SIA implies a different conclusion. To predict your observations under SIA, you should first sample a random universe proportional to its population, then sample a random observer in that universe. The probabilities of observing each index are the same conditional on the universe, but the prior probabilities of being in a given universe have changed.
We start with 1000:1 odds in favor of the 1-trillion universe, due to its higher population.
Can you elaborate on why under SIA we sample a universe proportional to its population? Is this because it’s like taking one sample from all these universes together uniformly, as if you’d indexed everyone together? Wouldn’t that kind of imply we’re in the universe with infinite people, though?
It’s like selecting a random observer from all possible universes taken as a single bag. E.g. if there are 2 possible universes with equal initial probability, and one has twice the population of the other, then if you select a random person across universes, you end up in the higher population one with higher probability. The doomsday argument motivates one reason why this might make sense. Also, if you imagine these alternative universes as actually existing due to some kind of big universe theory (just being very large, or many-worlds, or multiversal), then SSA and SIA will tend to agree.
SIA doesn’t handle cases with infinite universes in a well-defined manner. For that you might need some modification like selecting a universe with higher probability if it has more observers per unit computation, or similar. In general, the presumptuous philosopher problem is a counterintuitive implication of SIA.
SIA can be considered (IMO more naturally) as randomly sampling you from “observers in your epistemic situation”, so it’s not so much “increasing the prior” but rather “caring about the absolute number of observers in your epistemic situation” rather than “caring about the proportion of observers in your epistemic situation” as SSA does.
This has the same end result as “up-weighting the prior then using the proportion of observers in your epistemic situation”, but I find it to be much more intuitive than that, as the latter seems to me to be overly circuitous by multiplying by population then dividing by population (as part of taking the proportion of the reference class that you comprise), rather than just taking the number we care about (number of observers in your epistemic situation) in the first place.
Can you elaborate on why under SIA we sample a universe proportional to its population? Is this because it’s like taking one sample from all these universes together uniformly, as if you’d indexed everyone together? Wouldn’t that kind of imply we’re in the universe with infinite people, though?
It’s like selecting a random observer from all possible universes taken as a single bag. E.g. if there are 2 possible universes with equal initial probability, and one has twice the population of the other, then if you select a random person across universes, you end up in the higher population one with higher probability. The doomsday argument motivates one reason why this might make sense. Also, if you imagine these alternative universes as actually existing due to some kind of big universe theory (just being very large, or many-worlds, or multiversal), then SSA and SIA will tend to agree.
SIA doesn’t handle cases with infinite universes in a well-defined manner. For that you might need some modification like selecting a universe with higher probability if it has more observers per unit computation, or similar. In general, the presumptuous philosopher problem is a counterintuitive implication of SIA.
SIA can be considered (IMO more naturally) as randomly sampling you from “observers in your epistemic situation”, so it’s not so much “increasing the prior” but rather “caring about the absolute number of observers in your epistemic situation” rather than “caring about the proportion of observers in your epistemic situation” as SSA does.
This has the same end result as “up-weighting the prior then using the proportion of observers in your epistemic situation”, but I find it to be much more intuitive than that, as the latter seems to me to be overly circuitous by multiplying by population then dividing by population (as part of taking the proportion of the reference class that you comprise), rather than just taking the number we care about (number of observers in your epistemic situation) in the first place.