I would think that FDT chooses Bet 2, unless I’m misunderstanding something about the role of Peano Arithmetic here. Taking Bet 2 results in P being true, and vice versa for Bet 1; therefore, the only options that are actually possible are the bottom left and the top right.
In fact, this seems like the exact sort of situation in which FDT can be easily shown to outperform CDT. CDT would reason along the lines of “Bet 1 is better if P is true, and better if P is false, and therefore better overall” without paying attention to the direct dependency between the output of your decision algorithm and the truth value of P.
I’m not quite sure what Yudkowsky and Soares meant by “dominance” there. I’d guess on priors that they meant FDT pays attention to those dependencies when deciding whether one strategy outperforms another… but yeah, they kind of worded it in a way that suggests the opposite interpretation.
I would think that FDT chooses Bet 2, unless I’m misunderstanding something about the role of Peano Arithmetic here. Taking Bet 2 results in P being true, and vice versa for Bet 1; therefore, the only options that are actually possible are the bottom left and the top right.
In fact, this seems like the exact sort of situation in which FDT can be easily shown to outperform CDT. CDT would reason along the lines of “Bet 1 is better if P is true, and better if P is false, and therefore better overall” without paying attention to the direct dependency between the output of your decision algorithm and the truth value of P.
I’m not quite sure what Yudkowsky and Soares meant by “dominance” there. I’d guess on priors that they meant FDT pays attention to those dependencies when deciding whether one strategy outperforms another… but yeah, they kind of worded it in a way that suggests the opposite interpretation.
(See my response to gjm’s comment.)