We prove the sharp bound for the expected spread upon opinions of experts, who have access to different information sources represented by different σ-fields. Using symmetrization argument and direct combinatorial optimization we derive an explicit optimizer. Our results may turn out to be helpful not only for probabilists, but also for statisticians and economists.
The authors would like to thank an anonymous Referee for the very careful reading of the first version of the paper, for many helpful comments and suggestions.
"The maximal difference among expert’s opinions." Electron. J. Probab. 26 1 - 17, 2021. https://doi.org/10.1214/21-EJP675