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CuSithBell comments on When is further research needed? - Less Wrong
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Where? I see
It's always a good idea to read below the fold before commenting, an example of more information being a good thing.
(BTW, my deleted comment was a draft I had second thoughts about, then decided was right anyway and reposted here.)
P_c(u|o) is assumed to be known to the agent.
No need to be snide. I think the description of your theorem, as written above, is false. What conditions need to hold before it becomes true?
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.