Given any particular world size, SIA means the filter is more likely to be late.
No it doesn’t. It boost the probability of certain universes, some of which happen to have late filters—and some of which may have no filters at all. Consider the (very improbable) low-start simultaneous worlds universe, where it takes several billion years for life to get going, but life is never filtered at all, and now the galaxy is filled with civilizations at approximately our level. This universe is very unlikely—but SIA boosts its probability!
Now I believe that the total effect is to boost the probability of late filters—but this is very far from a proof.
Larger worlds with early filters can of course be made just as likely as smaller worlds with late filters, so if you double the size of the early filter worlds you look at, SIA makes no difference.
Unless I’m misunderstanding you, this is not the point. The effect of SIA depends on the relative probabilities of X and Y, and the relative probabilities of A and B—not, in any way, on the relative probabilities of A versus X or anything like that. I can make X and Y as unlikely as you want, and yet still be in a situation where SIA increases your probability of early filter.
Conclusion: I don’t think any of this makes much difference to the original argument.
The way it was presented to me (and I may have misunderstood this, but I did ask Robin), future civilizations were included in the argument. Just removing them makes a huge difference to the odds. Whether past civilizations should be included is a more tricky point, and depends tremendously on your choice of priors.
No it doesn’t. It boost the probability of certain universes, some of which happen to have late filters—and some of which may have no filters at all. Consider the (very improbable) low-start simultaneous worlds universe, where it takes several billion years for life to get going, but life is never filtered at all, and now the galaxy is filled with civilizations at approximately our level. This universe is very unlikely—but SIA boosts its probability!
Now I believe that the total effect is to boost the probability of late filters—but this is very far from a proof.
Unless I’m misunderstanding you, this is not the point. The effect of SIA depends on the relative probabilities of X and Y, and the relative probabilities of A and B—not, in any way, on the relative probabilities of A versus X or anything like that. I can make X and Y as unlikely as you want, and yet still be in a situation where SIA increases your probability of early filter.
The way it was presented to me (and I may have misunderstood this, but I did ask Robin), future civilizations were included in the argument. Just removing them makes a huge difference to the odds. Whether past civilizations should be included is a more tricky point, and depends tremendously on your choice of priors.