¹ There is another type of aggregation, i.e. intrapersonal aggregation. It concerns how the temporal parts of a person's life are combined within his life. I do not consider this type of aggregation here.

² Taurek, J., ‘Should the Numbers Count?’, Philosophy and Public Affairs 6 (1977), pp. 293–316Google ScholarPubMed.

³ For the survey of this literature, see Hirose, I., ‘Aggregation and Non-Utilitarian Moral Theories’, Journal of Moral Philosophy 4 (2007), pp. 273–84CrossRefGoogle Scholar.

⁴ See Nagel, T., ‘Equality’, in his Mortal Questions (New York, 1979), pp. 106–27, at 125Google Scholar; Nozick, R., Anarchy, State, and Utopia (Oxford, 1974), p. 33Google Scholar; and Scanlon, T. M., ‘Contractualism and Utilitarianism’, Utilitarianism and Beyond, ed. Sen, A. K. and Williams, B. A. O. (Cambridge, 1982), pp. 103–28, at 123CrossRefGoogle Scholar.

⁵ A relation F on a set X is reflexive just in case, for all x in X, x is at least as F as x. It is transitive just in case, for all x, y and z in X, if x is at least as F as y and if y is at least as F as z, then x is at least as F as z. It is complete just in case, for all x and y in X, either that x is at least as F as y or that y is at least as F as x. I assume that the set of alternatives is countable.

⁶ There is general scepticism about interpersonal comparability in both economics and philosophy. In economics, it is claimed that there is no scientific or objective basis for interpersonal comparisons of utility as utility represents a person's mental state. In ethics, some people are sceptical about interpersonal comparison because of incommensurability of values. However, I believe that those who advocate the notion of the separateness of persons are not concerned with interpersonal incomparability or incommensurability.

⁷ It is not my contention that this is the most plausible notion of impartiality. There might be other ways to define the notion of impartiality. All I claim is that aggregation entails the condition of impartiality I stated above. Needless to say, if there is a morally relevant difference between the two persons (e.g. one person is evil and the other is virtuous), we must consider additional elements such as desert, responsibility, and so on. In such a case, the notion of impartiality must be revised. However, the notion of impartiality holds that two alternatives are morally indifferent if they differ only with regard to the identities of people. Throughout this article, I assume that there are no morally relevant differences amongst people.

⁸ Notice that this version of Pareto is different from the Pareto condition in economics. In economics, the Pareto condition is defined in terms of preference: if x is strictly preferred to y by some individuals, and if y is not strictly preferred to x by any individual, x is collectively preferred to y. Notice also that the Pareto condition is logically independent of the person-affecting view in ethics. The person-affecting view holds that x is better than y only if x is better for some person than y. The Pareto condition holds that x is better than y if x is better for some person and no worse for any person than y.

⁹ For the general discussion of continuity, see Arrhenius, G., ‘Superiority in Value’, Philosophical Studies 123 (2005), pp. 97–114CrossRefGoogle Scholar; Arrhenius, G. and Rabinowicz, W., ‘Value and Unacceptable Risk’, Economics and Philosophy 21 (2005), pp. 177–97CrossRefGoogle Scholar; Jensen, K. K., ‘Unacceptable Risks and the Continuity Axiom’, manuscript (University of Copenhagen, 2010)Google Scholar. Some philosophers reject continuity in some cases. The most famous one would be John Stuart Mill. In Utilitarianism, he distinguishes higher and lower pleasures, and contends that any amount of higher pleasure is better than any amount of lower pleasure. However, Mill does not reject continuity within higher pleasure or lower pleasure. He only rejects continuity between higher and lower pleasure. It would be accurate to say that Mill constrains continuity. For more extensive and precise discussion concerning Mill's idea of discontinuity in values, see Arrhenius, G. and Rabinowicz, W., ‘Millian Superiorities’, Utilitas 17 (2005), pp. 127–46CrossRefGoogle Scholar.

¹⁰ Note that the rejection of continuity does not entail Leximin. See Carlson, E., ‘Aggregating Harms: Should We Kill to Avoid Headaches?’, Theoria 66 (2000), pp. 246–55CrossRefGoogle Scholar.

¹¹ Rawls appeals to psychological stability, self-respect and the strains of commitment when he criticizes average utilitarianism. See Rawls, J., A Theory of Justice (Cambridge, Mass., 1971), pp. 175–92Google Scholar. See also Scheffler, S., ‘Rawls on Utilitarianism’, The Cambridge Companion to Rawls, ed. Freeman, S. (Cambridge, 2003), pp. 426–59Google Scholar.

¹² Rawls, Justice, pp. 26–7. For the general discussion on the separateness of persons, see Brink, D., ‘The Separateness of Persons, Distributive Norms, and Moral Theory’, Value, Welfare, and Morality, ed. Morris, C. and Frey, R. (New York, 1993), pp. 252–89CrossRefGoogle Scholar; McKerlie, D., ‘Egalitarianism and the Separateness of Persons’, Canadian Journal of Philosophy 18 (1988), pp. 205–26CrossRefGoogle Scholar; Parfit, D., Reasons and Persons (Oxford, 1984)Google Scholar; Raz, J., The Morality of Freedom (Oxford: 1986)Google Scholar; and Scheffler, ‘Rawls’.

¹³ Nagel, T., The Possibility of Altruism (Princeton, 1970), p. 138Google Scholar.

¹⁴ Nozick, Anarchy, p. 33.

¹⁵ Nozick, Anarchy, p. 228.

¹⁶ When Jens Timmermann and Weyma Lübbe reject the conjunction of impartiality and Pareto as a solution to the Rescue Case, they seem to appeal to this sense. See , J., ‘The Individualist Lottery: How People Count, but not their Numbers’, Analysis 64 (2004), pp. 106–12CrossRefGoogle Scholar; Lübbe, W., ‘Taurek's No Worse Claim’, Philosophy and Public Affairs 36 (2008), pp. 69–85CrossRefGoogle Scholar.

¹⁷ If the argument is that there is more goodness in x than y, then there is a sense in which we are indeed ignoring the separateness of persons. The mere fact of reasoning in terms of goodness and badness of states of affairs seems to fail to take the separateness of persons seriously. On the other hand, saying that x would be preferred to y from each person's point of view (assuming they did not know who they were) would not violate the separateness of persons in the same way. John Harsanyi and other proponents of contractualist average utilitarianism would be happy to agree with this. This means that contractualist average utilitarianism respects the separateness of persons, and therefore that the separateness of persons does not lead us to non-aggregative principles. See Harsanyi, J. C., ‘Cardinal Welfare, Individualistic Ethics, and Interpersonal Comparisons of Utility’, Journal of Political Economy 63 (1955), pp. 309–21CrossRefGoogle Scholar.

¹⁸ Rawls, Justice, p. 26.

¹⁹ Nagel, Altruism, p. 138 and ‘Equality’, p. 123.

²⁰ Nozick, Anarchy, p. 33.

²¹ Some egalitarian principles combine the value of people's well-being and the disvalue of inequality. For example, if the relative goodness of states of affairs in the two-person case is given by ½ (w ₁+w ₂) − ¼ |w ₁ − w ₂|, where w_i denotes the person i's well-being, this principle is both aggregative and egalitarian.

²² Nagel, ‘Equality’, p. 125.

²³ Parfit, Reasons, p. 330.

²⁴ Notice that I am not claiming that the separateness of persons is best captured by a version of utilitarianism. All I claim is that there are many different interpretations concerning the separateness of persons, and that each interpretation is perfectly consistent with the idea of the separateness of persons in one way or another.

²⁵ Rawls, Justice, p. 163.

²⁶ See Rawls, Justice, p. 189.

²⁷ For example, see Arrow, K. J., ‘Some Ordinalist-Utilitarian Notes on Rawls's Theory of Justice’, Journal of Philosophy 70 (1973), pp. 245–63Google Scholar; Hare, R. M., ‘Rawls’ Theory of Justice I’, Philosophical Quarterly 23 (1973), pp. 144–55CrossRefGoogle Scholar; and , D., ‘Nature and Soundness of the Contract and Coherence Arguments’, Reading Rawls, ed. Daniels, N. (Cambridge, 1975), pp. 141–66Google Scholar.

²⁸ This is too quick. Harsanyi made two claims. The first claim is that if individual and social preferences satisfy the axioms of expected utility theory and the social welfare function satisfies the Pareto condition, then social utility must be represented by a weighted sum (precisely, an affine transformation) of individual utilities. This is known as the Aggregation Theorem. The second claim is that if individuals were placed behind the veil of ignorance, then they would rationally believe that each of them has an equal chance of being in any of these positions, and hence that the weight of each individual's utility must be 1/n in the n-person society. This is known as the Impartial Observer Theorem. The notion of the veil of ignorance is used for the second claim. See Harsanyi, ‘Cardinal’, and , J. C., Rational Behaviour and Bargaining Equilibrium in Games and Social Situations (Cambridge, 1977)Google Scholar. See also Weymark, J. A., ‘A Reconsideration of the Harsanyi–Sen Debate on Utilitarianism’, Interpersonal Comparisons of Well-being, ed. Elster, J. and Roemer, J. E. (Cambridge, 1991), pp. 255–320CrossRefGoogle Scholar.

²⁹ Rawls, Justice, p. 14.

³⁰ See Frohlich, N., Oppenheimer, J. A. and Eavey, C. L., ‘Laboratory Results on Rawls's Distributive Justice’, British Journal of Political Science 17 (1987), pp. 1–21CrossRefGoogle Scholar; Frohlich, N. and Oppenheimer, J. A., Choosing Justice: An Experimental Approach to Ethical Theory (Berkeley, 1993)Google Scholar; and Konow, J., ‘Which Is the Fairest One of All? A Positive Analysis of Justice Theories’, Journal of Economic Literature 41 (2003), pp. 1188–1239CrossRefGoogle Scholar.

³¹ Konow, ‘Fairest’, p. 1196.

³² Scanlon, ‘Contractualism’, pp. 120–23.

³³ Scanlon, ‘Contractualism’, p. 110.

³⁴ , M., ‘Scanlon and the Claims of the Many versus the One’, Analysis 60 (2000), pp. 288–93CrossRefGoogle Scholar.

³⁵ Scanlon, T. M., ‘Replies’, Social Theory and Practice 28 (2002), pp. 337–58, at 356CrossRefGoogle Scholar.

³⁶ Parfit makes a stronger claim. He argues that Scanlon should drop the individualist restriction because it limits the scope of his contractualism. , D., ‘Justifiability to Each Person’, Ratio 16 (2003), pp. 368–90CrossRefGoogle Scholar.