Determining whether there is a filter is a separate issue to updating on the size of our ‘reference class’ in given scenarios. All that is needed for my argument is that there is apparently a filter at the moment.
You are correct that civilizations who know they are in the future or the past aren’t added to our reference class for SIA purposes, but it looks to me like this makes no difference to the shift if the proportions of people in late filter and early filter worlds are the same across time, which I am assuming in a simple model, though you could of course complicate that.
″ Indeed, SIA, once we update on the present, cannot tell us anything about the future.”
For my argument it only need tell us about the present and the past. They can inform us on the future in the usual way (if we can work out where the filter has been in the past, chances are it hasn’t just moved, which has implications for our future).
Given any particular world size, SIA means the filter is more likely to be late. 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. If you were to include the one planet early filter world and the four planet late filter world in your original set, the usual shift toward late filter worlds would occur.
This doesn’t seem a trick specific to SIA—you can do the same thing to avoid updating on many things. e.g. consider the following non anthropic example:
There are two urns. A has odd and even numbered balls in it, and B just has odd numbered balls. An urn will be chosen and some unknown number of balls pulled from it. You will be told afterwards whether number 17 comes up or not.
Number 17 did come up. Does this increase your posterior on the urn being B?
Intuitively yes—around twice as many odd balls would have been drawn from the odd ball urn than the mixed one, giving twice as many opportunities for 17 to come up. But now consider these options:
X) Two balls drawn from even ball urn
Y) Four balls drawn from even ball urn
A) One ball drawn from odd ball urn
B) Two balls drawn from odd ball urn
With the same prior as in your example, you get the same results.
Conclusion: I don’t think any of this makes much difference to the original argument.
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.
Determining whether there is a filter is a separate issue to updating on the size of our ‘reference class’ in given scenarios. All that is needed for my argument is that there is apparently a filter at the moment.
You are correct that civilizations who know they are in the future or the past aren’t added to our reference class for SIA purposes, but it looks to me like this makes no difference to the shift if the proportions of people in late filter and early filter worlds are the same across time, which I am assuming in a simple model, though you could of course complicate that.
″ Indeed, SIA, once we update on the present, cannot tell us anything about the future.”
For my argument it only need tell us about the present and the past. They can inform us on the future in the usual way (if we can work out where the filter has been in the past, chances are it hasn’t just moved, which has implications for our future).
Given any particular world size, SIA means the filter is more likely to be late. 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. If you were to include the one planet early filter world and the four planet late filter world in your original set, the usual shift toward late filter worlds would occur.
This doesn’t seem a trick specific to SIA—you can do the same thing to avoid updating on many things. e.g. consider the following non anthropic example:
There are two urns. A has odd and even numbered balls in it, and B just has odd numbered balls. An urn will be chosen and some unknown number of balls pulled from it. You will be told afterwards whether number 17 comes up or not.
Number 17 did come up. Does this increase your posterior on the urn being B? Intuitively yes—around twice as many odd balls would have been drawn from the odd ball urn than the mixed one, giving twice as many opportunities for 17 to come up. But now consider these options:
X) Two balls drawn from even ball urn
Y) Four balls drawn from even ball urn
A) One ball drawn from odd ball urn
B) Two balls drawn from odd ball urn
With the same prior as in your example, you get the same results.
Conclusion: I don’t think any of this makes much difference to the original argument.
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.