¹ Some recognize AP as the ‘Suppes-Sen grading principle’. See: A. Sen, Collective Choice and Social Welfare (San Francisco, 1970); Suppes, Patrick, ‘Some Formal Model of Grading Principles’, Synthese 6 (1966), pp. 284–306CrossRefGoogle Scholar.

² See e.g. Otsuka, Michael, ‘Saving Lives Moral Theory, and the Claims of Individuals’, Philosophy & Public Affairs 34 (2) (2006), pp. 109–35CrossRefGoogle Scholar, at 122; McCarthy, David, ‘Distributive Equality’, Mind 124 (2015), pp. 1045–1109CrossRefGoogle Scholar, at 1059.

³ This feature distinguishes AP from ex-ante Pareto, with which it is sometimes conflated. What is AP superior is also ex-ante Pareto superior, but not vice versa.

⁴ Jonathan Dancy, for instance, believes that an equally valid version of the Pareto principle is one that ‘holds that one alternative is better than another if in it some better slots are occupied and no worse ones’. See Dancy, Jonathan, ‘Essentially Comparative Concepts’, Journal of Ethics & Social Philosophy 1 (2) (2005), pp. 1–15CrossRefGoogle Scholar, at 9. For a discussion of this idea at work, see Eyal, Nir and Voorhoeve, Alex, ‘Inequalities in HIV Care: Chances Versus Outcomes’, The American Journal of Bioethics 11 (12) (2001), pp. 42–4CrossRefGoogle Scholar.

⁵ Though not everyone, most people seem to accept that a change that is good for some and bad for no one, is – probably, or very often, or often enough – a change for the better (some even find it ‘hard to see how anyone could resist such a principle’. See Griffin, J., Well-Being: Its Meaning, Measurement, and Moral Importance (Oxford, 1986), p. 147Google Scholar. There might be exceptions, of course. There might be cases in which the status quo is so unjust that a Pareto improvement would seem morally neutral, or even strike us as a change for the worse. But as a general rule, (strict) Pareto improvements are taken to be non-controversially desirable: improvements that carry no moral cost; a case of all reasons counting in favour of the change in question and none against.

⁶ Hirose, Iwao, ‘Saving the Greater Number Without Combining Claims’, Analysis 61 (2001), pp. 341–2CrossRefGoogle Scholar; F. M. Kamm, Morality, Morality, vol. 1 (New York, 1993), p. 85.

⁷ J. Broome, Weighing Lives (New York, 2004), p. 136.

⁸ See e.g. Hirose, ‘Saving the Greater Number Without Combining Claims’, p. 341.

⁹ To say that it is permissible to do x rather than y is not to imply that there must be some aspect in which x outranks y (see also: L. Temkin, Rethinking the Good (New York, 2012), p. 196).

¹⁰ Some have interpreted the somewhat elusive notion of parity as a relation of equal permissibility: two alternatives, x and y, are on a par iff it is (i) permissible to prefer x to y and (ii) permissible to prefer y to x (Wlodek Rabinowicz, ‘Broome and the Intuition of Neutrality’, Philosophical Issues 19 (2009), pp. 389–411, at 402). If equally permissible actions are on a par, their relation may not be transitive (Ruth Chang, ‘The Possibility of Parity’, Ethics 112 (2002), pp. 659–88).

¹¹ Many people feel uncomfortable accepting that trivial differences, such as the difference between twenty years and twenty-one, should tip the balance in cases such as this. Some explain that such a minor difference is an ‘irrelevant utility’ (see, e.g. Kamm, Morality, Morality, p. 146). Others think that a trivial improvement is not enough to outweigh the badness of treating the other patient unfairly (see I. Hirose, Moral Aggregation (New York, 2014), ch. 8). The merits of these lines of argument should better be debated elsewhere. I am inclined to agree that given certain assumptions, twenty-one years might not be morally preferable to twenty. But my own reason for thinking so is different, as I explain below.

¹² I am grateful to Ittay Nissan-Rozen for pressing me on this point.

¹³ For an excellent discussion of a similar point in a slightly different context, see Lübbe, Weyma, ‘Taurek's No Worse Claim’, Philosophy and Public Affairs 36 (2008), pp. 69–85CrossRefGoogle Scholar.

¹⁴ The idea that people might not have a pre-institutional claim to what they have is famously associated with Rawls (J. Rawls, A Theory of Justice, (Cambridge, MA, 1971), pp. 103–4), though AP cannot be defended on strictly Rawlsian grounds (for more on this see n. 16 below).

¹⁵ This argument is due to Voorhoeve, Alex (‘Should Losses Count? A Critique of the Complaint Model’, LSE Choice Group Working Papers 2 (2006)Google Scholar, sect. 4). I am unsure to what extent he himself is still committed to it, but I find it very well worth considering.

¹⁶ Perhaps this is not as obvious. If our choice is guided by a Rawlsian maximin principle, we might not prefer the AP superior outcome. The distribution (3, 1) is AP superior to (1, 2), but it may not be better according to maximin, it might even be worse. Since the increased inequality involved in shifting from (1, 2) to (3, 1) does not work to the advantage of the least well-off, the change might be unjust (Rawls, A Theory of Justice, p. 151). By comparison, if what we are after is maximizing expected utility, any AP superior distribution would be considered better, but, of course, not vice versa. For instance, we would prefer (3, 0) to (1, 1). Hence, even in the absence of pre-institutional claims, we might either not prefer a Pareto superior distribution – for example, if it increases inequalities in a way that does not benefit the worst-off; or we might prefer a Pareto superior option only incidentally, as it is one among a number of ways to maximize our expected utility.

¹⁷ What if one of the things that people are owed is equal consideration? Does that undermine the case against AP? The answer is ‘no’. As I hope to have shown in section I, the fact that people's good counts equally does not entail that whatever is better than benefiting one of them is also better than benefiting the other. Moreover, it is important to stress, in this context, that people have a right to due, as well as equal, consideration. Their interest ought to be appropriately addressed, in absolute not just comparative terms. I thank the anonymous reviewer for this point.

¹⁸ Waldron, Jeremy, ‘Rights in Conflict’, Ethics 99 (1989), pp. 503–19CrossRefGoogle Scholar, at 506.

¹⁹ Feinberg, Joel, ‘Voluntary Euthanasia and the Inalienable Right to Life’, Philosophy and Public Affairs 7.2 (1978), pp. 93–123Google Scholar.

²⁰ Waldron, ‘Rights in Conflict’, p. 512.

²¹ I am grateful to the anonymous reviewer for suggesting this point to me.

²² Caspar Hare, The Limits of Kindness (Oxford, 2013).

²³ Hare's argument does not commit him to an intransitivity of identities in the strictest sense, because on his account each world is populated by a counterpart of the person in the world preceding it, rather than by the same person. He considers numerical identity to be ‘paradigmatically transitive’ (Hare, The Limits of Kindness, p. 129).

²⁴ Temkin, Rethinking the Good, ch. 6.

²⁵ A similar point has been made with regard to the compatibility of the Pareto principle and the person-affecting view, or the view according to which a state of affairs can only be good or bad if it is good or bad for someone. See Hirose, Iwao, ‘Review of Nils Holtug's Persons, Interests, and Justice’, Economics and Philosophy 28 (2012), pp. 98–102CrossRefGoogle Scholar, at 101; Tungodden, Bertil, ‘The Value of Equality’, Economics and Philosophy 19 (2003), pp. 1–44CrossRefGoogle Scholar, at 15.

²⁶ For a discussion of this point see Temkin, Larry, ‘Equality, Priority, or What?’, Economics and Philosophy 19 (2003), pp. 61–87CrossRefGoogle Scholar.

²⁷ I am sincerely grateful to Daniel Attas, Shlomi Segall, David Enoch, Ittay Nissan-Rozen, Ofer Malcai and the anonymous reviewers for their very helpful comments.