If the inequitable society has greater total utility, it must be at least as good as the equitable one.
No, the premises don't necessitate that. "A is at least as good as B", in our language, is ¬(A < B). But you've stated that the lack of an edge from A to B says nothing about whether A < B, now you're talking like if the premises don't conclude that A < B they must conclude ¬(A < B), which is kinda affirming the consequent.
It might have been a slip of the tongue, or it might be an indication that you're overestimating the significance of this alignment. These premises don't prove that a higher utility inequitable society is at least as good as a lower utility equitable one. They merely don't disagree.
I may be wrong here, but it looks as though, just as the premises support (A < B) ⇒ (utility(A) < utility(B)), they also support (A < B) ⇒ (normalizedU(A)) < normalizedU(B))), such that normalizedU(World) = sum(log(utility(life)) for life in elements(World)) a perfectly reasonable sort of population utilitarianism where utility monsters are fairly well seen to. In this case equality would usually yield greater betterness than inequality despite it being permitted by the premises.
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In your "Increasing population size", you put "Medium, Medium" as more valuable than "Medium", but that doesn't seem to derive from the premises you'd been using so far (apart from the "glue them together" part). I found that surprising, since you seem to go at bigger lengths to justify other things that seem more self-evident to me.
Would Xodarap agree that the premises are (assuming we have operator overloads for multisets rather than sets)
the better set is a superset (A ⊂ B) ⇒ (A < B)
or everything in the better set that's not in the worse set is better than everything that's in the worse set that's not in the better set, (∀a∈(A\B), b∈(B\A) value(a) < value(b)) ⇒ (A < B)