what is it that you authenticate? Do you mean trust in the same sense as "web of trust" in PGP-type crypto systems?

For starters, a system to be sure that a user or service is the same user or service it was previously. Web of trusts /or/ a central authority would work, but honestly we run into limits even before the gap between electronic worlds and meatspace. PGP would be nice, but PGP itself is closed-source, and neither PGP nor OpenPGP/GPG are user-accessible enough to even survive in the e-mail sphere they were originally intended to operate. SSL allows for server authentication (ignoring the technical issues), but isn't great for user authentication.

I'm not aware of any generalized implementation for other use, and the closest precursors (keychain management in Murmur/Mumble server control?) are both limited and intended to be application-specific. But at the same time, I recognize that I don't follow the security or open-source worlds as much as I should.

For reputation as an assessment of user ratings, you can obviously build a bunch of various metrics, but the real question is which one is the best. And that question implies another one: Best for what?

Oh, yeah. It's not an easy problem to solve Right.

I'm more interested in if anyone's trying to solve it. I can see a lot of issues with a user-based reputation even in addition to the obvious limitation and tradeoffs that fubarobfusco provides -- a visible metric is more prone to being gamed but obscuring the metric reduces its utility as a feedback for 'good' posting, value drift without a defined root versus possible closure without, so on.

What surprises me is that there are so few attempts to improve the system beyond the basics. IP.Board, vBulletin, and phpBoard plugins are usually pretty similar -- the best I've seen merely lets you disable them on a per-subfora basis rather than globally, and they otherwise use a single point score. Reddit uses the same Karma system whether you're answering a complex scientific question or making a bad joke. LessWrong improves on that only by allowing users to see how contentious a comment's scoring. Discourse uses count of posts and tags, almost embarrassingly minimalistic. I've seen a few systems that make moderator and admin 'likes' count for more. I think that's about the fanciest.

I don't expect them to have an implementation that matches my desires, but I'm really surprised that there's no attempts to run multi-dimensional reputation systems, to weigh votes by length of post or age of poster, spellcheck or capitalizations thresholds. These might even be /bad/ decisions, but usually you see someone making them.

I expect Twitter or FaceBook have something complex underneath the hood, but if they do, they're not talking about the specifics and not doing a very good job. Maybe its their dominance in the social development community, but I dunno.