Gustaf Arrhenius is the main person to look at on this topic. His website is here. Check out ch. 10-11 of his dissertation Future Generations: A Challenge for Moral Theory (though he has a forthcoming book that will make that obsolete). You may find more papers on his website. Look at the papers that contain the words “impossibility theorem” in the title.
Do average utilitarians have a standard answer to the question of what is the average welfare of zero people? The theory seems consistent with any such answer. If you’re maximizing the average welfare of the people alive at some future point in time, and there’s a nonzero chance of causing or preventing extinction, then the answer matters, too.
Usually, average utilitarians are interested in maximizing the average well-being of all the people that ever exist, they are not fundamentally interested in the average well-being of the people alive at particular points of time. Since some people have already existed, this is only a technical problem for average utilitarianism (and a problem that could not even possibly affect anyone’s decision).
Incidentally, not distinguishing between averages over all the people that ever exist and all the people that exist at some time leads some people to wrongly conclude that average utilitarianism favors killing off people who are happy, but less happy than average.
A related commonly missed distinction is between maximizing welfare divided by lives, versus maximizing welfare divided by life-years. The second is more prone to endorsing euthanasia hypotheticals.
Where can I find the theorems?
Gustaf Arrhenius is the main person to look at on this topic. His website is here. Check out ch. 10-11 of his dissertation Future Generations: A Challenge for Moral Theory (though he has a forthcoming book that will make that obsolete). You may find more papers on his website. Look at the papers that contain the words “impossibility theorem” in the title.
Do average utilitarians have a standard answer to the question of what is the average welfare of zero people? The theory seems consistent with any such answer. If you’re maximizing the average welfare of the people alive at some future point in time, and there’s a nonzero chance of causing or preventing extinction, then the answer matters, too.
Usually, average utilitarians are interested in maximizing the average well-being of all the people that ever exist, they are not fundamentally interested in the average well-being of the people alive at particular points of time. Since some people have already existed, this is only a technical problem for average utilitarianism (and a problem that could not even possibly affect anyone’s decision).
Incidentally, not distinguishing between averages over all the people that ever exist and all the people that exist at some time leads some people to wrongly conclude that average utilitarianism favors killing off people who are happy, but less happy than average.
A related commonly missed distinction is between maximizing welfare divided by lives, versus maximizing welfare divided by life-years. The second is more prone to endorsing euthanasia hypotheticals.