Conservation of Expected Evidence

Conservation of Expected Evidence is a consequence of probability theory which states that for every expectation of evidence, there is an equal and opposite expectation of counterevidence. [1] The mere expectation of encountering evidence–before you've actually seen it–should not shift your prior beliefs. It also goes by other names, including the law of total expectation and the law of iterated expectations.

A consequence of this principle is that absence of evidence is evidence of absence.

Consider a hypothesis H and evidence (observation) E. Prior probability of the hypothesis is P(H); posterior probability is either P(H|E) or P(H|¬E), depending on whether you observe E or not-E (evidence or counterevidence). The probability of observing E is P(E), and probability of observing not-E is P(¬E). Thus, expected value of the posterior probability of the hypothesis is:...

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