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This reminds me of this recent working paper, where they try to define what optimal news is (in order to be able to measure if it is biased). I suspect that outside of a few, well-defined, use cases, your measurement will be hopelessly vague. It is still an important goal.

https://www.nber.org/papers/w32512

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Interesting paper, it also references https://pubs.aeaweb.org/doi/pdfplus/10.1257/mic.20190133, which seems even more similar.

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