rwallace, nice reductio ad adsurdum of what I will call the Subjective Probability Anticipation Fallacy (SPAF). It is somewhat important because the SPAF seems much like, and may be the cause of, the Quantum Immortality Fallacy (QIF).
You are on the right track. What you are missing though is an account of how to deal properly with anthropic reasoning, probability, and decisions. For that see my paper on the ‘Quantum Immortality’ fallacy. I also explain it concisely on on my blog on Meaning of Probability in an MWI.
Basically, personal identity is not fundamental. For practical purposes, there are various kinds of effective probabilities. There is no actual randomness involved.
It is a mistake to work with ‘probabilities’ directly. Because the sum is always normalized to 1, ‘probabilities’ deal (in part) with global information, but people easily forget that and think of them as local. The proper quantity to use is measure, which is the amount of consciousness that each type of observer has, such that effective probability is proportional to measure (by summing over the branches and normalizing). It is important to remember that total measure need not be conserved as a function of time.
As for the bottom line: If there are 100 copies, they all have equal measure, and for all practical purposes have equal effective probability.
rwallace, nice reductio ad adsurdum of what I will call the Subjective Probability Anticipation Fallacy (SPAF). It is somewhat important because the SPAF seems much like, and may be the cause of, the Quantum Immortality Fallacy (QIF).
You are on the right track. What you are missing though is an account of how to deal properly with anthropic reasoning, probability, and decisions. For that see my paper on the ‘Quantum Immortality’ fallacy. I also explain it concisely on on my blog on Meaning of Probability in an MWI.
Basically, personal identity is not fundamental. For practical purposes, there are various kinds of effective probabilities. There is no actual randomness involved.
It is a mistake to work with ‘probabilities’ directly. Because the sum is always normalized to 1, ‘probabilities’ deal (in part) with global information, but people easily forget that and think of them as local. The proper quantity to use is measure, which is the amount of consciousness that each type of observer has, such that effective probability is proportional to measure (by summing over the branches and normalizing). It is important to remember that total measure need not be conserved as a function of time.
As for the bottom line: If there are 100 copies, they all have equal measure, and for all practical purposes have equal effective probability.