Note though that even if we don’t give suffering greater weight than pleasure (and thereby switch to average utilitarianism), the point to stop population growth must be in exactly the same place because that’s where the average component of change that can be classed as a gain starts to be outgunned by the average component of change that’s classed as a loss.
That’s not how the math works out, actually. If you multiply the Suffering curve by a quantity, you also multiply its derivative by the same quantity. If at x=3, d/dx(Benefit(x)-Suffering(x))=0 (which means that d/dx(Benefit(x))=d/dx(Suffering(x))), and ignoring the trivial case where both derivatives are zero (which doesn’t fit with your qualitative description of the curves), then d/dx(Benefit(x))=/=d/dx(5*Suffering(x))=5*d/dx(Suffering(x))=
That’s not how the math works out, actually. Let and Suf be the benefit and suffering in the world when there are x people, according to average utilitarianism. As you have described it, negative utilitarianism multiplies Suffering(x) by a quantity N, giving SufferingN(x)=N∗Suffering(x) Then ddx(SufferingN(x))=ddx(5∗Suffering(x))=5∗ddx(Suffering(x))
That’s not how the math works out, actually. If you multiply the Suffering curve by a quantity, you also multiply its derivative by the same quantity. If at x=3, d/dx(Benefit(x)-Suffering(x))=0 (which means that d/dx(Benefit(x))=d/dx(Suffering(x))), and ignoring the trivial case where both derivatives are zero (which doesn’t fit with your qualitative description of the curves), then d/dx(Benefit(x))=/=d/dx(5*Suffering(x))=5*d/dx(Suffering(x))=
That’s not how the math works out, actually. Let and Suf be the benefit and suffering in the world when there are x people, according to average utilitarianism. As you have described it, negative utilitarianism multiplies Suffering(x) by a quantity N, giving SufferingN(x)=N∗Suffering(x) Then ddx(SufferingN(x))=ddx(5∗Suffering(x))=5∗ddx(Suffering(x))