The more times a story gets submitted, the more upvotes it generally gets because more people have already read it. No matter how good a story is the odds are that it won't get past the new page simply because there aren't many people willing to triage stories. And by the time those who see a story in the new queue finish reading it and vote on it, it's often already too late for it to make the front page. Whereas lots of people are happy to vote for a story they've already seen.
Since stories usually hit the front page when their score is around 6, I think it would make sense to give the first five upvoters a share of the karma from the submission. (With the submitter getting the most, and the first upvoter getting more than the fifth.)