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Contradictory predictions
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Contradictory predictions
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We prove the sharp bound for the probability that two experts who have access to different information, represented by different $\sigma$-fields, will give radically different estimates of the probability of an event. This is relevant when one combines predictions from various experts in a common probability space to obtain an aggregated forecast. Our proof is constructive in the sense that, not only the sharp bounds are proved, but also the optimizer is constructed via an explicit algorithm.
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Defines private private signals and characterizes the optimal ones that maximize state informativeness subject to no cross-signal information leakage.
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