(That also means, of course, that when I say I choose 3⁄4 and 1⁄2 and then 2⁄3, I am smuggling in information; implicitly assuming the reward structure for “getting the right answer”. If I’d rather be right all the time if I’m the original and don’t care at all if I’m the clone then I can answer “probability 1.0 that I’m the original!” and make out like a bandit. In that sense, yes, all probabilities are meaningless, not just self-locating ones, until you know what decisions are being made based on them.)
I think the comments on https://www.lesswrong.com/posts/YyJ8roBHhD3BhdXWn/probability-is-a-model-frequency-is-an-observation-why-both are pretty good, btw. They really showcase how all the hand-waving goes away as soon as you specify the decisions the original/clone will be making based on their degree of belief that they’re the original.
(That also means, of course, that when I say I choose 3⁄4 and 1⁄2 and then 2⁄3, I am smuggling in information; implicitly assuming the reward structure for “getting the right answer”. If I’d rather be right all the time if I’m the original and don’t care at all if I’m the clone then I can answer “probability 1.0 that I’m the original!” and make out like a bandit. In that sense, yes, all probabilities are meaningless, not just self-locating ones, until you know what decisions are being made based on them.)