TL;DR: SIA favours infinities of highest order, but spends all its power on it and thus not very useful in distinguishing multiverses with different densities of observers.
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Imagine that there are two hypothetical variants of multiverse, both have countable infinite number of all possible observers, but in one variant there is a 1000 times higher concentration of observers-like-me than another. (“Hypothetical” here means not “physically possible”, but two different hypotheses to which we want to give priors; if they were physically possible, they both will co-exist, and I will be in region with higher density, assuming that the size of regions is the same. But it is SSA.)
The fact of my existence does not provide any new information which would help to choose between to hypothesis, as I exist in both variants.
But bona fide SIA seems to insists on the variant which with the higher density of observers anyway. However, two countable infinites are equal, so the fact that the second multiverse has a higher concentration of observers is also not an argument which favours the denser multiverse even under SIA. (I am not sure here, may return to this point later; anyway the next paragraph will overwrite this uncertainty.)
But if there is a third hypothetical multiverse which has a higher order of infinity of observers, say, uncountable number of them, it will win according to SIA. Therefore, SIA favours multiverse with the highest order of infinity of observers.
In practice, it means that SIA favors “many bubbles multiverse” over enteral inflation multiverse, as bubble are uncountable. It also favours mathematical multiverse over bubbles one, as mathematical multiverse includes all types of infinites. In short, higher orders of infinity by Tegmark are more likely according to SIA.
But SIA is one-time gun. Even if it works, it distinguishes different orders of infinity in Tegmark’s model, but after that it becomes completely useless practically: it doesn’t help us with any smaller task, like deciding what are “a priory” chances of abiogenesis or what is the density of observers.
Different possible multiverses can have different densities of particular observers.
The SIA predicts that you’re in those multiverses which have a higher density of observers exactly like you.
Sorry, long comment.
TL;DR: SIA favours infinities of highest order, but spends all its power on it and thus not very useful in distinguishing multiverses with different densities of observers.
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Imagine that there are two hypothetical variants of multiverse, both have countable infinite number of all possible observers, but in one variant there is a 1000 times higher concentration of observers-like-me than another. (“Hypothetical” here means not “physically possible”, but two different hypotheses to which we want to give priors; if they were physically possible, they both will co-exist, and I will be in region with higher density, assuming that the size of regions is the same. But it is SSA.)
The fact of my existence does not provide any new information which would help to choose between to hypothesis, as I exist in both variants.
But bona fide SIA seems to insists on the variant which with the higher density of observers anyway. However, two countable infinites are equal, so the fact that the second multiverse has a higher concentration of observers is also not an argument which favours the denser multiverse even under SIA. (I am not sure here, may return to this point later; anyway the next paragraph will overwrite this uncertainty.)
But if there is a third hypothetical multiverse which has a higher order of infinity of observers, say, uncountable number of them, it will win according to SIA. Therefore, SIA favours multiverse with the highest order of infinity of observers.
In practice, it means that SIA favors “many bubbles multiverse” over enteral inflation multiverse, as bubble are uncountable. It also favours mathematical multiverse over bubbles one, as mathematical multiverse includes all types of infinites. In short, higher orders of infinity by Tegmark are more likely according to SIA.
But SIA is one-time gun. Even if it works, it distinguishes different orders of infinity in Tegmark’s model, but after that it becomes completely useless practically: it doesn’t help us with any smaller task, like deciding what are “a priory” chances of abiogenesis or what is the density of observers.