Is there a flaw in the simulation argument?

Fun exercise: disprove your own post, using the idea that the same information can be synchronic or diachronic depending on the reference frame (Einstein 1905).

There is a flaw in your argument. I'm going to try to be very precise here and spell out exactly what I agree with and disagree with in the hope that this leads to more fruitful discussion.

Your conclusions about scenarios 1, 2 and 3 are correct.

You state that Bostrom's disjunction is missing a fourth case. The way you state (iv) is problematical because you phrase it in terms of a logical conclusion that "the principle of indifference leads us to believe that we are not in a simulation" which, as I'll argue below, is incorrect. Your disjunct should properly be stated as something like (iv) humanity reaches a stage of technological development that enables us to run a large number of ancestral simulations and we do run a large number of ancestral simulations, however we do this in a way so as to keep the number of simulated people well below the number of real people at any given moment. Stated that way, it is clear that Bostrom's (iii) is meant to include that outcome. Bostrom's argument is predicated only on the number of ancestral simulations, not whether they are run in parallel or sequentially or how much time they are run over. The reason Bostrom includes your (iv) in (iii) is because it doesn't change the logic of the argument. Let me now explain why.

For the sake of argument let's split (iii) into two cases (iii.a) and (iii.b). Let (iii.a) be all the futures in (iii) not covered by your (iv). For convenience, I'll refer to this as "parallel" even though there are cases in (iv) where some simulations could be run in parallel. Then (iii.b) is equivalent to your (iv). For convenience, I'll refer to this as serial even though again, it might not be strictly serial. I think we agree that if the future were guaranteed to be (iii.a), then we should bet we are in a simulation.

First, even if you were right about (iii.b), I don't think it invalidates the argument. Essentially, you have just added another case similar to (ii), and it would still be the case that there are many more simulations that real people because of (iii.a) and we should bet that we are in a simulation.

Second, if the future is actually (iii.b) we should still bet we are in a simulation just as much as with (iii.a). At several points, you appeal to the principle of indifference, but you are vague on how this should be applied. Let me give a framework for thinking about this. What is happening here is that we are reasoning under indexical uncertainty. In each of your three scenarios and the simulation argument, there is uncertainty about which observer we are. Your statement that by the principle of indifference we should conclude something is actually saying what the SSA say which is that we should reason as if we are a randomly chosen observer. In Bostrom's terms, you are uncertain which observer in your reference class you are. To make sure we are on the same page, let me go through your scenarios using this approach.

Scenario 1: You are not sure if you are in room X or room Y, the set of all people currently in room X and Y is your reference class. You reason as if you could be a randomly selected one so you have a 1000 to 1 chance of being in room X.

Scenario 2: You are told about the many people who have been in room Y in the past. However, they are in your past. You have no uncertainty about your temporal index relative to them, so you do not add them to your reference class and reason the same as in scenario 1. Bostrom's book is weak here in that he doesn't give you very good rules for selecting your reference class. I'm arguing that one of the criteria is that you have to be uncertain if you could be that person or not. So for example, you know you are not one of the many people not currently in room X or Y so you don't include them in your reference class. Your reference class is the set of people you are unsure of your index relative to.

Scenario 3: This one is more tricky to reason correctly about. I think you are wrong when you say that the only relevant information here is diachronic information. You know you are now in room Z that contains 1 billion people who passed through room Y and 10,000 people who passed through room X. Your reference class is the people in room Z. You don't have to reason about the temporal information or the fact that at any given moment there was only one person in room Y but 1,000 people in room X. The passing through room X or Y is now only a property of the people in room Z. This is equivalent to if I said you are blindfolded in a room with 1 billion people wearing red hats and 10,000 people wearing blue hats. Which hat color should you bet you are wearing? Reasoning with the people in room Z as your reference class you correctly give your self a 1 billion to 10,000 chance of having passed through room Y.

In (iii.b), you are uncertain whether you are in a simulation or reality. But if you are in a simulation you are also uncertain where you are chronologically relative to reality. Thus if a pair of simulations were run in sequence, you would be unsure if you were in the first or second simulation. You have both spatial and temporal uncertainty. You aren't sure what the proper now is. Your reference class includes everyone in the historical reality as well as everyone in all the simulations. Given that as your reference class, you should reason that you are in a simulation (assuming many simulations are run). It doesn't matter that those simulations are run serially, only that many of them are run. Your reference class isn't limited to the current simulation and the current reality because you aren't sure where you are chronologically relative to reality.

With regards to SIA or SSA. I can't say that they make any difference to your position because the problem is that you have chosen the wrong reference class. In the original simulation argument, SIA vs. SSA makes little or no difference because presumably, the number of people living in historical reality is roughly equal to the number of people living in any given simulation. SIA only changes the conclusions when one outcome contains many more observers than the other. Here we treat each simulation as a different possible outcome, and so they agree.

It shouldn’t. After all, if everyone currently in rooms X and Y were to bet that they’re in room X, just about everyone would win.

edit: separated wrongly quoted part Yet if everyone bet that they are in room Y vast majority would win (1 000 / 1 vs 1 000 000 000 / 10 000). In the scenario you can deduce that a lot less questions will be posed in room X.

You are tying to invoke that "right now" is always a relevant indifference breaker. It might be that you are imagining that people in room X will be posed a question NOW. But what if every Xer was asked only the question once when they entered? Then what the contents of the room NOW are becomes irrelevant to the distribuiton of questions. We can keep the amount of questions the same and keep more people in. In the limit we can have the whole 10000 stay for the whole duration when the single persons are driven throught the other. Still more questions will be asked in total in the single person room. But maybe crucially a new person entering the single room doesn't mean that eveyone in the big room will be reasked. What is proper to focus on is the first time everyone is asked and this only happens once for everyone in the big room (I guess we need to assume you would remember if asked the second time).

In problems where multiple different agents in the universe "could be you," (i.e. share information), you really don't have to do anything fancy. Just assign equal probability to all agents in the entire universe who, as far as you know, can match your current state of information.

If there are two copies of Earth, and, hypothetically, only these two copies of me in the universe, I assign 50% probability to being each. This stays the same whether these Earths are at different points in space, or at different times, or sped up or slowed down or played in reverse order due to strange entropic boundary conditions. All that matters is that on each Earth there is a copy of me that has the same information as me from their own internal perspective, and I just count these copies up.

This seems to me to be failing to account for the fact that we are not in fact totally blindfolded and know that we live in what appears to be a time prior to simulation. Your alternative scenario that contradicts (iii) seems to be making a bet on information that seems directly contradictory to what we know at the current time (that is, there are no simulations we know about yet). The problem isn't purely one of numbers, but one of where we perceive ourselves to be living now.

I do happen to agree that indifference is probably the most useful response to the simulation argument, though it sounds like probably for different reasons.

I'm confused by why you are constraining the argument to future-humanity as simulators, and further by why you are care what order the experimenters turn em on.

Like, it seems perverse to make up an example where we turn on one sim at a time, a trillion trillion times in a row. Yeah, each one is gonna get told that there are 6 billion real humans and one sim, so if they guess real or sim they might get tricked to guess real. Who cares? No reason to think that's our future.

The iv disjunct you are posing isn't one that we don't have familiarity with. How many instances of Mario Kart did we spin up? How bout Warcraft? The idea that our future versions are gonna be super careful with sims isn't super interesting. Sentience will increase forever, resources will increase forever, eventually someone is gonna press the button.