Weighted votes based on karma. Or restrict the number of votes a user can cast based on karma or account age.
A problem with these kinds of things is determining what does or does not work and picking up on unintended side-effects, and doing so in a timely manner.
For example, if "young" accounts have very limited votes available will new users be less likely to stick around long enough to become more active voters? How long would it take to see this? What if by the time you recognize an undesired side effect you've already sent the site down the road of ruin (or something)?
For example, how long will pg keep comment vote hidden? How many people have found this to be sufficiently detrimental that they have, or soon will, leave HN and not come back?
How do you craft meaningful site experiments like this while keeping risk to a minimum?
I suppose that depends on whether or not they are on the site to read submitted news articles and comments or to play the voting and karma game. I rarely vote (or comment for that matter), but I get value from the content. For that reason, I have continued to consistently visit the site for a couple of years.
Now that upvotes are non-public information, people can't know their own rank (at least not easily), so this looks at least halfway resistant to gaming.
Yes, vanilla Pagerank (where the "sites" are accounts and "links" are upvotes) is the first thing that came to my mind, mainly because it's been pretty well battle tested; running it on the comment graph is actually a much simpler problem than running it behind a search engine because you don't need the additional refinements based on search keyword. A comment's Pagerank is, by itself, enough to set an ordering.
If that's too much work, though, even a simple vote weighting based on some function of the upvoter's karma would be a decent approximation. Say every user's votes had an impact based on some sigmoid function of their karma (maybe a Gompertz function?), tuned so that the plateau is hit for the top 10% of users or something like that.
I came to the conclusion that using Karma as a score is a rather bad idea as it assumes that people who get voted up have better judgement: "If you post well you must vote well."
But I'm sceptical that this is the case, it's easy to see someone like patio11 has both excellent judgement and a high karma score. But vote power = karma probably means you're giving a casting vote to patio11 if he turns up but mainly you're giving vote power to the people who post the most.
The implementation I have is basically: "If you made hard decisions in the past and voted well, you get more vote power."
In order for this to work, you'd have to hide vote totals on all posts and comments, which, as jamesbritt pointed out above, eliminates a feedback mechanism that users may find desirable.
So the most vote power is assigned to someone who votes early on a contentious story which later becomes popular.
I'm not sure what the best tradeoff is; personally, I'd probably go with something like Pagerank for a while and see if the comment quality (above the fold, at least) improves, but perhaps pg has a desire to keep things more neutral and fair, I'm not sure.