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orthonormal comments on Self-indication assumption is wrong for interesting reasons - Less Wrong
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If you repeat the experiment, does who you call I stay the same (e.g., they might not get selected at all)? If so, then that person was labeled as special a priori, and if they find themself in a room, then the probability of blue is 0.99.
But.. I'm arguing that anyone who is selected, whether it is one person or 99 people, will all think of themselves as I. When you think of frequentist properties then, you have to think about the label switching each time. That changes everything. The fact that you were selected just means that someone was selected, and that was a probability 1 event. Thus, probability of blue door is .5.
Um, no. It's not even controversial that you're wrong in this case.
(For purposes of intuition, let's say there are just 100 people in the world. Do you really think that finding yourself selected is no evidence of blue?)
About what, precisely, is neq1 wrong? neq1 agreed with Jordan that the probability of blue in Jordan's scenario was 0.99. However, as neq1 rightly points out, in Jordan's scenario a specific individual is distinguished prior to the experiment. This doesn't happen in neq1's scenario.
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.