Contrastive explanations of free choices

Suppose you grant that a sufficient condition for P to be an explanation why Q rather than S is:
 (a) P is an explanation why Q and not S,
 (b) P could not be an explanation why S, and
 (c) Q and S are incompatible.

Then one can give contrastive explanations of libertarian-free actions.  For instance, suppose that we are trying to explain why x did A rather than B.  We can say:

• A and B are incompatible and x's reasons favored A with strength at least SA and favored B with strength at most SB.

This explains why x did A and why x did not do B.  It also could not be an explanation why x did B.  Hence it satisfies my contrastivity requirements (a)-(c).  And had x done B, the explanation of why x did B instead of A would have been of the form:

• A and B are incompatible and x's reasons favored A with strength at most SA and favored B with strength at least SB.

(The "at most" and "at least" are switched.)

We can also give contrastive explanations for quantum events.  Suppose the electron in state |up>+|down> collapses to |up>.  Explanation:

• |up> and |down> are incompatible and the electron's state contained at least proportion 2^-1/2 of |up> and at most 2^-1/2 of |down>.

This is an explanation why the electron collapsed to |up> and not to |down>, and it could not explain why the electron went to |down>.

There is a way in which my contrastivity requirement is a fairly natural weakening of the more common conditions:
 (a) P is an explanation why Q and not S, and
 (b') P&(Q or S) entails Q&~S.

For my (b) and (c) entail:
 (b'') P&(P explains Q or P explains S) entails Q&~S,
which does look like a fairly natural weakening of (b').

In other words, we switch from the requirement that the explanation entail which of the alternatives should happen to the requirement that the explanation could only explain one of the two alternatives.