¹ See, for example, Brink, David, ‘The Separateness of Persons, Distributive Norms, and Moral Theory’, Value, Welfare, and Morality, ed. Frey, R. G. and Morris, Christopher W. (Cambridge, 1993), pp. 252–89CrossRefGoogle Scholar, at 270; Scanlon, Thomas M., What We Owe To Each Other (Cambridge, MA, 1998), pp. 238–41Google Scholar; Otsuka, Michael, ‘Saving Lives, Moral Theory, and the Claims of Individuals’, Philosophy and Public Affairs 34 (2006), pp. 109–35CrossRefGoogle Scholar; Kamm, Frances M., Intricate Ethics (New York, 2007), pp. 287–98CrossRefGoogle Scholar, at 484–6; Dorsey, Dale, ‘Headaches, Lives and Value’, Utilitas 21 (2009), pp. 36–58CrossRefGoogle Scholar; Temkin, Larry, Rethinking the Good (New York, 2012)Google Scholar, chs. 2–3. Empirical research on the matter is limited, but Alex Voorhoeve reports a survey in which a substantial majority of subjects shared these intuitions in cases similar to Injuries and Tetanus in his ‘Why One Should Count Only Claims with which One Can Sympathize’, Public Health Ethics 10 (2017), pp. 148–58, at 149–50, and reviews some further, albeit imperfect, empirical evidence in his ‘Balancing Small Against Large Burdens’, Behavioural Public Policy (forthcoming).

² Voorhoeve, Alex, ‘How Should We Aggregate Competing Claims?’, Ethics 125 (2014), pp. 64–87CrossRefGoogle Scholar.

³ Voorhoeve's examples and his statement of what defines the strength of a claim slightly differ from mine. The persons in his examples are already burdened by certain diseases that lower their well-being and the agent can increase their well-being by helping them. Accordingly, Voorhoeve defines a person's claim as being stronger ‘a) the more her well-being would be increased by being aided; and b) the lower the level of well-being from which this increase would take place’ (Voorhoeve, ‘How Should We Aggregate Competing Claims?’, p. 66). I adjusted the definition to fit my speaking of harms instead of levels of well-being and to fit the situation in my examples in which the agent can prevent harms instead of reacting to their having already occurred.

⁴ Similar strategies of combining aggregative and non-aggregative elements have been discussed before. Parfit, Derek considers one in his ‘Justifiability to Each Person’, Ratio 16 (2003), pp. 368–90CrossRefGoogle Scholar, at 378–85, but ultimately rejects it because of a problem I will discuss in section III. Kamm endorses one in her Intricate Ethics, pp. 297–8, at 484–6. Voorhoeve, however, gives what I think is the most compelling rationale and the best-worked-out overall account of such an approach. For a recent critique of Voorhoeve's theory, see Halstead, John, ‘The Numbers Always Count’, Ethics 126 (2016), pp. 789–802CrossRefGoogle Scholar.

⁵ Voorhoeve, ‘How Should We Aggregate Competing Claims?’, pp. 70–2.

⁶ This unanimity-based consideration is first introduced as one among many reasons that speak in favour of ARC (see Voorhoeve, ‘How Should We Aggregate Competing Claims?’, pp. 73–5). In later sections, however, it becomes clear that this is the consideration ultimately supporting it (see Voorhoeve, ‘How Should We Aggregate Competing Claims?’, p. 77).

⁷ Voorhoeve, ‘How Should We Aggregate Competing Claims?’, p. 75.

⁸ Broome, John, Weighing Goods (Oxford, 1991), ch. 5Google Scholar.

⁹ Voorhoeve, Alex, ‘Vaulting Intuition: Temkin's Critique of Transitivity’, Economics and Philosophy 29 (2013), pp. 409–23CrossRefGoogle Scholar, at 414–15.

¹⁰ Parfit, ‘Justifiability to Each Person’, p. 384.

¹¹ The argument was first sketched in Ramsey, Frank P., ‘Truth and Probability’, The Foundations of Mathematics and other Logical Essays, ed. Braithwaite, R. B. (London, 1931), pp. 156–98Google Scholar, at 182. Davidson, Donald, McKinsey, J. C. C. and Patrick Suppes developed it further in their ‘Outlines of a Formal Theory of Value, I’, Philosophy of Science 22 (1955), pp. 140–60CrossRefGoogle Scholar, at 145–6.

¹² The foresight-based objection was first raised in Schick, Frederic, ‘Dutch Bookies and Money Pumps’, The Journal of Philosophy 83 (1986), pp. 112–19CrossRefGoogle Scholar. The view that an agent having cyclic preferences can be pumped even if she is foresighted is defended in Rabinowicz, Wlodek, ‘Money Pump with Foresight’, Imperceptible Harms and Benefits, ed. Almeida, Michael J. (Dordrecht, 2000), pp. 123–54CrossRefGoogle Scholar.

¹³ Voorhoeve does not say anything about how demanding his theory is. But if we assume that morality requires agents to do the right thing even if this comes at some (non-extreme) cost to themselves – an assumption that seems easy to justify – an even stronger point can be made. ARC would then in certain situations require agents to bear unnecessary costs.

¹⁴ The Broome/Voorhoeve-argument even yields that there is at least one best option for any given feasible set of alternatives – the condition ‘feasible’ ruling out sets that, for example, contain both (relevant-x) and (irrelevant-x).

¹⁵ Voorhoeve, ‘How Should We Aggregate Competing Claims?’, pp. 77–8.

¹⁶ I thank Kirsten Meyer and Gabriel Wollner for their very helpful comments on earlier versions of this article. I also benefited a lot from the comments of two anonymous reviewers and from extensive discussions with Jonas Harney, Roland Hesse, Lukas Tank, Stefanie Thiele, and with the participants of the Normative and Applied Ethics Colloquium at Humboldt-Universität zu Berlin.