Yes, but note that SSA can get this same result. All they have to do is say that their reference class is R—whatever set the SIA person uses, they use the same set. If they make this move, then they are reference-class-independent to exactly the same degree as SIA.
SSA is not reference class independent. If it uses R, then the SSA prob is P(Ui|sub) (rather that PR(Ui|sub)), which is (P(Ui)R0(Ui)/R(Ui))/(∑j∈IP(Uj)R0(Uj)/R(Uj)), which is not independent of R (consider doubling the size of R in one world only—that makes that world less likely relative to all the others).
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).
Yes, but note that SSA can get this same result. All they have to do is say that their reference class is R—whatever set the SIA person uses, they use the same set. If they make this move, then they are reference-class-independent to exactly the same degree as SIA.
SSA is not reference class independent. If it uses R, then the SSA prob is P(Ui|sub) (rather that PR(Ui|sub)), which is (P(Ui)R0(Ui)/R(Ui))/(∑j∈IP(Uj)R0(Uj)/R(Uj)), which is not independent of R (consider doubling the size of R in one world only—that makes that world less likely relative to all the others).
Ah, my mistake, sorry. I was thinking of a different definition of reference-class-independent than you were; I should have read more closely.
Oh, what definition were you using? Anything interesting? (or do you mean before updating on your own experiences?)
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).