Corroborating testimony, probability and surprise

Abstract
Jonathan Cohen has claimed that in cases of witness agreement there is an inverse relationship between the prior probability and the posterior probability of what is being agreed: the posterior rises as the prior falls. As is demonstrated in this paper, this contention is not generally valid. In fact, in the most straightforward case exactly the opposite is true: a lower prior also means a lower posterior. This notwithstanding, there is a grain of truth to what Cohen is saying, as there are special circumstances under which a thesis similar to his holds good. What characterises these circumstances is that they allow for the fact of agreement to be surprising. In making this precise, I draw on Paul Horwich's probabilistic analysis of surprise. I also consider a related claim made by Cohen concerning the effect of lowering the prior on the strength of corroboration. 1 Introduction 2 Cohen's claim 3 A counterexample 4 A weaker claim 5 A counterexample to the weaker claim 6 The grain of truth in Cohen's claim 7 Prior probability and strength of corroboration 8 Conclusion.
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