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
Respect for others’ risk attitudes and the long-run future – Andreas Mogensen (Global Priorities Institute, University of Oxford)
When our choice affects some other person and the outcome is unknown, it has been argued that we should defer to their risk attitude, if known, or else default to use of a risk avoidant risk function. This, in turn, has been claimed to require the use of a risk avoidant risk function when making decisions that primarily affect future people, and to decrease the desirability of efforts to prevent human extinction, owing to the significant risks associated with continued human survival. …
Ethical Consumerism – Philip Trammell (Global Priorities Institute and Department of Economics, University of Oxford)
I study a static production economy in which consumers have not only preferences over their own consumption but also external, or “ethical”, preferences over the supply of each good. Though existing work on the implications of external preferences assumes price-taking, I show that ethical consumers generically prefer not to act even approximately as price-takers. I therefore introduce a near-Nash equilibrium concept that generalizes the near-Nash equilibria found in literature on strategic foundations of general equilibrium…
In Defence of Moderation – Jacob Barrett (Vanderbilt University)
A decision theory is fanatical if it says that, for any sure thing of getting some finite amount of value, it would always be better to almost certainly get nothing while having some tiny probability (no matter how small) of getting sufficiently more finite value. Fanaticism is extremely counterintuitive; common sense requires a more moderate view. However, a recent slew of arguments purport to vindicate it, claiming that moderate alternatives to fanaticism are sometimes similarly counterintuitive, face a powerful continuum argument…