This is an interesting observation which may well be true, I'm not sure, but the more intuitive difference is that SSA is about actually existing observers, while SIA is about potentially existing observers. In other words, if you are reasoning about possible realities in the so-called "multiverse of possibilities," than you are using SIA. Whereas if you are only considering a single reality (e.g., the non-simulated world), you select a reference class from that reality (e.g., humans), you may choose to use use SSA to say that you are a random observer from that class (e.g., a random human in human history).

You are describing the SIA assumption to a T.

This is what I was thinking:

If simulations exist, we are choosing between two potentially existing scenarios, either I'm the only real person in my simulation, or there are other real people in my simulation. Your argument prioritizes the latter scenario because it contains more observers, but these are potentially existing observers, not actual observers. SIA is for potentially existing observers.

I have a kind of intuition that something like my argument above is right, but tell me if that is unclear.

And note: one potential problem with your reasoning is that if we take it to it's logical extreme, it would be 100% certain that we are living in a simulation with infinite invisible observers. Because infinity dominates all the finite possibilities.

I think you are overlooking that your explanation requires BOTH SSA and SIA, but yes, I understand where you are coming from.

Other people here have responded in similar ways to you; but the problem with your argument is that my original argument could also just consider only simulations in which I am the only observer. In which case Pr(I'm distinct | I'm in a simulation)=1, not 0.5. And since there's obviously some prior probability of this simulation being true, my argument still follows.

I now think my actual error is saying Pr(I'm distinct | I'm not in a simulation)=0.0001, when in reality this probability should be 1, since I am not a random sample of all humans (i.e., SSA is wrong), I am me. Is that clear?

Lastly, your final paragraph is akin to the SSA + SIA response to the doomsday paradox, which I don't think is widely accepted since both those assumptions lead to a bunch of paradoxes.

True, but that wasn't my prior. My assumption was that if I'm in a simulation, there's quite a high likelihood that I would be made to be so 'lucky' to be the highest on this specific dimension. Like a video game in which the only character has the most Hp.

But, on second thought, why are you confident that the way I'd fill the bags is not "entangled with the actual causal process that filled these bags in a general case?" It seems likely that my sensibilities reflect at least in some manner the sensibilities of my creator, if such a creator exists.

Actually, in addition, my argument still works if we only consider simulations in which I'm the only human and I'm distinct (on my aforementioned axis) from other human-seeming entities. So the 0.5 probability becomes identically 1, and I sidestep your argument. So if I assign any non-zero prior on this theory whatsoever, the observation that I'm distinct makes this theory way way way more likely.

The only part of your comment I still agree with is that SIA and SSA may not be justified. Which means my actual error may have been to set Pr(I'm distinct | I'm not in a sim)=0.0001 instead of identically 1 — since 0.0001 assumes SSA. Does that make sense to you?

But thank you for responding to me; you are clearly an expert in anthropic reasoning, as I can see from your posts.

I don't understand. We should entertain the possibility because it is clearly possible (since it's unfalsifiable), because I care about it, because it can dictate my actions, etc. And the probability argument follows after specifying a reference class, such as "being distinct" or "being a presumptuous philosopher."

You are misinterpreting the PP example. Consider the following two theories:

T1 : I'm the only one that exists, everyone else is an NPC

T2 : Everything is as expected, I'm not simulated. 

Suppose for simplicity that both theories are equally likely. (This assumption really doesn't matter.) If I define Presumptuous Philosopher=Distinct human like myself=1/(10,000) humans, then I get in most universes, I am indeed the only one, but regardless, most copies of myself are not simulated.