Here is a version of the Principle of Alternate Possibility that is immune to all of Frankfurt's counterexamples:
If x freely does A and Mr Black is nowhere near, x could have refrained from doing A.
It doesn't get you around the divine versions, though. It also doesn't handle cases where Black can act from a considerable distance.
What's worse, it doesn't get you around cases just like Frankfurt's, but where the neurosurgeon is named "Green". :-)
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