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
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There are some possible events that we could not possibly discover in our past. We could not discover an omnicidal catastrophe, an event so destructive that it permanently wiped out life on Earth. Had such a catastrophe occurred, we wouldn’t be here to find out. This space of unobservable histories has been called the anthropic shadow. Several authors claim that the anthropic shadow leads to an ‘observation selection bias’, analogous to survivorship bias, when we use the historical record to estimate catastrophic risks. …
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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…
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Even our most mundane decisions have the potential to significantly impact the long-term future, but we are often clueless about what this impact may be. In this paper, we aim to characterize and solve two problems raised by recent discussions of cluelessness, which we term the Problems of Decision Paralysis and the Problem of Decision-Making Demandingness. After reviewing and rejecting existing solutions to both problems, we argue that the way forward is to be found in the distinction between procedural and substantive rationality…