> Why should one need to buy a liability insurance policy on a self-driving car?
The same reason property owners in general by liability insurance for liabilities that may occur to do property they own.
> What driver exactly am I insuring?
Most likely, you're insuring against liability resulting from your obligation as the owner (or leaseholder-in-possession, in the case of a lease) of the autonomous vehicle to maintain the vehicle in condition for safe operation and to remove it from operation if that is not possible.
The same reason property owners in general by liability insurance for liabilities that may occur to do property they own.
> What driver exactly am I insuring?
Most likely, you're insuring against liability resulting from your obligation as the owner (or leaseholder-in-possession, in the case of a lease) of the autonomous vehicle to maintain the vehicle in condition for safe operation and to remove it from operation if that is not possible.