The structure of critical sets
Walter Bossert (University of Montreal), Susumu Cato (University of Tokyo) and Kohei Kamaga (Sophia University)
GPI Working Paper No. 4-2025
The purpose of this paper is to address some ambiguities and misunderstandings that appear in previous studies of population ethics. In particular, we examine the structure of intervals that are employed in assessing the value of adding people to an existing population. Our focus is on critical-band utilitarianism and critical-range utilitarianism, which are commonly-used population theories that employ intervals, and we show that some previously assumed equivalences are not true in general. The possible discrepancies can be attributed to the observation that critical bands need not be equal to critical sets. The critical set for a moral quasi-ordering is composed of all utility numbers such that adding someone with a utility level in this set leads to a distribution that is not comparable to the original (non-augmented) distribution. The only case in which critical bands and critical sets coincide obtains when the critical band is an open interval. In this respect, there is a stark contrast between critical-band utilitarianism and critical-range utilitarianism: the critical set that corresponds to a critical-range quasi-ordering always coincides with the interval that is used to define the requisite quasi-ordering. As a consequence, an often presumed equivalence of critical-band utilitarianism and critical-range utilitarianism is not valid unless, again, the critical band and the critical range (and, consequently, the requisite critical sets) are given by the same open interval.
Other working papers
Existential risk and growth – Leopold Aschenbrenner (Columbia University)
Human activity can create or mitigate risks of catastrophes, such as nuclear war, climate change, pandemics, or artificial intelligence run amok. These could even imperil the survival of human civilization. What is the relationship between economic growth and such existential risks? In a model of directed technical change, with moderate parameters, existential risk follows a Kuznets-style inverted U-shape. …
Do not go gentle: why the Asymmetry does not support anti-natalism – Andreas Mogensen (Global Priorities Institute, Oxford University)
According to the Asymmetry, adding lives that are not worth living to the population makes the outcome pro tanto worse, but adding lives that are well worth living to the population does not make the outcome pro tanto better. It has been argued that the Asymmetry entails the desirability of human extinction. However, this argument rests on a misunderstanding of the kind of neutrality attributed to the addition of lives worth living by the Asymmetry. A similar misunderstanding is shown to underlie Benatar’s case for anti-natalism.
Moral demands and the far future – Andreas Mogensen (Global Priorities Institute, Oxford University)
I argue that moral philosophers have either misunderstood the problem of moral demandingness or at least failed to recognize important dimensions of the problem that undermine many standard assumptions. It has been assumed that utilitarianism concretely directs us to maximize welfare within a generation by transferring resources to people currently living in extreme poverty. In fact, utilitarianism seems to imply that any obligation to help people who are currently badly off is trumped by obligations to undertake actions targeted at improving the value…