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Can Coherent Predictions be Contradictory?

Part of: Distribution theory - Probability

Published online by Cambridge University Press:  17 March 2021

Krzysztof Burdzy  and
Soumik Pal
Krzysztof Burdzy*
Affiliation:
University of Washington
Soumik Pal*
Affiliation:
University of Washington
*
*Postal address: Department of Mathematics, Box 354350, University of Washington, Seattle, WA 98195.
*Postal address: Department of Mathematics, Box 354350, University of Washington, Seattle, WA 98195.
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Abstract

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. The optimizer for the bound is explicitly described. This paper was originally titled ‘Contradictory predictions’.

Keywords

Conditional probabilityopinionjoint distribution of conditional expectations

MSC classification

Primary: 60E15: Inequalities; stochastic orderings
Type
Original Article
Information
Advances in Applied Probability , Volume 53 , Issue 1 , March 2021 , pp. 133 - 161
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Copyright
© The Author(s), 2021. Published by Cambridge University Press on behalf of Applied Probability Trust

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