The phrase "could have done otherwise" is almost essential to all discussions concerning free will. Most philosophers, as I understand the literature, believe this phrase characterizes and validates moral responsibility. My question relates to how one can make sense of this phrase in the context of libertarian free will.
Consider a choice C that a free agent A makes at t. In some sense, under libertarian free will, until t, the outcome of C is not decided. Instead, there are possible outcomes after t, meaning that it is both logically possible before t that at t A chooses C1 or C2. Now, suppose A chooses C1 at t. A could have chosen differently, thus A is responsible for his choice.
A, however, does not realize that he is inside of a time machine. The time machine rewinds the clock back until before t. This time at t, A chooses C2—which we know is logically possible.
We now have two equally valid outcomes. We have one timeline in which A chose C1, and one timeline in which A chose C2. Each timeline is equally valid morally-speaking, since in both timelines A is responsible for his choice.
From this, I see two implications. First, there seems to be no problem in saying that the man who controls the time machine can actualize whichever future he wants while still preserving the moral responsibility of A. Even if, on the second attempt, A chooses C1 again, as long as it is logically possible that A chooses C2 at t, the man in control can simply rewind again and again until A chooses C2. This would mean, of course, that for all free choices there are possible futures which are equally valid, and that whichever possible future becomes actual is an arbitrary matter (or dependent on the controller). "Arbitrary" here does not mean the choice itself is arbitrary; like I said, in both possible futures A is still responsible for his choice. But in some sense the actual world must be arbitrary. This, however, would be a monstrous threat to the kind of free will most religions wish to grant. Any omnipotent God has a power identical to that of the time machine (a power according to which that God might select the actual future from a set of possible futures). And since, according to this analysis of free will, both ends of a choice are possible futures, God can in theory actualize a world in which no free agent ever chooses evil, for example.
But, as a second implication, I would have to guess then that a free choice is not contingent in this indeterministic sense. There must be some defeater which says that A would contingently or would freely always choose C1 at t—giving the time machine no control of the actual future. Now, in order for A to remain morally responsible, we must still say that A could have done otherwise at t. But then, according to this analysis, we must also affirm that A would (never in a sense) have done other than A did at t. It seems to me, however, that saying A would never haven chosen C2 is equivalent to saying that A could never have willed to choose C2. But if A is restricted on what he can "will", then he seems to have no free will at all.
Two questions, then. Which is the correct understanding of free will: the one in which when we replay time the outcome of a free choice might be different (in which case a time machine can actualize whichever future it likes), or the one in which an agent would contingently always choose a particular end? And if the latter is correct, how does one make sense of "could have done otherwise" and moral responsibility with this kind of "would". I am having a hard time understanding this contingent kind of "would", which falls in between "might" (indeterminism, possibility) and "would" in the strong sense (determinism, necessity). Can someone help me construe this concept?