On the most recent episode of This Developer's Life Jon Skeet was interviewed, and mentioned that sometimes he didn't receive the "accepted answer" even though his answer was correct, and he was first, simply because the original poster thought Jon already had enough rep, and therefore accepted someone else's answer. Should there be a way to post anonymously, or should answers be shown anonymously for a short while so that somebody's identity does not change the results of the voting? I could see this working negatively in both ways. People not giving upvotes because they feel the person already has enough rep, or people completely glossing over answers because the person posting the answer didn't have much rep. I'm not too serious about this. I just kind of crossed my mind, and I was wondering about what others thought of it.
Already, anyone can post anonymously any time they like. It's one of the core principles of the site. If you happen to be logged in, simply log out first, and then proceed to post anonymously...
But really, this is a non-issue. Folks with real problems aren't making decisions based on rep, they're looking for the answer that solves their problem. If they're lucky enough to have multiple answers that meet this criteria, then sure, you're gonna get people who defer to the low-rep user... But you'll also get people who defer to the high-rep user. When the outcome doesn't matter, folks base their decisions on all sorts of arbitrary reasons... Realistically, it's not something you should waste time worrying about.
I don't like this at all. Putting aside SO reputation numbers, there are certain people that have a good reputation in my own eyes. I trust what they say and don't fact check them as much as I would someone who I am not familiar with.
As far as showing the rep number, this can be a very useful indicator of the answers abilities on SO. If a user has 50 rep and posts an answer that is incorrect, I might be faster or slower to downvote them (depends on how they are incorrect) depending on there rep level.