Previously, I asked about a feature request for adding a batting average, as a tool for giving more info on the person supplying the answer. From the answers given, it seems like I've been putting too much importance on the rep score - it shouldn't be taken seriously, it's just a number, judge answers by the answers, etc.
As a new user I simply associated a high rep score with expertise. Since we should be judging answers based solely on the answers, I'm thinking that having the answerer's rep score (and badges, too, by extension) appear under the name on an answer are misleading - it influences other people's participation on the site (both the questioner and other answerers). This is a contradiction - if the stated intention of the site is to develop quality answers, then it should not allow non-question-related information to influence or bias people's participation on the site, right? How about just hiding those bits of info on the various answers?
You could extend this argument to say that even the username of the answerer be hidden so that answers appear anonymous on the question page - individual user's profile page could still list everything as it is now for interested parties...
Hiding the name is probably not going to happen - it would be a drastic change to how SO operates.
Hiding the reputation seems feasible though. Got my vote!
The same idea was presented here and declined: Should there be anonymous answers (and questions)?
I really don't put much weight on the amount of rep - it shows a user's participation in the system. My brother's a great programmer, but doesn't have a really high rep on StackOverflow, but that's because he doesn't spend a lot of time actually participating. Doesn't make him any worse a programmer.
And if this were opposite world, and Jon Skeet asked a bad question, I would still vote him down. (Does the SO engine even allow users to vote him down?)
When you ask a C++ question in a group of people, and joe nobody gives you an answer that seems plausible, then Bjarne Stroustrup gives you an answer that seems plausible, you will tend to believe the answer given by the creator of the C++ language.
The reputation is not merely a sweetener for the website, it's an accounting of how many people believe this person has given good answers in the past and it is actually meant to help one evaluate an answer.
The person behind the answer matters, and Stack Overflow was developed with the idea in mind that the community can, over time, weed out the experts from the joe nobodies.
That's not to say that the expert is always better than joe, nor that joe doesn't provide useful information and correct answers.
But when Joe and Bjarne are giving C++ answers, even if they're the same, you're going to pay more attention to Bjarne - and that's appropriate.
Yes, this rep bias is cyclical, but you have to work hard to get to the point where people trust your answer more due to your rep, so by the time the system has weeded out all the joes (probably around 5-10k rep) chances are good those that are left aren't simply going to change their posting pattern and start BSing with the expectation that they'll get upvotes solely due to their rep.
There is the suggestion that people down-vote answers on high-rep users, which is an interesting additional argument to have a certain amount of anonymity - perhaps until an answer is selected.
I think the OP should have an indication of reputation if they want it, but it would be nice if other people were voting up / down based on the content not the user.
Ultimately, the up and down votes help the OP choose the best answer - rather than reputation.