That should be conclusive from this post, so for everyone who already read it, you can try to predict it before reading further.
So you’d have to input your probability distribution of possible universes, in this case that just has to specify where the filter is for different species. If you think the filter is at the same place for all species, then your distribution should look something like 1⁄3 * filter always late, 1⁄3 * filter always middle, 1⁄3 * filter always early and the SIA doomsday doesn’t apply (you’d have 3 trivial experiments). If you think for some it’s early and for some middle and for some late, then your distribution would just be 1 * filter varies for different species, then you’d have just one experiment which rolls a die in the beginning to decide where it puts the filter for us. Then the argument works. You could also mix those, if you think maybe it’s the same for everyone and maybe not. Then the argument kinda works.
But plausibly the filter, if it exists, is at the same place for everyone. So my theory mostly rejects the argument.
No, in God’s coin toss the probability is random. At least that’s what I took it as, since it’s described as a coin toss. The reason the answer is 1⁄2 there is just because the number of observations of being in room 1-10 is equal in the heads-case and the tails-case (10 in both). This is the image of the experiment I made in the post. If it was 2000 people in the tails-case, 2 in every room number, then the answer would be 1⁄3 for heads.
What is the prediction of your theory to the Grace’s SIA Doomsday?
That should be conclusive from this post, so for everyone who already read it, you can try to predict it before reading further.
So you’d have to input your probability distribution of possible universes, in this case that just has to specify where the filter is for different species. If you think the filter is at the same place for all species, then your distribution should look something like 1⁄3 * filter always late, 1⁄3 * filter always middle, 1⁄3 * filter always early and the SIA doomsday doesn’t apply (you’d have 3 trivial experiments). If you think for some it’s early and for some middle and for some late, then your distribution would just be 1 * filter varies for different species, then you’d have just one experiment which rolls a die in the beginning to decide where it puts the filter for us. Then the argument works. You could also mix those, if you think maybe it’s the same for everyone and maybe not. Then the argument kinda works.
But plausibly the filter, if it exists, is at the same place for everyone. So my theory mostly rejects the argument.
In other words, it is similar to the the God coin toss—you can’t update logical uncertainty based on your location?
No, in God’s coin toss the probability is random. At least that’s what I took it as, since it’s described as a coin toss. The reason the answer is 1⁄2 there is just because the number of observations of being in room 1-10 is equal in the heads-case and the tails-case (10 in both). This is the image of the experiment I made in the post. If it was 2000 people in the tails-case, 2 in every room number, then the answer would be 1⁄3 for heads.