Let me see if I can fit this to my picture of reality.
Randomly picking one of the 5 versions of yourself at T2 yields a winner with 80% probability. But this does not correspond to any real state of knowledge. Our actual degree of belief in winning the lottery depends on our knowledge of the “thread” or “threads” leading there from our current position. Obviously all these threads share an event of small probability. It shouldn’t matter how many times they split after that, they’re just splitting a sliver of probability mass.
More generally, picking ‘a random thread’ in a way that agrees with what we experience would involve looking at a separate ‘choice’ for each branching point. Figuring out what ‘you’ should expect to see, and with what probability, means finding in turn the probability of randomly picking each thread (or each that involves consciousness like ‘yours’) at each branching point, and multiplying those fractional probabilities for each individual thread.
Defining branching points in the case of the Boltzmann brain scenario seems trickier to me. But I do think this approach would work if I understood the setup better. Eliezer’s argument should still hold.
Let me see if I can fit this to my picture of reality.
Randomly picking one of the 5 versions of yourself at T2 yields a winner with 80% probability. But this does not correspond to any real state of knowledge. Our actual degree of belief in winning the lottery depends on our knowledge of the “thread” or “threads” leading there from our current position. Obviously all these threads share an event of small probability. It shouldn’t matter how many times they split after that, they’re just splitting a sliver of probability mass.
More generally, picking ‘a random thread’ in a way that agrees with what we experience would involve looking at a separate ‘choice’ for each branching point. Figuring out what ‘you’ should expect to see, and with what probability, means finding in turn the probability of randomly picking each thread (or each that involves consciousness like ‘yours’) at each branching point, and multiplying those fractional probabilities for each individual thread.
Defining branching points in the case of the Boltzmann brain scenario seems trickier to me. But I do think this approach would work if I understood the setup better. Eliezer’s argument should still hold.