I got a bit distracted by the “anthropic reasoning is wrong” discussion below, and missed adding something important.
The conclusion that “we would not expect to see the world as we in fact see it” holds in a big universe regardless of the approach taken to anthropic reasoning. It’s worth spelling that out in some detail.
Suppose I don’t want to engage in any form of anthropic reasoning or observation sampling hypothesis. Then the large universe model leaves me unable to predict anything much at all about my observations. I might perhaps be in a small civilisation, but then I might be in a simulation, or a Boltzmann Brain, or mad, or a galactic emperor, or a worm, or a rock, or a hydrogen molecule. I have no basis for assigning significant probability to any of these—my predictions are all over the place. So I certainly can’t expect to observe that I’m an intelligent observer in a small civilisation confined to its home planet.
Suppose I adopt a “Copernican” hypothesis—I’m just at a random point in space. Well now, the usual big and small universe hypotheses predict that I’m most likely going to be somewhere in intergalactic or interstellar space, so that’s not a great predictive success. The universe model which most predicts my observations looks frankly weird… instead of a lot of empty space, it is a dense mass of “computronium” running lots of simulations of different observers, and I’m one of them. Even then I can’t expect to be in a simulation of a small civilisation, since the sim could be of just about anything. Again, not a great predictive success.
Suppose I adopt SIA reasoning. Then I should just ignore the finite universes, since they contribute zero prior probability. Or if I’ve decided for some reason to keep all my universe hypotheses finite, then I should ignore all but the largest ones (ones with 3^^^3 or more galaxies). Among the infinite-or-enormous universes, they nearly all have expanded civilisations, and so under SIA, nearly all predict that I’m going to be in a big civilisation. The only ones which predict otherwise include a “universal doom”—the probability that a small civilisation ever expands off its home world is zero, or negligibly bigger than zero. That’s a massive future filter. So SIA and big universes can—just about—predict my observations, but only if there is this super-strong filter. Again, that has low prior probability, and is not what I should expect to see.
Suppose I adopt SSA reasoning. I need to specify the reference class, and it is a bit hard to know which one to use. In a big universe, different reference classes will lead to very different predictions: picking out small civilisations, large civilisations, AIs, SIMs, emperors and so on (plus worms, rocks and hydrogen for the whackier reference classes). As I don’t know which to use, my predictions get smeared out across the classes, and are consequently vague. Again, I can’t expect to be in a small civilisation on its home planet.
By contrast, look at the small universe models with only a few civilisations. A fair chunk of these models have modest future filters so none of the civilisations expand. For those models, SSA looks in quite good shape, as there is quite a wide choice of reference classes that all lead to the same prediction. Provided the reference class predicts I am an intelligent observer at all then it must predict I am in a small civilisation confined to its home planet (because all civilisations are like that). Of course there are the weird classes which predict I’m a worm and so on—nothing we can do about those—but among the sensible classes we get a hit.
So this is where I’m coming from. The only model which leads me to expect to see what I actually see is a small universe model, with a modest future filter. Within that model, I will need to adopt some sort of SSA-reasoning to get a prediction, but I don’t have to know in advance which reference class to use: any reference class which selects an intelligent observer predicts roughly what I see. None of the other models or styles of reasoning lead to that prediction.
I got a bit distracted by the “anthropic reasoning is wrong” discussion below, and missed adding something important. The conclusion that “we would not expect to see the world as we in fact see it” holds in a big universe regardless of the approach taken to anthropic reasoning. It’s worth spelling that out in some detail.
Suppose I don’t want to engage in any form of anthropic reasoning or observation sampling hypothesis. Then the large universe model leaves me unable to predict anything much at all about my observations. I might perhaps be in a small civilisation, but then I might be in a simulation, or a Boltzmann Brain, or mad, or a galactic emperor, or a worm, or a rock, or a hydrogen molecule. I have no basis for assigning significant probability to any of these—my predictions are all over the place. So I certainly can’t expect to observe that I’m an intelligent observer in a small civilisation confined to its home planet.
Suppose I adopt a “Copernican” hypothesis—I’m just at a random point in space. Well now, the usual big and small universe hypotheses predict that I’m most likely going to be somewhere in intergalactic or interstellar space, so that’s not a great predictive success. The universe model which most predicts my observations looks frankly weird… instead of a lot of empty space, it is a dense mass of “computronium” running lots of simulations of different observers, and I’m one of them. Even then I can’t expect to be in a simulation of a small civilisation, since the sim could be of just about anything. Again, not a great predictive success.
Suppose I adopt SIA reasoning. Then I should just ignore the finite universes, since they contribute zero prior probability. Or if I’ve decided for some reason to keep all my universe hypotheses finite, then I should ignore all but the largest ones (ones with 3^^^3 or more galaxies). Among the infinite-or-enormous universes, they nearly all have expanded civilisations, and so under SIA, nearly all predict that I’m going to be in a big civilisation. The only ones which predict otherwise include a “universal doom”—the probability that a small civilisation ever expands off its home world is zero, or negligibly bigger than zero. That’s a massive future filter. So SIA and big universes can—just about—predict my observations, but only if there is this super-strong filter. Again, that has low prior probability, and is not what I should expect to see.
Suppose I adopt SSA reasoning. I need to specify the reference class, and it is a bit hard to know which one to use. In a big universe, different reference classes will lead to very different predictions: picking out small civilisations, large civilisations, AIs, SIMs, emperors and so on (plus worms, rocks and hydrogen for the whackier reference classes). As I don’t know which to use, my predictions get smeared out across the classes, and are consequently vague. Again, I can’t expect to be in a small civilisation on its home planet.
By contrast, look at the small universe models with only a few civilisations. A fair chunk of these models have modest future filters so none of the civilisations expand. For those models, SSA looks in quite good shape, as there is quite a wide choice of reference classes that all lead to the same prediction. Provided the reference class predicts I am an intelligent observer at all then it must predict I am in a small civilisation confined to its home planet (because all civilisations are like that). Of course there are the weird classes which predict I’m a worm and so on—nothing we can do about those—but among the sensible classes we get a hit.
So this is where I’m coming from. The only model which leads me to expect to see what I actually see is a small universe model, with a modest future filter. Within that model, I will need to adopt some sort of SSA-reasoning to get a prediction, but I don’t have to know in advance which reference class to use: any reference class which selects an intelligent observer predicts roughly what I see. None of the other models or styles of reasoning lead to that prediction.