It might sound a bit weird, but I was thinking about a social networking site specifically focused on introducing people to total strangers. I suppose you might think of it as a non-dating dating site; people are introduced to others who the system reckons they might get on with. So straw poll time - is this a dumb idea?

Sounds like you need a bro search. Sadly brosearch.com just links to break.com. :

">As always bro search safely

I don't think it is a dumb idea. In fact, I would be amazed if it has not been done before. Here is a list of 100+ social networking sites in operation today. You may want to go through them and see if one of these sites is already doing that (which, like I said, I would highly doubt that no site is already doing this).

http://en.wikipedia.org/wiki/List_of_social_networking_websites

It is also notoriously hard to get a social networking site going. Lots of people have had big dreams of having the next MySpace or Facebook (just look at the size of that list). The problem is the beginning; the catch 22 of social networking sites: If no one is on it, people have nothing to do, so they leave. How do you get people to hang around in the beginning? When MySpace got big, there were not many competitors, and it was seen as one of the few alternatives to Friendster. Facebook got its start as a social network for a college (was it Harvard? I can't remember), so it had a built-in audience to start. Now a new site would be hard-pressed to get college-age students off of Facebook and Twitter for a newer, less-populated network.

Foursquare does this particularly well, because it's all based on location. You pull out your smart phone, "check in" to the bar or concert venue or whatever, and get a list of people in the same place at the same time. Then you've got at least a flimsy pretext to go and start a conversation. Meeting people online, meh. Tools for immediately meeting people in person = very cool.

I feel like there's a lot of potential that Foursquare is missing (and I won't complain about their currently-broken JSON API); the "mayor" thing is a good hint at where this can go. But anything more interesting/successful than Foursquare will at least build on the same model.

I think it's a good idea. There are sites out there that introduce you to complete strangers, but none of them provide any sort of matching to ensure you have common interests or will get along with the person. Alternatively, there are dating sites which strive to match you with people you will get along with, their main goal is certainly not to match you with just "friends".

I think one major issue would be getting people to actually trust it. Dating sites have had a tough time convincing people it's a good idea to meet strangers you've been matched with (and, often, rightfully so. Lot's of creepers out there). I think it would be just as hard, if not harder, to convince people it's a good idea to meet strangers just to be friends.