In these kinds of scenarios we need to define our reference class and then we calculate the probability for someone in this class.
No, that is not what probability theory tells us to do. Reference classes are a rough technique to try to come up with prior distributions. They are not part of probability theory per se, and they are problematic because often there is disagreement as to which is the correct reference class.
“They are not part of probability theory per se, and they are problematic because often there is disagreement as to which is the correct reference class”—I’ll write up a post on how to choose the correct reference class soon, but I want to wait a bit, because I’m worried that everyone on Less Wrong is all Sleeping Beauty’ed out. And yes, probability theory takes the set of possibilities as given, but that doesn’t eliminate the need for a justification for this choice.
Yes, in exactly the same sense that *any* mathematical / logical model needs some justification of why it corresponds to the system or phenomenon under consideration. As I’ve mentioned before, though, if you are able to express your background knowledge in propositional form, then your probabilities are uniquely determined by that collection of propositional formulas. So this reduces to the usual modeling question in any application of logic—does this set of propositional formulas appropriately express the relevant information I actually have available?
No, that is not what probability theory tells us to do. Reference classes are a rough technique to try to come up with prior distributions. They are not part of probability theory per se, and they are problematic because often there is disagreement as to which is the correct reference class.
“They are not part of probability theory per se, and they are problematic because often there is disagreement as to which is the correct reference class”—I’ll write up a post on how to choose the correct reference class soon, but I want to wait a bit, because I’m worried that everyone on Less Wrong is all Sleeping Beauty’ed out. And yes, probability theory takes the set of possibilities as given, but that doesn’t eliminate the need for a justification for this choice.
Yes, in exactly the same sense that *any* mathematical / logical model needs some justification of why it corresponds to the system or phenomenon under consideration. As I’ve mentioned before, though, if you are able to express your background knowledge in propositional form, then your probabilities are uniquely determined by that collection of propositional formulas. So this reduces to the usual modeling question in any application of logic—does this set of propositional formulas appropriately express the relevant information I actually have available?
Yeah, but standard propositions don’t support indexicals, only “floating” observers, so why is this relevant?