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Peter_de_Blanc comments on On Charities and Linear Utility - Less Wrong
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Comments (58)
I voted this post down. You claim to have done math, and you tell a narrative of doing math, but for the most part your math is not shown. This makes it difficult for someone to form an opinion of your work without redoing the work from scratch.
[Edit: I was unnecessarily rude here, and I've removed the downvote.]
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.