Ovo-lacto vegetarians live significantly longer than vegans

Where does it say that the difference is significant? The only mention of this I see in the cited paper is table 7, and the CIs there overlap a great deal. (And it goes on to say that the numbers should be "interpreted with caution because of the uncertainty of the dietary classification of subjects in the Health Food Shoppers Study".)

Yup, that's basically right. Silicon Valley is definitely an amazing place to be right now. I'd consider myself to be a good/solid engineer, but not remarkable. One thing to keep in mind is that the cost of living here is more, but unless you are a big spender (need nice house, etc...), you'll do better here than elsewhere.

The term refers to a specific subculture that calls itself "Effective Altruism".

I found that 51% of effective altruists had given blood compared to 47% of others - a difference which did not reach statistical significance.

I gave blood before I was an EA but stopped because I didn't think it was effective. Does being veg*n correlate with calling oneself an EA? That seems like a more effective intervention.

I'm a bit out of my depth here. I understood an "ordered group" as a group with an order on its elements. That clearly can be finite. If it's more than that the question would be why we should assume whatever further axioms characterize it.

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.

Ah, great, I understand more now - the linchpin is the premise that what we really want, is to preserve order when we add another person. So what sort of premise would lead to average utilitarianism?

How about - order should be preserved if we shift the zero-point of our happiness measurement. That seems pretty common-sense. And yet it rules out total utilitarianism. (2,2,2) > (5), but (1,1,1) < (4).

Or maybe we could allow average utilitarianism just by weakening the premise - so that we want to preserve the ordering only if we add an average member.

Two points:

1. I don't know the Holder theorem, but if it actually depends on the lattice being a group, that includes an extra assumption of the existence of a neutral element and inverse elements. The neutral element would have to be a life of exactly zero value, so that killing that person off wouldn't matter at all, either positively or negatively. The inverse elements would mean that for every happy live you can imagine an exactly opposite unhappy live, so that killing off both leaves the world exactly as good as before.

2. Proving this might be hard for infinite cases, but it would be trivial for finite generating groups. Most Less Wrong utilitarians would believe there are only finitely many brain states (otherwise simulations are impossible!) and utility is a function of brain states. That would mean only finitely many utility levels and then the result is obvious. The mathematically interesting part is that it still works if we go infinite on some things but not on others, but that's not relevant to the general Less Wrong belief system.

(Also, here I'm discussing the details of utilitarian systems arguendo, but I'm sticking with the general claim that all of them are mathematically inconsistent or horrible under Arrow's theorem.)

Near the beginning you write this:

Using modern mathematics, we can now prove the intuition of Mills and Bentham: because addition is so special, any ethical system which is in a certain technical sense "reasonable" is equivalent to total utilitarianism.

but then your actual argument includes steps like these:

The most obvious way of defining an ethics of populations is to just take an ordering of individual lives and "glue them together" in an order-preserving way, like I did above.

which, please note, does not amount to any sort of argument that we must or even should just glue values-of-lives together in this sort of way.

I do not see any sign in what you have written that Hölder's theorem is doing any real work for you here. It says that an archimedean totally ordered group is isomorphic to a subset of (R,+) -- but all the contentious stuff about total utilitarianism is already there by the time you suppose that utilities form an archimedean totally ordered group and that combining people is just a matter of applying the group operation to their individual utilities.

The most basic premise is that we have some way of ordering individual lives.

I reject this premise. Specifically, I believe I have some ordering, and you have some ordering, but strongly suspect those orderings disagree, so don't think we have one unambiguous joint ordering.

In either case, we require that the ranking remain consistent when we add people to the population.

I reject this premise. Specifically, I believe that lives interact. Suppose Bob by himself has a medium quality life, and Alice by herself has a medium quality life. Putting them in a universe together by no means guarantees that each of them will have a medium quality life.

Total utilitarianism is a dead simple conclusion from its premises--you don't need to bring in group theory. This is only a "pure math" argument for total utilitarianism because you're talking about the group (R,+) instead of addition, but the two are the same, and the core of the argument remains the contentious moral premises.