The mathematics works if the tests are independent, but paired testing requires subjects to be examined about the very same facts. Doesn that undermine independence?
It is the examinations themselves that have to be independent, not the particular facts that the subjects are examined about. Two flips of the same fair coin are as much independent trials as flips of two different coins. The paired testing concept works precisely because of the linkage between the subjects’ relation to the facts. When a pair of opposing witnesses is examined and both test deceptive or both test non-deceptive, then one of the conclusions is wrong. If one tests deceptive and the other tests non-deceptive, then the conclusions are either both right or both wrong, and the Protocol is structured to support a strong inference that they are both right. The same reasoning applies when a pair of corroborating witnesses is examined. If they both test deceptive, or both test non-deceptive, then the conclusions must either be both right or both wrong, and the probability is high that they are both right.
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