Both parts are independently correct. But I think there’s probably not enough step-by-step talk about symmetry for this to serve the social role of a proof for confused people. I’ve found it’s important, when explaining anthropics, to really focus on “centered possible worlds” (or hypotheses that reproduce your experiences, to frame it more like Solomonoff induction), and why a question like “what is the universe like outside my head?” can be answered by considering hypotheses anew when you have different memories.
I assume you mean from https://www.princeton.edu/~adame/papers/sleeping/sleeping.pdf ? The one about “if you knew it was Monday it would be 0.5, surely adding Tuesday as an option causes an update,” followed by a standard claim that symmetry implies 1/3?
Both parts are independently correct. But I think there’s probably not enough step-by-step talk about symmetry for this to serve the social role of a proof for confused people. I’ve found it’s important, when explaining anthropics, to really focus on “centered possible worlds” (or hypotheses that reproduce your experiences, to frame it more like Solomonoff induction), and why a question like “what is the universe like outside my head?” can be answered by considering hypotheses anew when you have different memories.