In the Dr. Who story Inferno, the Doctor’s malfunctioning TARDIS console drops him into a parallel universe inhabited by counterparts of the people of his home reality. Ever philosophical, the Doctor responds to his discovery by the following reasoning: “An infinity of universes. Ergo an infinite number of choices. So free will is not an illusion after all. The pattern can be changed.”
While the Doctor does not go into detail regarding his inference, his reasoning seems to be that since the one parallel universe he ended up in is different from his own in many ways (the United Kingdom is a fascist state in that universe and the Brigadier has an eye patch), it follows that at least some of the differences are due to different choices and this entails that free will is real.
While the idea of being able to empirically confirm free will is appealing, the Doctor’s inference is flawed: the existence of an infinity of universes and differences between at least some (two) of these universes does not show that free will is real. This is because the existence of differences between different universes would be consistent with there being no free will.
One possibility is that determinism is true, but different universes are, well, different. That is, each universe is a deterministic universe with no free will, yet they are not all identical. To use an analogy, two planets could be completely deterministic, yet different. As such, the people of Dr. Who’s universe were determined to be the way they are, while the people of the parallel universe were determined to be the way they are.
It could be objected that all universes are at least initially identical and hence any difference between them must be explained by metaphysical free will. However, even if it is granted for the sake of argument that all universes start out identical to each other, it still does not follow that the explanation for differences between them is due to free will.
The rather obvious alternative explanation is that randomness is the key factor—that is, each universe is random rather than deterministic. In this case, universes could differ from each other without there being any free will at all. To us an analogy, the fact that dice rolls differ from each other does not require free will to explain the difference—random chance would suffice. In this case, the people of the Doctor’s universe just turned out as they did because of chance and the same is true of their counterparts—only the dice rolls were a bit different, so their England was fascist and their Brigadier had an eye patch.
Interestingly enough, if the Doctor had ended up in a universe just like his own (which he might—after all, there would be no way to tell the difference), this would not have disproved free will. While it is unlikely that all the choices made in the two universes would be the same, given an infinity of universes it would not be impossible. As such, differences between universes or a lack thereof would prove nothing about free will.
My position, as usual, is that I should believe in free will. If I am right, then it is certainly the right thing to believe. If I am wrong, then I could not have done otherwise or perhaps it was just the result of randomness. Either way, I would have no choice. That, I think, is about all that can be sensibly said about metaphysical free will.