are not given in conjunction with replies, and often the replies I do get are ridiculous, shallow, and full of logical fallacies and senseless hate. I don't pay much attention to those, and once it becomes clear the person has no interest in actually holding a reasonable discussion, I see no point in trying to convince them of anything.
I can understand why people value upvotes and downvotes (instant gratification and all that), but the only times I value them are when it can A) make my post more noticeable (and let's face it, most people will read the "comment is below threshold" comments just as readily as the ones with high upvotes), or B) help to convince someone that I am right and they are, in fact, wrong.