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
Quadratic Funding with Incomplete Information – Luis M. V. Freitas (Global Priorities Institute, University of Oxford) and Wilfredo L. Maldonado (University of Sao Paulo)
Quadratic funding is a public good provision mechanism that satisfies desirable theoretical properties, such as efficiency under complete information, and has been gaining popularity in practical applications. We evaluate this mechanism in a setting of incomplete information regarding individual preferences, and show that this result only holds under knife-edge conditions. We also estimate the inefficiency of the mechanism in a variety of settings and show, in particular, that inefficiency increases…
Desire-Fulfilment and Consciousness – Andreas Mogensen (Global Priorities Institute, University of Oxford)
I show that there are good reasons to think that some individuals without any capacity for consciousness should be counted as welfare subjects, assuming that desire-fulfilment is a welfare good and that any individuals who can accrue welfare goods are welfare subjects. While other philosophers have argued for similar conclusions, I show that they have done so by relying on a simplistic understanding of the desire-fulfilment theory. My argument is intended to be sensitive to the complexities and nuances of contemporary…
Future Suffering and the Non-Identity Problem – Theron Pummer (University of St Andrews)
I present and explore a new version of the Person-Affecting View, according to which reasons to do an act depend wholly on what would be said for or against this act from the points of view of particular individuals. According to my view, (i) there is a morally requiring reason not to bring about lives insofar as they contain suffering (negative welfare), (ii) there is no morally requiring reason to bring about lives insofar as they contain happiness (positive welfare), but (iii) there is a permitting reason to bring about lives insofar as they…