¹ Examples include Rawls, John, A Theory of Justice (Oxford: Oxford University Press, 1999), pp. 23–26Google Scholar; Nozick, Robert, Anarchy, State, and Utopia (New York: Basic Books, 1974), pp. 32–33Google Scholar; Taurek, John M., Should the Numbers Count?, Philosophy & Public Affairs 6 (1977), pp. 293–316Google Scholar; Nagel, Thomas, Mortal Questions (Cambridge: Cambridge University Press, 1979), ch. 8Google Scholar; Scanlon, T. M., What We Owe to Each Other (Cambridge, MA: Belknap Press, 1998), pp. 238–41Google Scholar; and Kamm, F. M., Intricate Ethics (Oxford: Oxford University Press, 2007), pp. 31–40CrossRefGoogle Scholar. Opposition to full aggregation and non-consequentialism nonetheless are distinct positions. For example, some non-consequentialists only depart from consequentialism by accepting either deontological constraints or agent-centered prerogatives or both. These forms of non-consequentialism, however, are only partial departures that tame a basically consequentialist outlook of morality with additional considerations. They are half-hearted forms of non-consequentialism; see Sinclair, Thomas, Are We Conditionally Obligated to be Effective Altruists?, Philosophy & Public Affairs 46 (2018), pp. 36–59 (pp. 43–49)Google Scholar. The opposition to full aggregation which is subject of this article is instead a hallmark of a more thorough form of non-consequentialism.

² Kamm, F. M., Morality, Mortality, vol. 1 (New York: Oxford University Press, 1993), pp. 156–61Google Scholar, and Intricate Ethics, pp. 31–77; Scanlon, What We Owe to Each Other, pp. 238–41; Lefkowitz, David, On the Concept of a Morally Relevant Harm, Utilitas 20 (2008), pp. 409–23CrossRefGoogle Scholar; and Voorhoeve, Alex, How Should We Aggregate Competing Claims?, Ethics 125 (2014), pp. 64–87Google Scholar. In this article, I understand limited aggregation as a theory about what we ought to do and set aside a related view that interprets limited aggregation as part of our theory of the good. For the latter, see Temkin, Larry, Rethinking the Good (Oxford: Oxford University Press, 2012), ch. 3Google Scholar; and Dorsey, Dale, Headaches, Lives and Value, Utilitas 21 (2009), pp. 36–58CrossRefGoogle Scholar.

³ Tomlin, Patrick, On Limited Aggregation, Philosophy & Public Affairs 45 (2017), pp. 232–60CrossRefGoogle Scholar. Tomlin's criticism has been extended by Horton, Joe, Always Aggregate, Philosophy & Public Affairs 46 (2018), pp. 160–74CrossRefGoogle Scholar. Like Tomlin and Horton, I will set aside well-acknowledged objections that limited aggregation violates axioms of rational choice, namely transitivity and the independence of irrelevant alternatives. See Derek Parfit, Justifiability to Person, Each, Ratio 16 (2003), pp. 368–90Google Scholar (pp. 384–85); and Halstead, John, The Numbers Always Count, Ethics 126 (2016), pp. 789–802 (pp. 797–99)CrossRefGoogle Scholar. For responses to these criticisms see Kamm, Intricate Ethics, pp. 297–98, 484–87; Voorhoeve, How Should We Aggregate Competing Claims?, pp. 76–79; Voorhoeve, Alex, Why One Should Count Only Claims with which One Can Sympathize, Public Health Ethics 10 (2017), pp. 148–56 (pp. 152–53)Google Scholar; and Tomlin, On Limited Aggregation, p. 236, fn. 11.

⁴ See also Otsuka, Michael, Saving Lives, Moral Theory, and the Claims of Individuals, Philosophy & Public Affairs 34 (2006), pp. 109–35 (pp. 127–28)CrossRefGoogle Scholar.

⁵ See Lazar, Seth and Lee-Stronach, Chad, Axiological Absolutism and Risk, Noûs 53 (2019), pp. 97–113CrossRefGoogle Scholar. For objections similar to the one I raise see Otsuka, Saving Lives, Moral Theory, and the Claims of Individuals, p. 127 fn. 31 and Voorhoeve, Alex, Balancing Small Against Large Burdens, Behavioural Public Policy 2 (2018), pp. 125–142 (pp. 132–34)CrossRefGoogle Scholar.

⁶ See Kamm, Morality, Mortality, vol. 1, chs. 8–10 and Lefkowitz, On the Concept of a Morally Relevant Harm.

⁷ Throughout the article, I use the term ‘group’ liberally in a manner akin to the use of ‘set’ and sometimes refer to single individuals as a group.

⁸ Nagel, Mortal Questions, ch. 8, and Equality and Partiality (Oxford: Oxford University Press, 1991), chs. 2–8. Unlike me, Nagel sometimes speaks of impersonal concern as interchangeable with impartial concern. Impersonality might be one way to show impartiality but not the only one. Respect for the separateness of persons dictates that we should not equate impartiality with impersonality. For the contrast see Rawls, A Theory of Justice, pp. 165–68.

⁹ Nagel, Mortal Questions, pp. 126–27.

¹⁰ Nagel, Equality and Partiality, pp. 33–40.

¹¹ I borrow this argument from Voorhoeve, How Should We Aggregate Competing Claims?.

¹² Victor Tadros has provided a critique of this test for determining when claims are relevant which some philosophers writing on aggregation have found to be convincing. I, myself, remain unconvinced by Tadros's challenge, but addressing this disagreement would take me too far afield from my aim in this article. I hope to engage with Tadros's challenge on another occasion. See Tadros, Victor, Localized Restricted Aggregation, Oxford Studies in Political Philosophy, vol. 5, ed. Sobel, David, Vallentyne, Peter, and Wall, Steven (Oxford: Oxford University Press, 2019), pp. 171–204 (pp. 176–78)Google Scholar. Tadros's objection is an important reason for the development of Alec Walen's alternative view on aggregation that he dubs ‘weak aggregation’ in his Risks and Weak Aggregation: Why Different Models of Risk Suit Different Types of Cases, Ethics (forthcoming).

¹³ Voorhoeve, How Should We Aggregate Competing Claims?.

¹⁴ Tomlin, On Limited Aggregation.

¹⁵ In the first version of her argument for a balancing view Frances Kamm did speak about canceling (Kamm, Frances Myrna, Equal Treatment and Equal Chances, Philosophy & Public Affairs 14 (1985), pp. 177–94Google Scholar). Later on, Kamm admits that the canceling metaphor is misleading (Morality, Mortality, vol. 1, pp. 116–17). Kumar, Rahul used a neutralizing metaphor in later work (Contractualism on Saving the Many, Analysis 61 (2001), pp. 165–70)CrossRefGoogle Scholar. Kumar's argument was criticized on similar grounds to the ones presented here by Otsuka (Saving Lives, Moral Theory, and the Claims of Individuals, pp. 118–19).

¹⁶ The idea of tie-breaking brings out how balancing differs subtly from ordinary aggregation. We can see this with the help of the following analogy. There are two ways in mathematics to determine whether one set is larger than the other. One way counts the members of the set and then compares the number of elements in the set. Here the cardinal number, or sum-total, matters. Another way of comparing the size of sets does not require any numeracy skills or even knowledge of numbers. We can see whether there is a bijection, a one-to-one correspondence mapping between all elements of the two sets. In this method we only need to map individual members against one another. Balancing is like this second approach. In this sense, balancing employs a similar form of reasoning as the anonymous Pareto principle. B&C is anonymously Pareto superior to A because while B's claim can be matched by A's claim, C's claim cannot be matched. For an argument that Paretian reasoning departs from aggregative reasoning see Hirose, Iwao, Saving the Greater Number Without Combining Claims, Analysis 61 (2001), pp. 341–43CrossRefGoogle Scholar.

¹⁷ Both Kamm and Scanlon rest their argument for views similar to Balance Relevant Claims on this moral difference argument. See Kamm, Morality, Morality, vol. 1, pp. 101, 114–19, Intricate Ethics, p. 33; and Scanlon, What We Owe to Each Other, pp. 231–35. The objection that one can make a moral difference in other ways is due to Michael Otsuka (Saving Lives, Moral Theory, and the Claims of Individuals, pp. 114–18). David Wasserman and Alan Strudler helpfully distinguish between what they call the marginal difference argument and the balancing argument. Kamm and Scanlon think that the marginal difference argument grounds the balancing argument. My point here is that we can retain balancing by giving it fresh foundations. Wasserman, David and Strudler, Alan, Can a Nonconsequentialist Count Lives?, Philosophy & Public Affairs 31 (2003), pp. 71–94 (pp. 82–89)CrossRefGoogle Scholar.

¹⁸ Might A insist on a weighted lottery that gives her a one-third chance to be saved? I think not, since I believe a weighted lottery involves a failed attempt to reconcile two different approaches, which ends up abandoning a commitment to equal claims shared by these approaches. One way to reflect the equal claim of all three is to find a procedure for the distribution of the good that reflects this equality. This is what balancing does. Another way to reflect the equal claim of all three is to give everyone an equal chance of receiving the good. But a weighted lottery does not do this since both B and C will receive a two-thirds chance of being saved. Insofar as we are moved by this model of fairness, we should be holding out for the equal chance of a fair coin toss as Taurek (Should the Numbers Count?) advocates. Of course, this model of fairness is disputed by limited aggregation.

¹⁹ For this see Kamm, Intricate Ethics, pp. 297–98, 484–87; Lefkowitz, On the Concept of a Morally Relevant Harm, pp. 421–23; and Voorhoeve, Why One Should Count Only Claims with which One Can Sympathize, pp. 152–53.

²⁰ Balancing, as I understand it here, is not a symmetric relation. For example, if A's life is at stake and B and C have a claim against a severe impairment, then it is plausible that we should save A. In this case A would have balanced B and C, but B and C would not have balanced A. However, when two groups that have equal claims (e.g. A versus B suffering from equal conditions) oppose each other, then both groups balance each other. Thus, balancing is neither symmetric nor asymmetric.

²¹ Kamm, Morality, Mortality, vol. 1, pp. 144–64.

²² Tomlin, On Limited Aggregation, pp. 240–44.

²³ Tomlin, On Limited Aggregation, pp. 244–47.

²⁴ van Gils, Aart and Tomlin, Patrick, Relevance Rides Again? Aggregation and Local Relevance, Oxford Studies in Political Philosophy, vol. 6, ed. Sobel, David, Vallentyne, Peter, and Wall, Steven (Oxford: Oxford University Press, 2020), pp. 221–55Google Scholar. Already in On Limited Aggregation Tomlin tentatively suggests a view of local relevance (pp. 259–60). He credits Victor Tadros and Garrett Cullity for the idea. For Tadros's version see his Localized Restricted Aggregation.

²⁵ Kamm, Morality, Mortality, vol. 1, pp. 101–2, 146–47, Intricate Ethics, p. 34.

²⁶ Van Gils and Tomlin, Relevance Rides Again?, pp. 242–44. Kamm's own treatment of irrelevant utilities is susceptible to this related problem. See Kamm, Intricate Ethics, pp. 63–64.

²⁷ See e.g. Brown, Campbell, Is Close Enough Good Enough?, Economics & Philosophy 36 (2020), pp. 29–59 (pp. 41–42)CrossRefGoogle Scholar; van Gils and Tomlin, Relevance Rides Again?, pp. 231–42; and Korbinian Rüger, Aggregation with Constraints, Utilitas (forthcoming).

²⁸ Horton, Always Aggregate, pp. 168–71. I changed the precise example so that it fits the stipulations about relevance that I have used throughout the article.

²⁹ Horton, Always Aggregate, pp. 171–73.

³⁰ See Horton, Always Aggregate, p. 173.

³¹ For an example of such an agglomeration argument (against ex-post contractualism) see my Contractualism, Complaints, and Risk, Journal of Ethics and Social Philosophy (forthcoming).

³² In his article Horton claims that his argument shows why intransitivity is not as innocuous as proponents of limited aggregation have claimed (Always Aggregate, pp. 170–71). What my response here shows is that Horton's agglomeration problem is not any more troubling to limited aggregationists than previous challenges were. My reply here invokes the importance of moral relations and relational properties, the very same considerations that are invoked to argue why transitivity and the independence of irrelevant alternatives fail.

³³ I presented a version of this article at the London Workshop in Moral and Political Philosophy at University College London and the LSE Choice Group. For their comments, criticisms, and suggestions I thank the audiences as well as Nicolas Côté, Joe Horton, Todd Karhu, Michael Otsuka, Jonathan Parry, Thulasi K. Raj, Korbinian Rüger, Alex Voorhoeve, and multiple anonymous reviewers.