If neq1 was saying that any person who finds themselves selected in that scenario should conclude “blue” with probability 0.99, then I’ve misunderstood his/her last sentence.
If Laura exists, she’ll ask P(blue door | laura exists). Laura=I
If Tom exists, he’ll ask P(blue door | Tom exists). Tom=I
If orthonormal exists, s/he will ask P(blue door | orthonormal exists). orthonormal=I
and so on. Notice how the question we ask depends on the result of the experiment? See how the label switches?
What do Tom, Laura and orthonormal have in common? They are all conscious observers.
So, if orthonormal wakes up in a room, what orthonormal knows is that at least one conscious observer exists. P(blue room | at least one conscious observer exists)=0.5
neq1′s first paragraph refers to Jordan’s scenario. neq1′s second paragraph alters the scenario to be more like the one in the OP. In the altered version, we view the situation “from the outside”. We have no way to specify any particular individual as I before the experiment begins, so our reasoning can only capture the fact that someone ended up in a room. Since we already knew that that would happen, we are still left with the prior probability of .5 that the coin came up heads.
If neq1 was saying that any person who finds themselves selected in that scenario should conclude “blue” with probability 0.99, then I’ve misunderstood his/her last sentence.
It’s a hidden label switching problem.
If Laura exists, she’ll ask P(blue door | laura exists). Laura=I
If Tom exists, he’ll ask P(blue door | Tom exists). Tom=I
If orthonormal exists, s/he will ask P(blue door | orthonormal exists). orthonormal=I
and so on. Notice how the question we ask depends on the result of the experiment? See how the label switches?
What do Tom, Laura and orthonormal have in common? They are all conscious observers.
So, if orthonormal wakes up in a room, what orthonormal knows is that at least one conscious observer exists. P(blue room | at least one conscious observer exists)=0.5
neq1′s first paragraph refers to Jordan’s scenario. neq1′s second paragraph alters the scenario to be more like the one in the OP. In the altered version, we view the situation “from the outside”. We have no way to specify any particular individual as I before the experiment begins, so our reasoning can only capture the fact that someone ended up in a room. Since we already knew that that would happen, we are still left with the prior probability of .5 that the coin came up heads.