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.
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.
This is a good point, what I was trying to say is slightly different. Basically, we know that (A < B) ==> (f(A) < f(B)), where f is our order embedding. So it is indeed true that f(A) > f(B) ==> ¬(A < B), by modus tollens.
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))
Yeah, that’s a pretty clever way to get around the constraint. I think my claim “If the inequitable society has greater total utility, it must be at least as good as the equitable one” would still hold though, no?
“If the inequitable society has greater total utility, it must be at least as good as the equitable one” would still hold though, no?
Well… …. yeah, technically. But for example in the model ( worlds={A, B}, f(W)=sum(log(felicity(e)) for e in population(W)) ), such that world A=(2,2,2,2), and world B=(1,1,1,9). f(A) ≥ f(B), IE ¬(f(A) < f(B)), so ¬(A < B), IE, the equitable society is also at least as good as the inequitable, higher sum utility one. So if you want to support all embeddings via summation of an increasing function of the units’ QoL.. I’d be surprised if those embeddings had anything in common aside from what the premises required. I suspect anything that agreed with all of them would require all worlds the original premises don’t relate to be equal, IE, ¬(A<B) ∧ ¬(B<A).
… looking back, I’m opposed to your implicit definition of a ” “baseline” ”, the original population partial ordering premises are the baseline, here, not total utilitarianism.
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.
This is a good point, what I was trying to say is slightly different. Basically, we know that (A < B) ==> (f(A) < f(B)), where f is our order embedding. So it is indeed true that f(A) > f(B) ==> ¬(A < B), by modus tollens.
Yeah, that’s a pretty clever way to get around the constraint. I think my claim “If the inequitable society has greater total utility, it must be at least as good as the equitable one” would still hold though, no?
Well… …. yeah, technically. But for example in the model ( worlds={A, B}, f(W)=sum(log(felicity(e)) for e in population(W)) ), such that world A=(2,2,2,2), and world B=(1,1,1,9). f(A) ≥ f(B), IE ¬(f(A) < f(B)), so ¬(A < B), IE, the equitable society is also at least as good as the inequitable, higher sum utility one. So if you want to support all embeddings via summation of an increasing function of the units’ QoL.. I’d be surprised if those embeddings had anything in common aside from what the premises required. I suspect anything that agreed with all of them would require all worlds the original premises don’t relate to be equal, IE, ¬(A<B) ∧ ¬(B<A).
… looking back, I’m opposed to your implicit definition of a ” “baseline” ”, the original population partial ordering premises are the baseline, here, not total utilitarianism.