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Kaj_Sotala comments on A Pure Math Argument for Total Utilitarianism - Less Wrong
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Not sure if that's an application as much as a tautology. Valuing equality means that you reject the assumption of "we require that the ranking remain consistent when we add people to the population", so of course accepting that assumption is incompatible with valuing equality.
At least, that's assuming that you value equality as an intrinsic good. As James Miller pointed out, one can also oppose inequality on the ground that it ends up making people's lives worse off, which is an empirical claim separate from utilitarianism.
It's a proof, so sure it's a tautology.
Here's a better way of masking it though: suppose we believe:
This is exactly what it means to be order preserving, but maybe when phrased this way the result seems more surprising (in the sense that those axioms are harder to refute)?