I won't explain how Pagerank works, there is a good explanation here:

http://www.ams.org/featurecolumn/archive/pagerank.html

Let's drop the "every vote counts equal" scheme. Say you want to get a global measure for how important every person's votes are to the site. This means you want to assign a number to every person. This is analogous to the pagerank number assigned to a web page. The votes a person has got on all his comments and submissions corresponds to the inbound links of a webpage. The votes a person gives correspond to outbound links from a webpage. You would like that the authority every user gives equals the authority every user receives (both via upvotes, let's ignore downvotes for now). Every user's importance gets divided equally among the submissions/comments that he has upmoded. These are exactly the rules Pagerank operates on, except that one user may have upmoded another several times and you need to account for downmods too.

What are the advantages this would bring to sites like news.YC? Such an algorithm would be pretty resistant to voting circles in the same way pagerank is resistant to spam (one user with lots of karma will weight more than a lot of sockpuppets with no karma). It gives a global estimate of people's importance to the site and it should allow a site to preserve it's culture better as it scales.

Drawbacks? Some people may object that it is unfair not to count votes equally. It is harder to implement (especially as you need to modify the karma-rank on the fly, although if this turns out to be hard, you can use an approximation and recalculate karma-rank daily, for example). Last but not least, it puts serious performance requirements on the site implementing it that Arc is probably not ready to handle.