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
Population ethical intuitions – Lucius Caviola (Harvard University) et al.
Is humanity’s existence worthwhile? If so, where should the human species be headed in the future? In part, the answers to these questions require us to morally evaluate the (potential) human population in terms of its size and aggregate welfare. This assessment lies at the heart of population ethics. Our investigation across nine experiments (N = 5776) aimed to answer three questions about how people aggregate welfare across individuals: (1) Do they weigh happiness and suffering symmetrically…
In defence of fanaticism – Hayden Wilkinson (Australian National University)
Consider a decision between: 1) a certainty of a moderately good outcome, such as one additional life saved; 2) a lottery which probably gives a worse outcome, but has a tiny probability of a far better outcome (perhaps trillions of blissful lives created). Which is morally better? Expected value theory (with a plausible axiology) judges (2) as better, no matter how tiny its probability of success. But this seems fanatical. So we may be tempted to abandon expected value theory…
A paradox for tiny probabilities and enormous values – Nick Beckstead (Open Philanthropy Project) and Teruji Thomas (Global Priorities Institute, Oxford University)
We show that every theory of the value of uncertain prospects must have one of three unpalatable properties. Reckless theories recommend risking arbitrarily great gains at arbitrarily long odds for the sake of enormous potential; timid theories recommend passing up arbitrarily great gains to prevent a tiny increase in risk; nontransitive theories deny the principle that, if A is better than B and B is better than C, then A must be better than C.