What if I split, amoeba-style, into two future persons, one of whom is promptly shot? In general, I should split my expectations evenly between my future branches. Perhaps I should anticipate the experiences of each branch, separately. (I do not, of course, experience both lives together, in any mutually-accessible kind of way.) If one branch has no experiences at all - being killed before ever awakening, say - then all there is to anticipate is the other, surviving branch. But if it gets to experience a little before dying, then it would seem one allotment of my expectations should capture precisely this: to experience seeing the bullet approaching (or whatever), and then no more.
This is important because if the "no collapse" (or many-worlds) interpretation of Quantum Mechanics is correct, then we are actually splitting all the time. If you shoot me, there exists some (extremely low intensity) state in the superposition in which the bullet passes right through me. However often I die, there is always some version of me that survives. Should I expect, then, to be immortal? Lewis thinks so (p.19):
Suppose you're fairly sure that there are no collapses, and you're willing to run a risk in the service of truth. Go and wander about on a busy road, preferably a few minutes after closing time. When and if you find yourself still alive, you will have excellent evidence [for the no-collapse view]. If that's not yet enough to convince you, try the experiment a few more times.
What should you expect to happen?
(1) You miraculously emerge unscathed (perhaps the cars pass right through you by some quantum fluke).
(2) You get hit by a car, and then have no further experiences (due to being dead).
(3) You get hit by a car, but then miraculously survive (perhaps your crushed body reassembles itself by some quantum fluke).
On the no collapse view, all these outcomes occur, but (presumably) the second does so with much higher frequency or "intensity". Still, even if the overwhelmingly majority of superimposed states involve your getting hit by a car, you will always have some branch that survives this. So there are always further experiences to anticipate. Does this mean we should never anticipate ending up on a dead branch, i.e. one that has no further experiences?
It's not quite enough to ask whether we should expect to be immortal. On the no-collapse view, we are undoubtedly immortal, in the sense that we will always have some surviving branch. But we also die a lot, in that we have a great many terminating branches! So the real question is whether we should ever expect to die. Can our expectations be distributed over branches that contain no further experiences? Or are they restricted to the survivors only?