To condense my response to a number of comments here:

It seems to me that there's some level on which, even if I say very firmly, "I now resolve to care only about future versions of myself who win the lottery! Only those people are defined as Eliezer Yudkowskys!", and plan only for futures where I win the lottery, then, come the next day, I wake up, look at the losing numbers, and say, "Damnit! What went wrong? I thought personal continuity was strictly subjective, and I could redefine it however I wanted!"

You reply, "But that's just because you're defining 'I' the old way in evaluating the anticipated results of the experiment."

And I reply, "...I still sorta think there's more to it than that."

To look at it another way, consider the Born probabilities. In this case, Nature seems to have very definite opinions about how much of yourself flows where, even though both copies exist. Now suppose you try to redefine your utility function so you only care about copies of yourself that see the quantum coin land heads up. Then you are trying to send all of your measure to the branch where the coin lands up heads, by exercising your right to redefine personal continuity howsoever you please; whereas Nature only wants to send half your measure there. Now flip the coin a hundred times. I think Nature is gonna win this one.

Tired of being poor? Redefine personal continuity so that tomorrow you continue as Bill Gates and Bill Gates continues as you - just better hope Gates doesn't swap again the next day.

It seems to me that experience and anticipation operate at a more primitive level than my utility function. Perhaps I am wrong. But I would like a cleaner demonstration of how I am wrong, than pointing out how convenient it would be if there were no question.

Of course it must be a wrong question - it is unanswerable, therefore, it is a wrong question. That is not the same as there being no question.