Now this is just an idea, but take a look at the "average" facebook user and you'll see that they have 100, 200, 300 or more friends.
More friends than one could ever possibly keep in touch with on anything approaching a meaningful basis. But there's a sort of prestige to this social networking thing, defined by your number of friends, so people keep on collecting them despite the fact they never chat, see each other or in anyways meaningfully communicate. I'll ignore this though as it's irrelevant to the purpose I'll describe.
This is it: Once a year - We'll call it "Facebook Friend Swap Day" (or "FFSD" as the internet loves acronyms). On that day facebook will automatically send you a list of friends (and a simlar list to your friends, and all users) that you/they haven't communicated with for, say, 6 months.
6 months is arbitrary, depending on how the idea takes hold we can adjust this. It's 6 months for the sake of argument.
Now with this list is a letter suggesting that they or you perhaps recommend to them friends more to your/their tastes. And so you drop them and take on a new friend request - someone with whom you'll doubtless have a little more in common with. It doesn't even have to be a "drop", which by implication is negative (and who likes to drop or be dropped?), it could simply be recommendation to a new friend, the acceptance of which constitutes a "swap".
Single people (Note the bare-chested profile photos of "Men interested in Women") will certainly benefit, as obviously they weren't doing so well if they're still single and they'll have a whole new cadre of unsuspecting suckers friends to try their charms upon. Those not single will benefit by having new friends possibly a little more to their tastes. And everyone will have a chance to make new friends and to exchange (without seeming rude) those friends they've very little in common with.
Facebook Friend Swap Day. I should start a group.