Personally I think the multiverse explanation is exceedingly lame. It takes away our freedom of choice and the consequences of actions, which I firmly believe in--both for religious reasons as well as from the evidence of my own experience. Conversely, there's absolutely no evidence for a multiverse. There's also no current evidence for, say, string theory--but string theory at least holds the promise of one day being able to produce verifiable or falsifiable predictions. The multiverse theory does not. In my opinion it's not science, it's philosophy.
Sorry for the mini-rant.
While I agree it is a philosophical question, I do not in any way think that it absolves us of personal accountability in THIS, our universe. And I do not entirely discount the idea of multiple universes, in fact the fringe aspects of the LDS faith more or less confirms there are multiple universes.
To wit, this is "our" God's universe, but we know that God was once as we are, and as God is we may become, so would that be in this universe or some other? I would posit that it makes more sense for it to occur in a different universe entirely, as it has already been established that our God has "worlds without number" in this universe, it would begin to get crowded if everyone who achieves Godhood merely continues in this self-same universes where our God already rules worlds without number.
And in that light, it isn't such a big stretch to imagine that there is some connections between the universes. I don't even think it is a gigantic stretch to imagine each of us living a separate life in another universe, and then at some cosmic point in the eternal continuum all of our "selves" get rolled back into one, with lifetimes worth of experiences preparing us to rule over our own universe in kind.
n fact, to me that kind of resolves a concern I have always had in the back of my mind concerning a loving God, who supposedly loves his children but who, by his own scripture and representatives here on earth, more or less is condemning the vast majority of these children to less than they could potentially achieve. What percentage of his children will reach the highest glory in the celestial kingdom? From my understanding that is, even by design, a very very small number, and how could he truly bask in the eternal glory of eternal progression knowing that billions upon billions of his children will be in essence cut off from his presence? How happy would it make you if even 1 of your say 3 or 4 kids would never have anything to do with you again in their lives? Could it be a multiverse construct that provides far more of us the chance to progress as God intended? I figure, why not?
But, as has been stated, this is a philosophical discussion far more than a physics one.