The interesting question is how good self-driving has to be before people tolerate it.
It's clear that having half the casualty rate per distance traveled of the median human driver isn't acceptable. How about a quarter? Or a tenth? Accidents caused by human drivers are one of the largest causes of injury and death, but they're not newsworthy the way an accident involving automated driving is. It's all too easy to see a potential future where many people die needlessly because technology that could save lives is regulated into a greatly reduced role.
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