This is a thought-provoking journal article discussing cases where:
You have something with two possible states, A and B, and you can perform fairly accurate, mostly independent tests which distinguish between A and B.
However, there is some failure case with a low prior probability, in which the actual state may be B, but something confounds all your tests and makes them look like they favor A regardless.
If you then perform many tests, and they all favor A, the first few tests will make you update towards A, but then if you keep performing more tests whose results favor A, you will actually start updating towards B, because you will start to think you are in the failure case.
An interesting anecdote which I haven’t verified:
Under ancient Jewish law one could not be unanimously convicted of a capital crime—it was held that the absence of even one dissenting opinion among the judges indicated that there must remain some form of undiscovered exculpatory evidence.
When apparently positive evidence can be negative evidence
Link post
This is a thought-provoking journal article discussing cases where:
You have something with two possible states, A and B, and you can perform fairly accurate, mostly independent tests which distinguish between A and B.
However, there is some failure case with a low prior probability, in which the actual state may be B, but something confounds all your tests and makes them look like they favor A regardless.
If you then perform many tests, and they all favor A, the first few tests will make you update towards A, but then if you keep performing more tests whose results favor A, you will actually start updating towards B, because you will start to think you are in the failure case.
An interesting anecdote which I haven’t verified:
Via Hacker News.