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Anatoly_Vorobey comments on On Charities and Linear Utility - Less Wrong
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I'm unsure of what more I could have done, to be honest. The math involved is just Taylor's formula, and I pointed at its exact form in Wikipedia. Would it be better if I wrote out the exact result of substituting n=1 into the equation? I figured anyone who knows what a partial derivative is can do that on their own, and I wouldn't be helping much to those who don't know that, so it'd just be a token effort.
OK, I guess my biggest complaint is this:
"If this approximation is close enough to the true value, the rest of the argument goes through: given that the sum Δx+Δy+Δz is fixed, it's best to put everything into the charity with the largest partial derivative at (X,Y,Z)."
What does "close enough" mean? I don't see this established anywhere in your post.
I guess one sufficient condition would be that a single charity has the largest partial derivative everywhere in the space of reachable outcomes.