I've got the answer (I think.) It's a pretty simple idea, really. I even have a proof-of-concept website up for it, but I'm not going to link it here because there's nothing to see. What I mean is that if you go to the site it will challenge your browser to provide a client certificate to authenticate, and since you don't have a cert it won't let you in and you'll get a blank page or an "UNAUTHORIZED" message from your browser or something.
So how do you get a cert? A friend (who is already a member) gives you a one-time access URL to a page that lets you download a new client cert. Install that in your browser and now you can access the site, and you can generate your own "new cert" URLs like the one your friend gave you to give to your friends for them to join.
So that's how the network grows: word-of-mouth direct personal connections. And all these connections are public: recorded in a public DB (Sqlite file) and published regularly (say, every four hours or so) so the membership graph is known to all.
How do you use it? Well, the other thing you can do with the site (besides minting new "join URLs") is to propagate information (not to be coy, URLs to some article or whatever, like the submissions here on HN) through the network. You go to the site (auth w/ client cert), enter the URL of the thing you want to propagate, and you get back what I call a "bump URL" that has a code that identifies the subject and the sender (you). You send this "bump URL" to your contacts (via email, Twitter, whatever) who can click on it to see a page that has the original subject URL and a new "bump" URL customized for that contact, for them to send to their contacts. There are two buttons: "Engage" and "Reject". "Engage" redirects you to the subject site after recording the "engage event" in the public DB; "Reject" likewise enters a "reject event" in the public DB. Both are optional, you don't have to click on either (it probably doesn't make sense to click on both.)
And that's pretty much it: you have a public graph of members, and a public sub-graph for each subject URL with public "engage"/"reject" events, and all the data are published in a public DB that anyone can download and analyze. (Have I mentioned that it's all done in public enough yet?)
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So how does it work? Why would you use it? And how does it kill the ads market?
Simple (and as yet theoretical): Let's say I'm a small business with some widgets to sell. I create a sales page and make a "bump" URL for it and send it to my contacts, who forward it to theirs, who forward it to theirs, and so on. When someone "engages" with that URL/page and actually buys a widget, I can check the public DB to find out the "chain" of word-of-mouth links that led to that sale and reward each of those folks somehow.
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I am not spelling it all out here, there are additional details, but the above is the crux of the idea. There are also some pretty obvious problems (e.g. how many "bump URLs" are going to be flying around? Billions!?) but I think most of the potential problems are solved by the direct interpersonal nature of the thing:
Spam? No, why would you forward spam to your friends? If a friend sends you spam you can talk to them and tell them to stop, or just stop clicking on their "bump" URls.
As far as I can anticipate, most problems would be solved by the open feedback between members in light of the public DB.
Moderation? Everyone is a moderator, and then some: people who don't participate can still read the DB, so the moderation "team" is larger than the userbase!
Censorship? No, because no information (other than the URLs themselves) goes through the network, so there's nothing to censor. (Of course someone could use an offensive URL, but again, if you get a link to something that offends you (for whatever reason, in whatever way) you can "reject" it, or just not propagate it.)
Anyhow, I can go on but I want to know what y'all think? I've been sitting on the demo for months now because I just don't know if I really want to do this or not, but I really DO think it's "got something", that there's potential in this idea. What do you think?