Over the years several people have suggested not displaying comment scores. I finally decided to try it. There are so many users now that voting is starting to have a bit of a mob feel to it. We'll see if this makes the site feel better.
Voting still has all the same effects (on karma, and on position on the page), so I encourage users to keep doing it. The only difference is that comment scores aren't displayed in threads.
* If a comment is sitting at 1 or 0, I'll try to avoid downvoting it unless I really think the comment subtracts value from the site.
* If a child is attracting more votes than the parent, and I think this is because the child commenter didn't comprehend what the parent was saying, I vote to level out the comments.
* If I see a comment sitting in negative territory that I feel should only be a 0 or 1 because it wasn't that bad, I'll upvote it even if I otherwise wouldn't have.
* If a thread is already dominated by a couple of high-scoring comments, relative to its age, I'm less likely to post a new top level comment. My feeling is that if a good comment just sits at the bottom because it arrived slightly too late, I've only added noise to the thread. The lack of visible points makes it much harder to gauge how a new comment will 'compete' on the thread.
* If the scores indicate that something is being widely misunderstood, I might comment where I otherwise would not have to try to restore sanity.
Of course, if this change were to stick, it would alter the character of the site, and we would all develop new voting and commenting systems. I can already tell that this change magnifies my tendency to vote with an eye toward reordering comments rather than voting on each comment in relative isolation.