Even cooler would be to have each person (explicitly or implicitly) set other people's vote importance. I can imagine a complicated system wherein voting cliques are detected, and used to feed back into the rankings of what papers show up on your page.
Ideally, the voting could be more than just "+1/-1" as well, potentially with a couple different axes, so that I could, for instance, say that I think a paper is important to the field, but likely wrong. Just because a paper is controversial doesn't mean I don't want it to be discussed (for instance, if it introduces a new computational technique, but the input data is flawed somehow).
You're matching an engineering solution to a social problem. Trying to map a paper's social significance to an abstract number is really hard, and in the process you lose a lot of ability to present papers based on taste. Showing me a paper because "these numbers are high and you tend to like these kinds of numbers" is fundamentally different than "you should see this because it is groundbreaking." On the other hand, if we can create a metric for elegance and another for "brings the reader closer to enlightenment," then I'm all for it.
Ideally, the voting could be more than just "+1/-1" as well, potentially with a couple different axes, so that I could, for instance, say that I think a paper is important to the field, but likely wrong. Just because a paper is controversial doesn't mean I don't want it to be discussed (for instance, if it introduces a new computational technique, but the input data is flawed somehow).