The problem with that thought experiment is that actual observer can’t have this information. We can’t know how many being are in the universe, and there are probably infinitely many of them. But in your experiment you know how many of them exist and also that there is no infinitely many of them. So the experiment models completely impossible world and its results are non relevant.
The model is not dependent on there being infinite beings. Admittedly, if you believe that there are the same number of people in two universes if there is a bijection between people, then you’ll get the result that this doesn’t work when there are infinite people. This is the way infinities are usually dealt with in mathematics, but I would argue that this is flawed, that it is actually possible to have one infinite that is twice another.
Anyway, there is no requirement to know exactly how many observers exist. We can just guess.
The problem with that thought experiment is that actual observer can’t have this information. We can’t know how many being are in the universe, and there are probably infinitely many of them. But in your experiment you know how many of them exist and also that there is no infinitely many of them. So the experiment models completely impossible world and its results are non relevant.
But from the same logic we may claim that I belong to the biggest class of all actually exiting (if SSA is true https://en.wikipedia.org/wiki/Self-sampling_assumption) or possible observers (if SIA is true https://en.wikipedia.org/wiki/Self-indication_assumption). In infinitely big universe all possible observers exist, so there will not be difference between SIA and SSA.
The model is not dependent on there being infinite beings. Admittedly, if you believe that there are the same number of people in two universes if there is a bijection between people, then you’ll get the result that this doesn’t work when there are infinite people. This is the way infinities are usually dealt with in mathematics, but I would argue that this is flawed, that it is actually possible to have one infinite that is twice another.
Anyway, there is no requirement to know exactly how many observers exist. We can just guess.