Similar to the excellent Slashdot moderation system. Moreover on Slashdot you couldn't just moderate at will, occasionally you would find yourself with 5 moderation points to spend upvoting or downvoting 5 comments.
Even more occasionally you would find yourself with some 'meta-moderation' points - where it displays some moderation decisions and asks whether you agree/disagree that this was good moderation
Slashdot's moderation has still yet to be beaten IMO, when up/downvoting a post you had to specify why you were doing so from a defined list, including things like Funny, Informative, Flamebait, and Trolling. Then as mentioned meta-moderation would occasionally ask a user to review those votes, asking the question "Was this post funny" for example. User's who's moderation points were upheld in meta-moderation would be more likely to get given more than someone who flung them out at random.
The real genius of the system though was the amount of configurability attached to those topics. Each user could define what those categories meant to them, so if you only wanted the serious stuff you could say Funny didn't get a +1 boost when displaying comments, and give it a -1 instead. Or -5 if you really hated Slashdot humour. In the other direction lovers of a good flame war could boost comments flagged as flamebait up in the sorting order. This also extended to relationships, where you could flag people as either friends or foes, allowing you to make sure you always saw comments from people who's comments you enjoyed, and squash anything by people you just didn't like.
All of that was an absolute nightmare for performance I'm sure, which is probably why we don't see it these days, but it was a thing of beauty.
Another great thing about the Slashdot moderation system was the "overrated" and "underrated" tags. A comment could get moderated as "-1 Flamebait" then get moderated as "+1 Underrated" all the way up to "+5 Flamebait". My personal favourite quirk of the system.
Slashdot's mod system was ... reasonably good at deprecating garbage. It did poorly at elevating true quality, however. The mod activity was too thin and non-convergent (each moderation moved. by a full point on a +5 -- (-2) scale).
I'd been on the site since before registration and moderation existed, and had a very low UID, back when that ... still really didn't matter.
Kuro5hin's "mean of moderation" system converged (within a five point scale, much like Amazon star ratings), though in practice people vastly overaward high scores.
Explicit scoring systems are difficult to design. They also leak insane amounts of personal information.
Even more occasionally you would find yourself with some 'meta-moderation' points - where it displays some moderation decisions and asks whether you agree/disagree that this was good moderation