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taw comments on Averaging value systems is worse than choosing one - Less Wrong
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How about this function?
You keep trying to guess proper caveats, I can giving you trivial counterexamples.
This one has: range over entire R, values in [-11,+10], average value 0, global maximum 10, average of local maxima -2.6524 ?
Any function which is more bumpy when it's low, and more smooth when it's high will be like that. This particular one chosen for prettiness of visualization.
That's what I just said:
You are hyper-focusing on this as if it made a difference to my proofs. Please note my previous comment: It does not matter; I never talked about the average IC over all possible agents. I only spoke of IC over various recombinations of existing agents, all of which I assumed to have IC that are local minima. The "random agent" is not an agent taken from the whole space; it's an agent gotten by recombining values from the existing agents.