This is a restatement of the law of iterated expectations. LIE says E[Y]=E[E[Y|X]]. Replace Y with an indicator variable for whether some hypothesis H is true, and interpret X as an indicator for binary evidence about H. Then this immediately gives you a conservation of expected evidence: if E[Y|X=1]>E[Y], then E[Y|X=0]<E[X], since E[X] is an average of the two of them so it must be in between them.
You could argue this is just an intuitive connection of the LIE to problems of decisionmaking, rather than a reinvention. But there’s no acknowledgement of the LIE anywhere in the original post or comments. In fact, it’s treated as a consequence of Bayesianism, when it follows from probability axioms. (Though one comment does point this out.)
Conservation of expected evidence
This is a restatement of the law of iterated expectations. LIE says E[Y]=E[E[Y|X]]. Replace Y with an indicator variable for whether some hypothesis H is true, and interpret X as an indicator for binary evidence about H. Then this immediately gives you a conservation of expected evidence: if E[Y|X=1]>E[Y], then E[Y|X=0]<E[X], since E[X] is an average of the two of them so it must be in between them.
You could argue this is just an intuitive connection of the LIE to problems of decisionmaking, rather than a reinvention. But there’s no acknowledgement of the LIE anywhere in the original post or comments. In fact, it’s treated as a consequence of Bayesianism, when it follows from probability axioms. (Though one comment does point this out.)
To see it formulated in a context explicitly about beliefs, see Box 1 in these macroeconomics lecture notes.
Thanks—agree or disagree with it, this is a really nice example of what I was hoping for.