I took the time to think all this through before replying. I think I grok now your and Alicorn and the other posters' theory(s). And I pretty much accept it now. Thanks for your explanations.
The problem with my old approach, as I now see it, is the impossibility of empirically distinguishing it from infinitely many other possible theories. In such a situation, it is indeed best to choose an approach that optimizes outcome over all my configuration-descendants, because I might subjectively become any of them.
Of course, if I give up personal continuity, then the above statement becomes merely "because each of them will have memories indicating it is my descendant". But I am forced to this point of view due to the apparent impossibility of describing a personal continuity in terms of physics, which does not break down in the face of (arbitrarily short) lapses of consciousness.
Thanks again to everyone else who participated and helped convince me.
From the dawn of civilization humans believed in eternal life. The flesh may rot, but the soul will be reborn. To save the soul from the potential adverse living conditions (e.g. hell), the body, being the transient and thus the less important part, was expected to make sacrifices. To accumulate the best possible karma, pleasures of the flesh had to be given up or at least heavily curtailed.
Naturally the wisdom of this trade-off was questioned by many skeptical minds. The idea of reincarnation may have a strong appeal to imagination, but in absence of any credible evidence the Occam’s razor mercilessly cuts it into pieces. Instead of sacrificing for the sake of the future incarnations, a rationalist should live for the present. But does he really?
Consider the “incarnations” of the same person at different ages. Upon reaching the age of self-awareness, the earlier “incarnations” start making sacrifices for the benefit of the later ones. Dreams of becoming an astronaut at 25 may prompt a child of nine to exercise or study instead of playing. Upon reaching the age of 25, the same child may take a job at the bank and start saving for the potential retirement. Of course, legally all these “incarnations” are just the same person. But beyond jurisprudence, what is it that makes you who you are at the age of nine, twenty five or seventy?
Over the years your body, tastes, goals and the whole worldview are likely to undergo dramatic change. The single thing which remains essentially constant through your entire life is your DNA sequence. Through natural selection, evolution has ensured that we preferentially empathize with those whose DNA sequence is most similar to our own, i.e. our children, siblings and, most importantly, ourselves. But, instinct excepted, is there a reason why a rational self-conscious being must obey a program implanted in us by the unconscious force of evolution? If you identify more with your mind (personality/views/goals/…) than with the DNA sequence, why should you care more for someone who, living many years from now will resemble you less than some actual people living today?
P.S. I am aware that the meaning of “self” was debated by philosophers for many years, but I am really curious about the personal answers of “ordinary” rationalists to this question.