[EDIT:] Warning: This post was based on a misunderstanding of the OP. Thanks orthonormal for pointing out the the mistake! I leave this post here so that the replies stay in context.
I think that decision matrix of the agent waking up in green room is not complete: it should contain the outcome of losing $50 if the answers are not consistent.
Therefore, it would compute that even if the probability of the coin was flipped to 1 is 90%, it still does not make sense to answer “yes” since two other copies would answer “no” and therefore the penalty for not giving a uniform answer will outweigh the potential) win of $5.60. (Even without the penalty, the agent could infer that there were two dissenting copies of itself in that case and he has no ways to generate all the necessary votes to get the money.)
The error of the agent is not the P=90% estimate, but the implicit assumption that he is the only one to influence the outcome.
Thanks for pointing that out. Now I understand the problem.
However, I still think that the mistake made by the agent is the implicit assumption the he is the only one influencing the outcome.
Since all of the copies assume that they solely decide the outcome, they overestimate the reward after the anthropic update (each of the copies claim the whole reward for his decision, although the decision is collective and each vote is necessary).
By the way, please don’t delete a comment if you change your mind or realize an error; it makes the conversation difficult for others to read. You can always put in an edit (and mark it as such) if you want.
I’d only delete one of my comments if I felt that its presence actually harmed readers, and that there was no disclaimer I could add that would prevent that harm.
[EDIT:] Warning: This post was based on a misunderstanding of the OP. Thanks orthonormal for pointing out the the mistake! I leave this post here so that the replies stay in context.
I think that decision matrix of the agent waking up in green room is not complete: it should contain the outcome of losing $50 if the answers are not consistent.
Therefore, it would compute that even if the probability of the coin was flipped to 1 is 90%, it still does not make sense to answer “yes” since two other copies would answer “no” and therefore the penalty for not giving a uniform answer will outweigh the potential) win of $5.60. (Even without the penalty, the agent could infer that there were two dissenting copies of itself in that case and he has no ways to generate all the necessary votes to get the money.)
The error of the agent is not the P=90% estimate, but the implicit assumption that he is the only one to influence the outcome.
The copies in red rooms don’t get to vote in this setup.
Thanks for pointing that out. Now I understand the problem.
However, I still think that the mistake made by the agent is the implicit assumption the he is the only one influencing the outcome.
Since all of the copies assume that they solely decide the outcome, they overestimate the reward after the anthropic update (each of the copies claim the whole reward for his decision, although the decision is collective and each vote is necessary).
By the way, please don’t delete a comment if you change your mind or realize an error; it makes the conversation difficult for others to read. You can always put in an edit (and mark it as such) if you want.
I’d only delete one of my comments if I felt that its presence actually harmed readers, and that there was no disclaimer I could add that would prevent that harm.
OK, sorry. (In this special case, I remember thinking that your remark was perfectly understandable even without the context.)