Sometimes when people say SIA is reference-class independent & SSA isn’t, they mean it as an argument that SIA is better than SSA, because it is philosophically less problematic: The choice of reference class is arbitrary, so if we don’t have to make that choice, our theory is overall more elegant. This was the sort of thing I had in mind.
On that definition, SSA is only more arbitrary than SIA if it makes the reference class different from the class of all observers. (Which some proponents of SSA have done) SIA has a concept of observer too, at least, a concept of observer-indistinguishable-from-me (which presumably is proper subset of observer, though now that I think about it this might be challenged. Maybe I was doubly wrong—maybe SIA only needs the concept of observer-indistinguishable-from-me).
Sometimes when people say SIA is reference-class independent & SSA isn’t, they mean it as an argument that SIA is better than SSA, because it is philosophically less problematic: The choice of reference class is arbitrary, so if we don’t have to make that choice, our theory is overall more elegant. This was the sort of thing I had in mind.
On that definition, SSA is only more arbitrary than SIA if it makes the reference class different from the class of all observers. (Which some proponents of SSA have done) SIA has a concept of observer too, at least, a concept of observer-indistinguishable-from-me (which presumably is proper subset of observer, though now that I think about it this might be challenged. Maybe I was doubly wrong—maybe SIA only needs the concept of observer-indistinguishable-from-me).