Can anyone tell me what's wrong with the following "refutation" of the simulation argument? (I know this is a bit long -- my apologies! I also posted an earlier draft several months ago and got some excellent feedback. I don't see a flaw, but perhaps I'm missing something!)

Consider the following three scenarios:

Scenario 1: Imagine that you’re standing in a hallway, which we’ll label Location A. You are blindfolded and then escorted into one of two rooms, either X or Y, but you don’t know which one. While in the unknown room, you are told that there are exactly 1,000 people in room X and only a single person in room Y. There is no way of communicating with anyone else, so you must use the information given to guess which room you’re in. If you guess correctly, you win 1 million dollars. Using the principle of indifference as your guide, you guess that you’re in room X—and consequently, you almost certainly win 1 million dollars. After all, since betting odds are a guide to rationality, if everyone in room X and Y were to bet that they’re in room X, just about everyone would win.

Scenario 2: Imagine that you’re standing in a hallway, which we’ll label Location A. You are blindfolded and then escorted into one of two rooms, either X or Y, but you don’t know which one. While in the unknown room, you are told that there are exactly 1,000 people in room X and only a single person in room Y. You are also told that over the past year, a total of 1 billion people have been in room Y at one time or another whereas only 10,000 people have been in room X. There is no way of communicating with anyone else, so you must use the information given to guess which room you’re in. If you guess correctly, you win 1 million dollars. The question here is: Does the extra information about the past histories of rooms X and Y change your mind about which room you’re in? 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.

Scenario 3: Imagine that you’re standing in a hallway, which we’ll label Location A. You are blindfolded and then told that you’ll be escorted into room Z through one of two rooms, either X or Y, but you won’t know which one. At any given moment, or timeslice, there will always be exactly 1,000 people in room X and only a single person in room Y. (Thus, as one person enters each room another one exits into room Z.) Once you arrive in room Z at time T2, you are told that between T1 and T2 a total of 1 billion people passed through room Y whereas only 10,000 people in total passed through room X, where all of these people are now in room Z with you. There is no way of communicating with anyone else, so you must use the information given to guess which room, X or Y, you passed through on your way from Location A to room Z. If you guess correctly, you win 1 million dollars. Using the principle of indifference as your guide, you now guess that you passed through room Y—and consequently, you almost certainly win 1 million dollars. After all, if everyone in room Z at T2 were to bet that they passed through room Y rather than room X, the large majority would win.

Let’s analyze these scenarios. In the first two, the only relevant information is synchronic information about the current distribution of people when you answer the question, “Which room am I in, X or Y?” (Thus, the historical knowledge offered in Scenario 2 doesn’t change your answer.) In contrast, the only relevant information in the third scenario is diachronic information about which of the two rooms had more people pass through them from T1 to T2. If these claims are correct, then the simulation argument proposed by Nick Bostrom (2003) is flawed. The remainder of this paper will (a) outline this argument, and (b) show how the ideas above falsify the argument’s conclusion.

According to the simulation argument, one or more of the following disjuncts must be true: (i) humanity goes extinct before reaching a stage of technological development that would enable us to run a large number of ancestral simulations; (ii) humanity reaches a stage of technological development that enables us to run a large number of ancestral simulations but we decide not to; and (iii) humanity reaches a stage of technological development that enables us to run a large number of ancestral simulations and we do, in fact, run a large number of ancestral simulations. The third disjunct entails that we would almost certainly live in a computer simulation because (a) a sufficiently high-resolution simulation would be sensorily and phenomenologically indistinguishable from the “real” world, and (b) the indifference principle tells us to distribute our probabilities evenly among all the possibilities if we have no special reason to favor one over another. Since the population of sims would far outnumber the population of non-sims in scenario (iii), ex hypothesi, then we would almost certainly be sims. This is the simulation hypothesis.

But consider the following possible Posthuman Future: instead of running a huge number of ancestral simulations in parallel, as Bostrom seems to assume we would, future humans run a huge number of simulations sequentially, one after another. This could be done such that at any given moment the total number of extant non-sims far exceeds the total number of extant sims, yet over time the total number of sims who have existed far exceeds the total number of non-sims who also have existed. (This could be accomplished by running simulations at speeds much faster than realtime.) If the question is, “Where am I right now, in a simulation or not?,” then the principle of indifference instructs you to answer, “I am not a sim.” After all, if everyone were to bet at some timeslice Tx that they are not a sim, nearly everyone would win.

Here the only information that matters is synchronic information; diachronic information about how many sims, non-sims, or “observer-moments” there have been has no bearing on one’s credence about one’s present ontological status (sim or non-sim?)—that is, no more than historical knowledge about rooms X and Y in Scenario 2 have any bearing on one’s response to the question, “Which room am I currently in?” This is problematic for the simulation argument because the Posthuman Future outlined above satisfies the condition of disjunct (iii) yet it doesn’t entail that one is almost certainly living in a simulation. Thus, Bostrom’s assertion that “at least one of the following propositions is true” is false.

One might wonder: but what if we run a huge number of simulations sequentially and then stop. Wouldn’t this be analogous to Scenario 3, in which we would have reason for believing that we passed through room Y rather than room X, i.e., that we were (and thus still are) in a simulation rather than the “real” world? The answer is no, it’s not analogous to Scenario 3 because in our case we would have some additional relevant information about our actual history—that is, we would know that we were in “room X,” which held more people at every given moment, since we would have control over the ratio of sims to non-sims (always making sure that the latter far outnumbers the former). Even more, if we were to stop all simulations, then the ratio of sims to non-sims would be zero to whatever the human population is at the time, thus making a bet that we are non-sims virtually certain. So far as I can tell, these conclusions follow whether one accepts the self-sampling assumption (SSA), strong self-sampling assumption (SSSA), or the self-indication assumption (SIA) (Bostrom 2002).

In sum, the simulation argument is missing a fourth disjunct: (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, yet the principle of indifference leads us to believe that we are not in a simulation. It will, of course, be up to future generations to decide whether to run a large number of ancestral simulations, and if so whether to run these sequentially or in parallel, given the ontological-epistemic implications of each.