Riding alone? If so, they send a 1 person vehicle to pick you up. Riding with a friend? Two person vehicle. etc.
Right now they need humans to drive their cars around but as soon as they can they will surely shift to automated cars. If they've already built the scheduling systems necessary they'll be able to combine that with the mindshare they've been building and be in a great position.
Uber is Netflix in 1997, sending DVDs through the mail to people's mailboxes, carefully awaiting the day when the technological infrastructure will support their true purpose.
In fact, I think self-driving cars together with decent electric engines (which already exist) can revolutionize urban landscape.
Just imagine how quiet and pollution free our cities will be if the only traffic allowed inside are electric cars, who automatically go to charge themselves when necessary.
EDIT: Possibly I'm being too pessimistic. I expect automated cars could be really, really awesome and if so, and if they're allowed anywhere, eventually there'll be pressure in other cities to allow them too.
Maybe this won't be as widespread a problem as I think it could be. Zipcar seems to be rather successful, although I've never used one.
Generally, the number of livery service drivers and cars is not limited.
That said, the Washington, DC taxi commission has been hassling the Internet-based Uber. Last month they ran a sting against an Uber-arranged driver and impounded his car.[1]
[1] http://www.washingtonpost.com/blogs/mike-debonis/post/uber-c...