Isn’t the conclusion to the Sleeping Beauty problem that there are two different but equally valid ways of applying probability theory to the problem; that natural language and even formal notation makes it very easy to gloss over the difference; and that which one you should use depends on exactly what question you mean to ask? Would those same lessons apply to SIA vs. SSA?
In Sleeping Beauty, IIRC the distinction is between “per-experiment” probabilities and “per-observation” probabilities. My interpretation of these was to distinguish between the question “what’s the probability that the coin came up heads” (a physical event that happened exactly once, when the coin landed on the table) from “what’s the probability that Beauty will witness the coin being heads” (an event in Beauty’s brain that will occur once or twice). The former having probability 1⁄2 and the latter having probability 1⁄3. Though it might be a bit more subtle than that.
For SSA vs. SIA, who do you want to be right most often? Do you want a person chosen uniformly at random from among all people in all possible universes to be right most often? If so, use SIA. Or do you want to maximize average-rightness-per-universe? If so, use SSA, or something like it, I’m not exactly clear.
Let’s be concrete, and look at the “heads: 1 person in a white room and 9 chimps in a jungle; tails: 10 people in a white room” situation.
If God says “I want you to guess whether the coin landed heads or tails. I will exterminate everyone who guesses wrong.”, then you should guess tails because that saves the most people in expectation. But if God says “I want to see how good the people of this universe are at reasoning. Guess whether the coin landed heads or tails. If most people in your universe guess correctly, then your universe will be rewarded with the birth of a single happy child. Oh and also the coin wasn’t perfectly fair; it landed heads with probability 51%.”, then you should guess heads because that maximizes the chance that the child is born.
I’m not sure that’s all exactly right. But the point I’m trying to make is, are we sure that “the probability that you’re in the universe with 1 person in the white room” has an unambiguous answer?
By far the biggest and most sudden update I’ve ever had is Dominion, a documentary on animal farming:
https://www.youtube.com/watch?v=LQRAfJyEsko
It’s like… I had a whole pile of interconnected beliefs, and if you pulled on one it would snap most of the way back into place after. And Dominion pushed the whole pile over at once.