As you mention, the three examples here work regardless of whether SSA or SIA is true because none of the estimated outcomes affect the total number of observers. But the Doomsday Argument is different and does depend on SSA. If SIA is true, the early population of a long world is just as likely to exist as the total population of a short world, so there’s no update upon finding yourself in an early-seeming world.
A total utilitarian observing from outside both worlds will care just as much about the early population of a long world as the total population of a short world, so the expected value of both reference classes is the same. This suggests to me that if I care about myself, I should be indifferent between the possibilities that I’m early and that I’m in a world with a short lifespan. Of course, if my decisions in one world will affect more people, then I should adjust my actions accordingly.
There is a way to escape this by using the universal doomsday argument. In it, we try not to predict the exact future of the Earth, but the typical life expectancy of Earth-like civilizations, that is, the proportion of long civilizations to short ones.
If we define a long civilization as one which has 1000 times more observers, the fact that we find ourselves early means that short civilizations are at least 1000 times more numerous.
In short, it is SSA, but applied to a large set of civilizations.
The universal doomsday argument still relies on SSA, because under SIA, I’m equally surprised to exist as an early person whether most civilizations are short or long. If most civilizations are long, I’m surprised to be early. If most civilizations are short, I’m surprised to exist at all. I could have been any of the late people who failed to exist because most civilizations are short. In other words, the surprise of existing as an early person is equivalent in both cases under SIA, so there’s no update. Only under SSA am I certain I will exist but unsure where in the universe I will be.
I think that SIA is generally* valid but it uses all its power to prove that I live in the infinite universe where all possible observers exist. After that we have to use SSA to find in which region of the multiverse I am more likely to be located.
*I think that the logically sound version of SIA is “if I am in a unique position, generated by some random process, then there were many attempts to create me” – like many earth-like-but-lifeless planets are in the galaxy.
Another point is that the larger number of short civilizations can compensate for their “shortness.” We can live in the region of multiverse where there are many short civilizations and almost all of them die off.
As you mention, the three examples here work regardless of whether SSA or SIA is true because none of the estimated outcomes affect the total number of observers. But the Doomsday Argument is different and does depend on SSA. If SIA is true, the early population of a long world is just as likely to exist as the total population of a short world, so there’s no update upon finding yourself in an early-seeming world.
A total utilitarian observing from outside both worlds will care just as much about the early population of a long world as the total population of a short world, so the expected value of both reference classes is the same. This suggests to me that if I care about myself, I should be indifferent between the possibilities that I’m early and that I’m in a world with a short lifespan. Of course, if my decisions in one world will affect more people, then I should adjust my actions accordingly.
There is a way to escape this by using the universal doomsday argument. In it, we try not to predict the exact future of the Earth, but the typical life expectancy of Earth-like civilizations, that is, the proportion of long civilizations to short ones.
If we define a long civilization as one which has 1000 times more observers, the fact that we find ourselves early means that short civilizations are at least 1000 times more numerous.
In short, it is SSA, but applied to a large set of civilizations.
The universal doomsday argument still relies on SSA, because under SIA, I’m equally surprised to exist as an early person whether most civilizations are short or long. If most civilizations are long, I’m surprised to be early. If most civilizations are short, I’m surprised to exist at all. I could have been any of the late people who failed to exist because most civilizations are short. In other words, the surprise of existing as an early person is equivalent in both cases under SIA, so there’s no update. Only under SSA am I certain I will exist but unsure where in the universe I will be.
I think that SIA is generally* valid but it uses all its power to prove that I live in the infinite universe where all possible observers exist. After that we have to use SSA to find in which region of the multiverse I am more likely to be located.
*I think that the logically sound version of SIA is “if I am in a unique position, generated by some random process, then there were many attempts to create me” – like many earth-like-but-lifeless planets are in the galaxy.
Another point is that the larger number of short civilizations can compensate for their “shortness.” We can live in the region of multiverse where there are many short civilizations and almost all of them die off.