I can see that is a difference between the two cases. What I’m struggling to understand is why that leads to a different answer.

My understanding of the steps of the anthropic shadow argument (possibly flawed or incomplete) is something like this:

You are an observer → We should expect observers to underestimate the frequency of catastrophic events on average, if they use the frequency of catastrophic events in their past → You should revise your estimate of the frequency of catastrophic events upwards

But in the coin/tile case you could make an exactly analogous argument:

You see a blue tile → We should expect people who see a blue tile to underestimate the frequency of heads on average, if they use the frequency of heads in their past → You should revise your estimate of the frequency of heads upwards.

But in the coin/tile case, this argument is wrong, even though it appears intuitively plausible. If you do the full bayesian analysis, that argument leads you to the wrong answer. Why should we trust the argument of identical structure in the anthropic case?

I can see that is a difference between the two cases. What I’m struggling to understand is why that leads to a different answer.

My understanding of the steps of the anthropic shadow argument (possibly flawed or incomplete) is something like this:

You are an observer → We should expect observers to underestimate the frequency of catastrophic events on average, if they use the frequency of catastrophic events in their past → You should revise your estimate of the frequency of catastrophic events upwards

But in the coin/tile case you could make an exactly analogous argument:

You see a blue tile → We should expect people who see a blue tile to underestimate the frequency of heads on average, if they use the frequency of heads in their past → You should revise your estimate of the frequency of heads upwards.

But in the coin/tile case, this argument is wrong, even though it appears intuitively plausible. If you do the full bayesian analysis, that argument leads you to the wrong answer. Why should we trust the argument of identical structure in the anthropic case?