In total utilitarianism, it is a morally neutral act to kill someone (in a painless and unexpected manner) and creating/giving birth to another being of comparable happiness (or preference satisfaction or welfare). In fact if one can kill a billion people to create a billion and one, one is morally compelled to do so. And this is true for real people, not just thought experiment people - living people with dreams, aspirations, grudges and annoying or endearing quirks. To avoid causing extra pain to those left behind, it is better that you kill off whole families and communities, so that no one is left to mourn the dead. In fact the most morally compelling act would be to kill off the whole of the human species, and replace it with a slightly larger population.

We have many real world analogues to this thought experiment. For instance, it seems that there is only a small difference between the happiness of richer nations and poorer nations, while the first consume many more resources than the second. Hence to increase utility we should simply kill off all the rich, and let the poor multiply to take their place (continually bumping off any of the poor that gets too rich). Of course, the rich world also produces most of the farming surplus and the technology innovation, which allow us to support a larger population. So we should aim to kill everyone in the rich world apart from farmers and scientists - and enough support staff to keep these professions running (Carl Shulman correctly points out that we may require most of the rest of the economy as "support staff". Still, it's very likely that we could kill off a significant segment of the population - those with the highest consumption relative to their impact of farming and science - and still "improve" the situation).

Even if turns out to be problematic to implement in practice, a true total utilitarian should be thinking: "I really, really wish there was a way to do targeted killing of many people in the USA, Europe and Japan, large parts of Asia and Latin America and some parts of Africa - it makes me sick to the stomach to think that I can't do that!" Or maybe: "I really really wish I could make everyone much poorer without affecting the size of the economy - I wake up at night with nightmare because these people remain above the poverty line!"

I won't belabour the point. I find those actions personally repellent, and I believe that nearly everyone finds them somewhat repellent or at least did so at some point in their past. This doesn't mean that it's the wrong thing to do - after all, the accepted answer to the torture vs dust speck dilemma feels intuitively wrong, at least the first time. It does mean, however, that there must be very strong countervailing arguments to balance out this initial repulsion (maybe even a mathematical theorem). For without that... how to justify all this killing?

Hence for the rest of this post, I'll be arguing that total utilitarianism is built on a foundation of dust, and thus provides no reason to go against your initial intuitive judgement in these problems. The points will be:

[edit: sorry, the formatting of links and italics in this is all screwy.  I've tried editing both the rich-text and the HTML and either way it looks ok while i'm editing it but the formatted terms either come out with no surrounding spaces or two surrounding spaces]

In the latest Rationality Quotes thread, CronoDAS  quoted  Paul Graham: 

It would not be a bad definition of math to call it the study of terms that have precise meanings.