Important summary: For SSA, the reference class to be used is defined in the question asked.

I said that SSA derives from the following question:

Q: What proportion of universes, where versions of me exist, will be large?

And it's sort of true, that sort of is the SSA question. But only when talking about probabilities of universes, not when updating on information.

For example, consider the sleeping beauty problem. If the coin is tails ( $T$ ), Sleeping Beauty ( $S B$ ) is awoken twice, on Monday and Tuesday. On heads ( $H$ ), she is only awoken on Monday.

Then if the "large" universe is the tails universe, and "versions of me" cover both Monday and Tuesday (reference class $R_{S B}$ ), then the answer to that question will be " $1 / 2$ ". So, writing $P_{S B}$ for the notationally unwieldy $P_{R_{S B}}^{S S A}$ , we have:

$P_{S B} (T) = 1 / 2$ ,

the standard halfer/SSA answer.

Now suppose that every version of Sleeping Beauty is (eventually) told which day it is. Suppose she is told it is Monday. What is the correct question now? It seems like it should be:

QM: What proportion of universes, where versions of me exist on Monday, will be large?

However, the answer to that question is... also $1 / 2$ . The fact of it being Monday has not updated anything at all! This is surprising, because if the question had asked about Tuesday, it would have updated to $1$ on the universe being large (ie tails).

Sliding reference classes

What's happening is that the reference class has changed between question Q and question QM. For QM, the reference class is the set of all Sleeping Beauties who are eventually told that it is a Monday (call this $R_{S B M}$ ). For that, we still have:

$P_{S B M} (T | Monday) = P_{S B M} (T) = 1 / 2$ .

What about $P_{S B} (T | Monday)$ , using the original reference class, which is equal to $1 / 4$ ? Well, the best question I could come up with that captures that is:

Q': What proportion of universes, where a randomly selected version of me exists on a Monday, will be large?

Randomly selected meaning "randomly selected from the versions of me that exist in the universe".

This question doesn't feel as natural as either Q or QM. And it highlights the importance of the reference class, the set of "versions of me". So let's look in more details at the reference class.

What are reference classes for?

There are several purposes for reference classes. We can use them in decision theory, when considering the class of agents that will reach the same decisi

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