Three is the magic number
Social software = software that *improves in functionality* when n > 2. I dunno -- eBay becomes more useful as n grows (and, in the classic example, so do fax machines), but that's just network effects.
Clay's definitions, provisional as they are, are the best attempt I've seen at describing what social means in relation to software. But the term social software is still kind of confusing... is it a) software that allows us to be social (IM, IRC, email, the web); or b) software built for group use; or c) software that exposes and exploits our social networks?
Of course, the really interesting thing is that even though several smart people are thinking about it, social software remains a very fuzzy donkey. Funny that Clay Shirky's definitions are so different from Matt Jones's (well, in fairness, Matt's thoughts were speculative and kind of sci-fi, but still cool).
I like Clay's idea that a threshold is crossed between n = 2 and n = 3. Although, still being skeptical about the whole social software thing (not sure if it's just a fashionable meme or a durable concept), I think the threshold between 2 and 3 might be ultimately less interesting than the threshold between 1 and 2. As for software that "treats groups as first-class objects"--I'd probably have to see an example to really understand how this would work.
But in the thread a couple of people mentioned eBay as an example of social software, and I found that idea a little chafing. I have a hard time accepting a definition of social software that is merely "gets more useful the more people use it" (I mean, that would make Microsoft Word social software fer chrissakes). Matt Jones pointed out that instant messaging is social--i.e. more than just a "software phone," as someone put it--because of the buddylist which tells you when someone's available to chat (here's a great diagram).
(Tangent: speaking of both networks and protocols that enable communication, I've been reading a bit about international postal treaties and the Universal Postal Union, since those treaties created a kind of proto-network. In 1874.)
We're probably very close to an explosion of social network software, but I'm curious see to some applications of Clay's ideas. In fact, I'd be happy to just understand how Clay's ideas would really work.
And, finally, to add to the ad hoc list of social software criteria, maybe we should make social software truly social and bot-free. Or, put another way, everyone who uses it should be able to pass a Turing Test.

