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The problem with that is that if the accused is only 30% likely to have done something, then there may be an equal or greater likelihood that the accuser is maliciously lying (allowing for some likelihood of genuine misunderstanding).


Not necessarily. Unless the presence of the accusation already was used to get that 30% number, you also need to take into account the a priori probability of someone maliciously lying (or better yet, the particular accuser to be lying in this case) and apply Bayes's theorem.


I should have expected Simpson's Paradox here. Nevertheless, I think the possibility of witch-hunting is high.




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