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.

From Conservation of Expected Evidence:

If you expect a strong probability of seeing weak evidence in one direction, it must be balanced by a weak expectation of seeing strong evidence in the other direction. If you’re very confident in your theory, and therefore anticipate seeing an outcome that matches your hypothesis, this can only provide a very small increment to your belief (it is already close to 1); but the unexpected failure of your prediction would (and must) deal your confidence a huge blow. On average, you must expect to be exactly as confident as when you started out. Equivalently, the mere expectation of encountering evidence—before you’ve actually seen it—should not shift your prior beliefs.If you expect a strong probability of seeing weak evidence in one direction, it must be balanced by a weak expectation of seeing strong evidence in the other direction. If you’re very confident in your theory, and therefore anticipate seeing an outcome that matches your hypothesis, this can only provide a very small increment to your belief (it is already close to 1); but the unexpected failure of your prediction would (and must) deal your confidence a huge blow. On average, you must expect to be exactly as confident as when you started out. Equivalently, the mere expectation of encountering evidence—before you’ve actually seen it—should not shift your prior beliefs.

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