Sure, in some sense :) This model exists under a number of names: Pesero, Jittney, Monit Sherut (to name a few). That said, it's not just an app that we've built. It's a system that can make dynamic decisions about which routes merit being paired together, and communicates with our drivers about any changes that need to be made to the current route. Of course, we take on-road safety into account, and so changes are only made while the vehicle is stationary.

Absolutely :) There are lot of systems like this that we took as inspiration. See my comment below on how we formalized this type of transit, and built something that can make more objective decisions as to whether the pairing "makes sense."

Also reminds me of Halting State by Charlie Stross. The buses in that book have an auction system where people bid against each other for it to go to their stop next.

Lyft pairs one passenger (or equivalently, one party) to one driver. We've built a system which will actually take your route into consideration, and pair you with additional passengers that are en-route (relative to you). In other words, your ride is shared with other people heading in the same direction you are.

While are drivers are for-hire at this phase (in order to provide a reliable and available supply-side), there is much higher utilization in the car as multiple riding parties are paired to it.

EDIT:

I see the question was changed slightly. Higher utilization makes all the difference. Our current public transit system is just as you've stated: a vehicle being shared by "more strangers" (in your own words). We envision our system creating a completely adaptive and dynamic transit grid, which lends itself to predominant way in which people get around in the future.

It looks like you'd be splitting the ride with others so filling up more of the car and thus paying less. Perhaps even meeting others. Sounds like enough of a difference to me.