These thoughts aren't part of a system - I'm just responding to different things individually, just because one part is instantiated in the final forum doesn't mean that every part must be, there are an almost infinite variety of ways this thing could be set up finally, some will work and some will fail, but the only way to know is to try.
Given a system of accountability, mirror it on real life, in that if enough people support a single person, they will become their 'ruler'. Given the nature of the experiment, I believe that the majority of the forum would NOT want that to happen. If anyone not banned is allowed to mod people up or down and post, only those modded 50%+ are allowed to post new threads, only those 80%+ are allowed to delete/edit posts (to a history, Wikipedia style), the top 10% are allowed to ban, and the first person (only one at a time, people may settle for a representative 'democracy', but it's doubtful they would settle for a monarchy) rated 100% is promoted to über-moderator (ban more than one person in a day, actually delete posts [as opposed to having edits go to a history], and anything else you all can come up with. Perhaps they would have every power that Hal has, except the ability to change Hal's password or modify his priviledges.). I think that people would want to prevent anyone from getting absolute power like that, and so would really put effort into modding people down, and so on. If someone did get that power (even if they didn't abuse it) I think most people would quickly come into action to pull them back down to their own level.
As far as bans go (and edits, deletions, and really any act of public moderation) not only should they be logged, but they should be prominently presented to the community, and a reason should be given for each act of moderation. Some reasons may be simple ("posted illegal material", "racist comments", etc...), but someone going around thrashing people's posts would have several entries, right on the main page, and if all the reasons were the same (or going between a couple things) it would be likely they were abusing their power, and others could mod them down. I think there should only be allowed one ban per day per user - why would any one person have the need to ban five people in a single day? If there happen to be five people causing a lot of trouble on a certain day, there should be several other people around to take care of the rest.
Bans shouldn't be permanent, or by IP address (it's useless - I'm on AOL dialup [I know, it's not my choice, and I can't get any broadband but prohibitively expensive satellite where I live], which uses dynamic IPs, so you ban my IP address and I can sign off and get back on and be right back in the action. Ban a higher-level IP group [172.129.22.*, for example] and you've just banned 128 possible users, which may have had nothing to do with me, since sometimes I sign on and have a different top-level IP [ie... 152.x.x.x] ). A single day ban, by username, should be fine for most cases, if someone is really really causing problems, I suppose Hal could do perma-bans, but at that point we're starting to wander further from the anarchistic principles.
Some things (adding new forums, deleting old forums and such) should start with a request-for-comment, having the entire board (including those modded below priviledge) discuss the change. At the end, have a final poll, and if it is approved (51%+, let's say) Hal would have to implement it, even if it is in his better judgement not to. I don't think he would be against that, considering the ideals of the proposed community. (Granted, I just joined a few days ago, so maybe I've got Hal read totally wrong
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I'm not sure about how to be (relatively) sure that 1-account=1-person, and that permabanned users don't just re-register. Maybe allow them to post a membership request in a special new-members forum (a forum I used to regularly post in did this), and after proving their worth to a member (any member with the 80%+ mod-ability, let's say - in the other forum, it was only those with actual moderator titles) their account could be fully instated. I think this would give some opportunity to the community to recognize writing styles of banned members, try to spot spammers, and even hear out the cases of people who were permabanned.
In my opinion (regardless of dictionary definition), an anarchy is a society which has no formal governing body, no enforced rules (in this case, prevention of the dissemination of illegal content would have to be enforced, it would be one thing if we were all on an uncharted island in the middle of the Pacific, but there are underlying laws in our case, which must be followed), and operates on the will of individuals, as opposed to committees or elected bodies. There may be some elements which would fall under a meritocracy, but what makes it neccessary that meritocracy wouldn't be a part of a true anarchy? There may be a 'governing body' of sorts, but even someone with an approval rating of 1% could have their voice heard, and moderate someone within that 'governing body' right out of it.