SSA is a generalized single halfism reasoning. It’s very obviously wrong in Sleeping Beauty as it implies that if the Beauty knows that she is awakened on Monday, she expects that there is 3⁄2 chance that the coin is Heads. Generally if you actually do the math, SSA can’t produce correct betting odds for Sleeping Beauty problem. It’s, in a sense, even worse than SIA for SB, but ultimately both of them are based on the flawed and unjustified framework of “centred possible worlds”.
Double halfism is the correct approach and has no problem with correct betting odds. All your argument in favor of halfism are, in fact, double halfer reasoning. However you mistakenly credit them to SSA.
Took me a while to get back to you because I wanted to read your whole sequence (linked to me by someone else) before responding.
Anyway, it was far better than anything I wrote, and the thinking was much clearer.
I’m also a bit surprised that I hadn’t seen more discussion about double-halferism. It’s a single, barely comprehensible paragraph on the Sleeping Beauty wikipedia page, and you can barely find any links to it when googling “Sleeping Beauty” or “anthropics.” All this, despite the fact that it’s clearly the correct solution!
Anyway, thank you for the good read. I’m hoping to take a second attempt at this problem that should be a bit more thorough. I think I had gotten most of the way there, reasoning wise, but there were pieces I was clearly missing.
Good overall, but you are making a serious mistake: confusing single halfism, with double halfism.
SSA is a generalized single halfism reasoning. It’s very obviously wrong in Sleeping Beauty as it implies that if the Beauty knows that she is awakened on Monday, she expects that there is 3⁄2 chance that the coin is Heads. Generally if you actually do the math, SSA can’t produce correct betting odds for Sleeping Beauty problem. It’s, in a sense, even worse than SIA for SB, but ultimately both of them are based on the flawed and unjustified framework of “centred possible worlds”.
Double halfism is the correct approach and has no problem with correct betting odds. All your argument in favor of halfism are, in fact, double halfer reasoning. However you mistakenly credit them to SSA.
Took me a while to get back to you because I wanted to read your whole sequence (linked to me by someone else) before responding.
Anyway, it was far better than anything I wrote, and the thinking was much clearer.
I’m also a bit surprised that I hadn’t seen more discussion about double-halferism. It’s a single, barely comprehensible paragraph on the Sleeping Beauty wikipedia page, and you can barely find any links to it when googling “Sleeping Beauty” or “anthropics.” All this, despite the fact that it’s clearly the correct solution!
Anyway, thank you for the good read. I’m hoping to take a second attempt at this problem that should be a bit more thorough. I think I had gotten most of the way there, reasoning wise, but there were pieces I was clearly missing.