Say Alice would drive from A to B. She calls a Lyft instead. The car takes her for exactly the same trip, PLUS having to drive to pick her up at A, and to pick someone else after B (or to take the driver home.) It's strictly MORE driving than before. It can, however, reduce parking demand.
A group of people who would have carpooled are the same.
A group of people who would have individually driven DOES reduce driving if they take one rideshare vehicle instead.
The biggest potential is probably in arranged shared rides, Lyft Line or UberPool. If Alice would drive from A to C, and Bob would drive from B to D, and the routes overlap or parallel a lot, then driving to pick up Alice at A, driving to B for Bob, driving to D, and then C, might be a reduction. Depends on how much endpoint driving (including backtracking to pick up Bob after already going part way to C) there is compared to the shared component. Picking up two people at the airport who live half a mile apart five miles away is a clear win. Picking up people five blocks apart who are going to places ten blocks away and five blocks apart themselves would not be a win. (10+10 vs. 5+10+5.)
So the shared rides can reduce driving, and we'd need actual data on algorithms and trip patterns to evaluate that. But it's more likely for longer trips than short ones within a squarish area.
And of course all this ignores taking trips from transit, or stimulating new trips that wouldn't have happened.
See the DW comments at https://mindstalk.dreamwidth.org/526674.html#comments