What is the answer to the question of anthropic probabilities? I've claimed before that there was no answer - anthropic decision theory (ADT) was the only way to go.

But actually, there are answers - the problem is simply that there are multiple versions of "the question of anthropic probabilities", each with their own answer. And what decision theory did was unambiguously select the right question (and the right answer) for the job.

Frequentist anthropic probabilities

It is much easier for humans to think in terms of frequencies, and anthropic probabilities are no exceptions. So imagine that either a small universe (with one copy of you) or a large universe (with $ω$ copies of you) is created, with equal probability. Then your copies will independently observe a large sequence of $Ω$ random bits, with $2^{Ω} >> ω$ . After that, the universe ends, and the whole experiment begins again, with a small or large universe being created again. This experiment will then be repeated a very large number of times, so we can coherent talk about frequencies.

Then there are three questions you might ask yourself during these experiments:

What proportion of my versions will be in a large universe?
What proportion of universes, where versions of me exist, will be large?
What proportion of universes, where exact copies of me exist, will be large?

In the limit as these experiments are run a large number of times, the answers to these questions will converge on $ω / (1 + ω)$ , $1 / 2$ , and "it depends on how many random bits you have seen when you ask the question". In other words, the probabilities given by SIA, SSA, and FNC.

Notice there is a fourth question that we could ask to complete the three:

What proportion my exact copies will be in a large universe?

But this question will also converge to $ω / (1 + ω)$ , ie SIA, showing how SIA is independent of the reference class as long as the reference class contains at least the exact copies.

The issues with the questions

All three questions are well-posed questions with exact and correct answers. From outside, however, there are issues with all three.

Question 2 has the perennial "reference class problem": what are you counting as "versions of me"? If we change the reference class, we change the question, and therefore its not surprising it gives a different answer.

Question 3 has the same time inconsistency that FNC has: the answer will be (p

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