Peer Disagreement and Independence Preservation
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It has often been recommended that the differing probability distributions of a group of experts should be reconciled in such a way as to preserve each instance of independence common to all of their distributions. When probability pooling is subject to a universal domain condition, along with state-wise aggregation, there are severe limitations on implementing this recommendation. In particular, when the individuals are epistemic peers whose probability assessments are to be accorded equal weight, universal preservation of independence is, with a few exceptions, impossible. Under more reasonable restrictions on pooling, however, there is a natural method of preserving the independence of any fixed finite family of countable partitions, and hence of any fixed finite family of discrete random variables.