Can you spell that out more formally? It seems to me that so long as I’m removing the corpses from my reference class, 100% of people in my reference class remember surviving every time so far just like I do, so SSA just does normal bayesian updating.
Sure, as discussed for example here: https://www.lesswrong.com/tag/self-sampling-assumption, if there are two theories, A and B, that predict different (non-zero) numbers of observers in your reference class, then on SSA that doesn’t matter. Instead, what matters is what fraction of observers in your reference class have the observations/evidence you do. In most of the discussion from the above link, those fractions are 100% on either A or B, resulting, according to SSA, in your posterior credences being the same as your priors.
This is precisely the situation we are in for the case at hand, namely when we make the assumptions that:
The reference class consists of all survivors like you (no corpses allowed!)
The world is big (so there are non-zero survivors on both A and B).
So the posteriors are again equal to the priors and you should not believe B (since your prior for it is low).
I did mean to use the trivial reference class for the SSA assesment, just not in a large world. And, it still seems strange to me that it would change the conclusion here how large the world is.
I completely agree, it seems very strange to me too, but that’s what SSA tells us. For me, this is just one illustration of serious problems with SSA, and an argument for SIA.
If your intuition says to not believe B even if you know the world is small then SSA doesn’t reproduce it either. But note that if you don’t know how big the world is you can, using SSA, conclude that you now disbelieve the combination small world + A, while keeping the odds of the other three possibilities the same—relative to one another—as the prior odds. So basically you could now say: I still don’t believe B but I now believe the world is big.
Finally, as I mentioned, I don’t share your intuition, I believe B over A if these are the only options. If we are granting that my observations and memories are correct, and the only two possibilities are: I just keep getting incredibly lucky OR “magic”, then with every shot I’m becoming more and more convinced in magic.
Reference class issues.
I think it’s not necessarily true that on SSA you would also have to believe B, because the reference class doesn’t necessarily have to involve just you. Defenders of SSA often have to face the problem/feature that different choices of a reference class yield different answers. For example, in Anthropic Bias Bostrom argues that it’s not very straightforward to select the appropriate reference class, some are too wide and some (such as the trivial reference class) often too narrow.
The reference class you are proposing for this problem, just you, is even narrower than the trivial reference class (which includes everybody in your exact same epistemic situation so that you couldn’t tell which one you are.) It’s arguably not the correct reference class, given that even the trivial reference class is often too narrow.
Reproducing your intuitions.
It seems to me that your intuition of not wanting to keep playing can actually be reproduced by using SSA with a more general reference class, along with some auxiliary assumptions about living in a sufficiently big world. This last assumption is pretty reasonable given that the cosmos is quite likely enormous or infinite. It implies that there are many versions of Earth involving this same game where a copy of you (or just some person, if you wish to widen the reference class beyond trivial) participates in many repetitions of the Russian roulette, along with other participants who die at the rate of 1 in 6.
In that case, after every game, 1 in 6 of you die in the A scenario, and 0 in the B scenario, but in either scenario there are still plenty of “you”s left, and so SSA would say you shouldn’t increase your credence in B (provided you remove your corpses from your reference class, which is perfectly fine a la Bostrom).
My take on the answer.
That said, I don’t actually share your intuition for this problem. I would think, conditional on my memory being reliable etc., that I have better and better evidence for B with each game. Also, I fall on the side of SIA, in large part because of the weird reference class issues involved in the above analysis. So to my mind, this scenario doesn’t actually create any tension.