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RichardKennaway comments on When is further research needed? - Less Wrong
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I think it is true. I don't see whatever problem you see.
As you indicated, the information assumed in the proof is not assumed in your gloss.
Perhaps it should read something like, "the expected difference in the expected value of a choice upon learning information about the choice, when you are aware of the reliability of the information, is non-negative," but pithier?
Because it seems that if I have a lottery ticket with a 1-in-1000000 chance of paying out $1000000, before I check whether I won, going to redeem it has an expected value of $1, but I expect that if I check whether I have won, this value will decrease.
"The prior expected value of new information is non-negative."
But summaries leave out details. That is what makes them summaries.