TL;DR: If I am untypical, then many more observers exist. If this claim is necessarily true, then classical SIA is false.

There is a situation where we could prove something like SIA, let’s call it Untypical SIA. Imagine that there are 100 green dots and one red dot on a bow’s target (and they cover all the space). We know that there were either 10 or 100 attempts to hit the target with a random arrow. We only know that the red dot was eventually hit (maybe we are in it). Now we can give higher credence to the theory that there were 100 attempts (P1(red)=0.6339) over the theory of only 10 attempts (P2(red)=0.0956) to hit the red dot. Credence in 100 attempts = P1/(P1+P2) = 0.86.

The resonating above is made from God’s view and seems to have high epistemic status: it is not an assumption, it is a proof.

Examples of application of such untypical-SIA reasoning in the real life: if there is life on Earth, there are many other planets out there, which tried but fail to develop life. If humans are the only intelligent species, there are many others species that “tried” and fail to become intelligent. If our universe is fine-tuned, there are many other universes which are not fine-tuned, so the multiverse theory is true.

 

If Untypical SIA is a necessary condition for a larger set of observers, then classical SIA is false.

Untypical SIA requires that the red dot is different from the green dots. If all dots are red, and we learn that one of the dots was hit, it doesn’t give us any new information to update. If uniqueness is the necessary (=if and only if) condition for update when the lack of uniqueness means no update. In that case, classical SIA is false (it is not a problem in the infinite universe, where something like SIA still works, as we should look at relative concentrations of observers in different regions of the multiverse instead; all our SIA-based cosmological constructions are safe herein).

In other words, the fact of my existence is an argument in favor that more observers exist – only if I am special. In classical SIA, the mere fact that I exist at all is evidence that many more attempts to create me were made, without any mention that I should be different from all other observers.

Obviously, I can’t just say that my random name is rare. Because anyone can say that, and we are all in the same “epistemic situation”. If it is an experiment, un-typicality should be defined a priori, before the experiment. 

I should count as unique only something which a priory can be considered unique, like a name AAAA AAAAAA or a time of my birth like 11.111.1111. Having consciousness or being fine-tuned are examples of such a priory uniqueness, but being named “bgjkuytvnki” is not.  

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SIA is equivalent to making a Bayesian update as if god  (a non-reference class external observer) asks the question "Does the person with these characteristics (the characteristics of the physical person "I") exist?" and gets a positive answer. (AKA. Update on one's existence)

But why would god focus on those specific characteristics and raise that question at all. It makes sense for someone to be biased towards themself, such as you focusing on the name avturchin, and me on the name dadadarren, but why would a non-reference class external observer pay special attention to either?

If am understanding correctly, you are suggesting there is no reason to focus on characteristics like an ordinary name as it is only special to that person themself. But if a characteristic is indeed objectively special, like the color of dots in your example, then it is ok to perform the Bayesian update to more observers. 

But it is impossible to say what characteristic is objectively special. There could be infinite ways to differentiate and group the dots, e.g. we could label them 1-100, isn't the No.1 just as special as the red dot? Even from the god's eye view, the purposed Bayesian update requires a prior sampling to justify. E.g. if god specifically asks "Is there an arrow on the red dot?"(instead of asking other questions such as "is there an arrow on No.1?" or something similar) and gets a positive answer. Then the calculation follows. 

I agree with you that there needs to be some sense of "priory uniqueness" for the existing observer to suggest there are more of their kind, or else the evidence is just blandly "there is an observer". I simply don't agree there is any way to justify this uniqueness. SIA falsely created this sense of uniqueness using first-person bias. Yet that is not applicable from the god's eye view whose supporters want to perform the calculation from.  

In some sense, situation with SIA looks like as p-hacking: we select a hypothesis after we got the data.

But if we preselect uniqueness, any type of uniqueness works. For example, cells are numbered. Before the experiment, we choose the number 73. In that case, discovering that 73 was hit will be strong update for 100 attempts vs. only 10 attempts. 

Yes! any characteristic works as long as it is preselected. But it needs to be actually selected or sampled. 

Yet there is no sampling in anthropic problems. SIA assumes the first-person "I" (or "now") is equivalent to a random sample. So it treats finding myself as the person who's been created in room 73 the same way as if an external observer selected room 73 and finds someone exists in it. It is just an assumption that lacks any logical backing.

The same can be said about SSA too.