(Oh-ho, a former Fark admin? My condolences. I remember my days as a TFer fondly, but I eventually got fed up with the over/slanted moderation and cliques.)
I'm going to the model of 'invitations' where you have to know someone already in the community to get an invite -- because then if we get someone being an ass, we can suspend their friends' accounts, too (giving them some external pressure to not be a dick), or prune the whole tree of accounts if that doesn't help.
Even if that helped with trolling*, this is an excellent way to create an echo chamber/circlejerk. Since your friends likely have similar opinions to you, the site will maintain a steady consensus about topics for some time. By the time invites branch out to people who have opinions that are very different (but still reasonable), they'll be awash with mob mentality the moment they make their first counter-consensus post and likely just leave.
If you're not trying to have a serious discussion site or are going for the insular angle, that would be okay, though.
* I think that once you hit a certain (fairly low) threshold it will become nearly ineffective against trolling. "Friend" will become "anyone who asks me for a referral"/"uses the referral codes I post on another site", much like the early days of Gmail and pretty much any invite-only site, and trolls will use this to not only cause the general site anguish, but extra special and indirect harassment upon the person who gave them the invite