The way you derive a confidence interval is by assessing the likelihood function, which is across the distribution of populations. Bayes’ Theorem, as presented by Scott Alexander and Eliezer Yudkowski, does NOT include those tools; you can’t use what they present to derive an actual confidence interval. Your claim of ‘confidence’ on a prediction market is NOT the same as Dirichlet saying “95% of the possible populations’ likelihood MASS lies within these bounds.” THAT is a precise and valuable fact which “Bayes as presented to Rationalists” does NOT have the power to derive.
The way you derive a confidence interval is by assessing the likelihood function, which is across the distribution of populations. Bayes’ Theorem, as presented by Scott Alexander and Eliezer Yudkowski, does NOT include those tools; you can’t use what they present to derive an actual confidence interval. Your claim of ‘confidence’ on a prediction market is NOT the same as Dirichlet saying “95% of the possible populations’ likelihood MASS lies within these bounds.” THAT is a precise and valuable fact which “Bayes as presented to Rationalists” does NOT have the power to derive.