How do you do Bayesian belief revision when one of your alternative hypotheses uses the anthropic principle? Can you give a strong preference to the hypothesis that does not require it? Because I know that I would.
Your existence can never be Bayesian evidence for you either way due to conservation of expected evidence. Your non-existence can never be Bayesian evidence the other way for you.
In a wider sense it seems far from obvious that a claim like “most observers are instances of probable observers” is true, and even if it is true it’s not clear that you are allowed to draw inferences from that as though being a particular instance of you was a random sample, that may be just a malfunction of human reasoning caused by the particular way we evolved. Updateless reasoning suggests that you should not distinguish between yourself and other instances of you in that way.
That’s not the question I’m asking. If you have two hypotheses to explain something, and one of them uses anthropic reasoning, and the other does not, how much can you favor the one that does not?
If anthropic reasoning is used to get around a prior of 10^-11, can I favor the hypothesis not requiring anthropic reasoning by a factor of 100? If I favor the latter hypothesis at all, shouldn’t that show up in the priors; and shouldn’t anthropic reasoning therefore lose out to, eg., the God hypothesis?
My other reply to the post about the updateless perspective probably fits better.
I’m not sure what a hypothesis without anthropic reasoning would be. Anthropic reasoning is just that you are certain to observe a world where your existence is possible. if two different hypotheses both allow your existence they both benefit from anthropic reasoning, if any hypothesis ever does. If your existence is drastically more likely conditional on one hypothesis being true than it is conditional on the other being true then the first benefits more from anthropic reasoning itself, while the latter implies more anthropic reasoning for the observation that you exist. Which of those hypotheses would you describe as using anthropic reasoning?
If hypothesis A has a prior of 10^-10, hypothesis B a prior of 10^-15, P(PhilGoetz|A)=10^-20 and P(PhilGoetz|B)=10^-5, then I think it’s permissible for PhilGoetz to drastically favor hypothesis B over A whenever the importance of the decision directly scales with P(PhilGoetz).
Your existence can never be Bayesian evidence for you either way due to conservation of expected evidence. Your non-existence can never be Bayesian evidence the other way for you.
In a wider sense it seems far from obvious that a claim like “most observers are instances of probable observers” is true, and even if it is true it’s not clear that you are allowed to draw inferences from that as though being a particular instance of you was a random sample, that may be just a malfunction of human reasoning caused by the particular way we evolved. Updateless reasoning suggests that you should not distinguish between yourself and other instances of you in that way.
That’s not the question I’m asking. If you have two hypotheses to explain something, and one of them uses anthropic reasoning, and the other does not, how much can you favor the one that does not?
If anthropic reasoning is used to get around a prior of 10^-11, can I favor the hypothesis not requiring anthropic reasoning by a factor of 100? If I favor the latter hypothesis at all, shouldn’t that show up in the priors; and shouldn’t anthropic reasoning therefore lose out to, eg., the God hypothesis?
My other reply to the post about the updateless perspective probably fits better.
I’m not sure what a hypothesis without anthropic reasoning would be. Anthropic reasoning is just that you are certain to observe a world where your existence is possible. if two different hypotheses both allow your existence they both benefit from anthropic reasoning, if any hypothesis ever does. If your existence is drastically more likely conditional on one hypothesis being true than it is conditional on the other being true then the first benefits more from anthropic reasoning itself, while the latter implies more anthropic reasoning for the observation that you exist. Which of those hypotheses would you describe as using anthropic reasoning?
If hypothesis A has a prior of 10^-10, hypothesis B a prior of 10^-15, P(PhilGoetz|A)=10^-20 and P(PhilGoetz|B)=10^-5, then I think it’s permissible for PhilGoetz to drastically favor hypothesis B over A whenever the importance of the decision directly scales with P(PhilGoetz).