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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Various philosophers accept moral views that are impartial, additive, and risk-neutral with respect to betterness. But, if that risk neutrality is spelt out according to expected value theory alone, such views face a dire reductio ad absurdum. If the expected sum of value in humanity’s future is undefined—if, e.g., the probability distribution over possible values of the future resembles the Pasadena game, or a Cauchy distribution—then those views say that no real-world option is ever better than any other. And, as I argue…
The freedom of future people – Andreas T Schmidt (University of Groningen)
What happens to liberal political philosophy, if we consider not only the freedom of present but also future people? In this article, I explore the case for long-term liberalism: freedom should be a central goal, and we should often be particularly concerned with effects on long-term future distributions of freedom. I provide three arguments. First, liberals should be long-term liberals: liberal arguments to value freedom give us reason to be (particularly) concerned with future freedom…
A non-identity dilemma for person-affecting views – Elliott Thornley (Global Priorities Institute, University of Oxford)
Person-affecting views in population ethics state that (in cases where all else is equal) we’re permitted but not required to create people who would enjoy good lives. In this paper, I present an argument against every possible variety of person- affecting view. The argument takes the form of a dilemma. Narrow person-affecting views must embrace at least one of three implausible verdicts in a case that I call ‘Expanded Non- Identity.’ Wide person-affecting views run into trouble in a case that I call ‘Two-Shot Non-Identity.’ …