Monday (heads): 0.4, Monday (tails): 0.3, Tuesday: 0.3 for SSA
Monday (heads): 0.25, Monday (tails): 0.375, Tuesday: 0.375 for SIA
Thus the SSA SB would always guess Monday (heads) and the SIA SB would guess either Monday (tails) or Tuesday to maximize her odds. Suppose she always picks Tuesday. In 1000 simulations there are 400 heads and 600 tails. 400 SSA SBs survive vs 600 SIA SBs, so the SIA is the way to go.
You’re using the SIA way of counting (considering each agent in tails as separate), and getting an SIA-favouring result.
An SSA way of counting would be that you have to guess what day and coin flip it was, and your chances of surviving is the average number of times you guessed right. Guessing Tuesday(tails) or Monday(tails) would give you a 50-50 chance of surviving in the tails world, since one of the versions of you will get it wrong. Guessing Monday(heads) would give you a certainty of surviving in the heads world (since there is only one of you). 400 SSA SB survive versus 300 SIA SB.
OK, I understand the SSA setup now, though it does look a little contrived to me. I guess I need to read your arxiv paper in more detail to see when this is reasonable. Thanks.
Let’s consider p(head)=2/5. Then the odds are:
Monday (heads): 0.4, Monday (tails): 0.3, Tuesday: 0.3 for SSA
Monday (heads): 0.25, Monday (tails): 0.375, Tuesday: 0.375 for SIA
Thus the SSA SB would always guess Monday (heads) and the SIA SB would guess either Monday (tails) or Tuesday to maximize her odds. Suppose she always picks Tuesday. In 1000 simulations there are 400 heads and 600 tails. 400 SSA SBs survive vs 600 SIA SBs, so the SIA is the way to go.
What am I missing?
Note what we’re doing in these situations: we’re determining the ‘right’ answer, without having to use the anthropic probabilities at all.
You’re using the SIA way of counting (considering each agent in tails as separate), and getting an SIA-favouring result.
An SSA way of counting would be that you have to guess what day and coin flip it was, and your chances of surviving is the average number of times you guessed right. Guessing Tuesday(tails) or Monday(tails) would give you a 50-50 chance of surviving in the tails world, since one of the versions of you will get it wrong. Guessing Monday(heads) would give you a certainty of surviving in the heads world (since there is only one of you). 400 SSA SB survive versus 300 SIA SB.
OK, I understand the SSA setup now, though it does look a little contrived to me. I guess I need to read your arxiv paper in more detail to see when this is reasonable. Thanks.