(Edit: Apologies for how harsh this sounds. No meanness was meant, though it is basically all criticism, which is hard to do collegially on the internet.)
I disagree with this entire genre of posts. I think Probability is Subjectively Objective (when we aren’t worrying about logical uncertainty). Probabilities are objective in the sense that they express how what you know can be used to predict what you don’t know—a logic problem that you can compute the answer to in your brain, but not the sort of thing you can change the answer to by wishing.
There’s an analogy with the idea of the selfish gene, where you realize that genes don’t become widespread by only caring about the reproduction of the organism they’re in at the time, a gene just gets evaluated on if it increases the number of copies of itself by any means. Probabilities should be scored from the perspective of a state of information—a particular state of information implies some probability, and it’s the probability that best reflects the state of the unknown that is compatible with that state of information.
So since I start with thoughts like these, I feel like you rather miss the point. Yes, probability depends on who calculates it (or rather what they know), but we’re clearly talking about Sleeping Beauty. Yes, probability is not directly measurable, but neither is the square of the number of apples on a table—it’s a function of sense data and knowledge. Even framing this as if we were worrying about the bias of the coin feel like you’re not quite exploiting the knowledge that sometimes the “bias” or “fairness” is in the state of knowledge of the calculator.
(Edit: Apologies for how harsh this sounds. No meanness was meant, though it is basically all criticism, which is hard to do collegially on the internet.)
I disagree with this entire genre of posts. I think Probability is Subjectively Objective (when we aren’t worrying about logical uncertainty). Probabilities are objective in the sense that they express how what you know can be used to predict what you don’t know—a logic problem that you can compute the answer to in your brain, but not the sort of thing you can change the answer to by wishing.
There’s an analogy with the idea of the selfish gene, where you realize that genes don’t become widespread by only caring about the reproduction of the organism they’re in at the time, a gene just gets evaluated on if it increases the number of copies of itself by any means. Probabilities should be scored from the perspective of a state of information—a particular state of information implies some probability, and it’s the probability that best reflects the state of the unknown that is compatible with that state of information.
So since I start with thoughts like these, I feel like you rather miss the point. Yes, probability depends on who calculates it (or rather what they know), but we’re clearly talking about Sleeping Beauty. Yes, probability is not directly measurable, but neither is the square of the number of apples on a table—it’s a function of sense data and knowledge. Even framing this as if we were worrying about the bias of the coin feel like you’re not quite exploiting the knowledge that sometimes the “bias” or “fairness” is in the state of knowledge of the calculator.