So, for instance, let's say there are 9 new posts in the "queue" and there are 3 concurrent visitors to the front page. Visitor A will see links 1-3 from the new queue, visitor B will see links 4-6, etc. After being shown at least 3 times to front page visitors the link get's dropped from the new queue if it did not gather a single up vote. However, if it does get an up vote, that also resets it's show counter, and it has 3 more chances to gather another up vote.
The number of showings (lives) can be adjusted based on the ratio of new submissions to front page visitors. But I suspect that that ratio is more than high enough to accommodate 3-5 showings.
I feel like this would be a relatively easy system to implement, and could result in better overall content. Thoughts?