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Anatoly_Vorobey comments on A Mathematical Explanation of Why Charity Donations Shouldn't Be Diversified - Less Wrong
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dU is a linear approximation to the change in preference level, not the change itself. By assuming the linear approximation is good enough, you beg the question. Consider that if that is to be assumed, you could just take U, A and B to be linear functions to begin with, and maximize the values explicitly without bothering to write out any partial derivatives.
I had a detailed analysis written up a while ago.
It's not so much an assumption, as an intermediate conclusion that follows from the dependence of U on A and B being smooth enough (across the kind of change that dM is capable of making) and nothing else. My only claim is that under this assumption, the non-diversification conclusion follows. U(A,B) being linear is a hugely more restrictive assumption.
This is incorrect. Being smooth is not a license to freely replace function values with linear approximation values; that's not what smoothness means. You have to analyze the error term, most easily presented as the higher-order remainder in the Taylor approximation. Such an analysis is what I'd tried to supply in the post I linked to.