**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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