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Realistically, they need to be many times safer than human-driven cars for acceptance.Yes, many times yes. The promise of self-driving cars is that they are totally safe, that is, nothing will happen except in exceptional, unforeseeable circumstances.
The reason for this is, in a self-driving car, nobody's in charge, and therefore, any incident (let alone, a fatal accident) is immensely more complicated than the same incident with a human driver.
(It's obvious that a self-driving car with a safety driver at the wheel doesn't provide any benefit whatsoever and isn't, in fact, a self-driving car).
A self-driving car needs to:
- transport people who are unable to drive or are "irresponsible" in the legal sense (kids, seniors, drunk people, injured/sick people going to the hospital, etc.)
- drive itself with absolutely nobody onboard
The analogy with trains is flawed because trains have drivers that deal with problems when there is one. Even "autonomous" metro trains are monitored individually.
In fact, save for special conditions like a closed network on a campus, etc., I'm less and less sure self-driving cars will ever be a thing.