Sorry I've been out of the discussion for a little bit - have been talking to people from this thread about the possibility of pursuing this, which is great
That implementation is pretty kickass! Like I said through PM, it has a ton of potential! It's also really interesting that it has a backend with the data, and then a separate front-end. This should be fairly critical to the system we've been thinking of. You only implement the system once, and then implement lightweight interfaces for, say, Facebook, different forums, stand-alone applications, mobile applications, etc.
Eagleon, there's no worry in creating the Singularity using this, it eventually just becomes a system of equations
Nodes don't really do any computation!
I guess the proposal here is, in general, give the ability to formally debate things to communities that are open to it. If the community isn't open to it, because it lets in too many trolls, or because people don't really care about it, it's not going to work. The community is its own moderator, through the means of voting.
Either way, it should be fairly straightforward theory-wise to make sense of having people with heavier weights in their votes. This allows for the system of currency, reputation, credibility, reliability, or positive/negative feedback on users. That could be an interesting feature for more closed communities, although it could put newer members of a community at a disadvantage... And it adds overhead.
If a new guy NG participates in debate A, his votes are very little weight. He then participates in lots of other debates. By the time he is participating in debate Z, he has more reputation, so his votes are now worth more. You don't want the now stagnant debate A to change because NG has gotten more reputation due to posterior debates. So you need to store the reputation of each vote, and add that to the computation.
Moderators can simply be added application-side (as opposed to theory-side) by allowing them to add or remove nodes/attacks, rather than just vote.
I still feel that you don't need to lose the forum structure, or whatever underlying, typically hierarchical structure. It should be just as easy (or easier) to navigate as a forum like this one. That information simply isn't used in computation of debate outcomes... but it's there, as meta-data. Certain posts could be identified as being "first posts" or "debate starting posts" within a subforum of a forum. There's no problem with that. Once you get to within a thread, however, you're in graph country. You can still try to display things with a sense of time, by highlighting new posts since your last visit, or by having older posts in the centre, newer posts in the periphery, or try to maintain similarity with a thread by having newer posts nearer the bottom of the screen, if at all possible.
But again, that becomes meta-data, maybe secondary to the fact that you can now reason with other people in a more formal way, in a system that tells you who ends up being right or wrong. Heck, it goes deeper than that. Each node/argument is given a strength, so that you can have any number of participants proposing any number of arguments, and each of those arguments, not sides or people, has a degree of acceptability, so to speak, calculated from votes and from attacks (and votes on the attackers, and so on almost recursively).
The fact that we are writing huge amounts of text here is due to the fact that we only have the forum structure. We are forced to, in text, reply to everything that's been said before, and, in text, explain why it attacks or doesn't attack another point somebody else made. It makes everything more verbose. Hopefully people will get used to using smaller, to-the-point sentences. Instead of replying with one post, they'd reply with maybe half a dozen arguments.