Suffering is not additive in this way. The discomfort of each of a large number of individuals experiencing a minor headache does not add up to anyone’s experiencing a migraine.
John Taurek, ‘Should the Numbers Count?, Philosophy & Public Affairs, vol. 6, no. 4 (Summer, 1977), p. 308
[D]o not be oppressed by the frightful sum of human suffering; there is no sum; two lean women are not twice as lean as one, and two fat women are not twice as fat as one. Poverty and pain are not cumulative; you must not let your spirit be crushed by the fancy that it is.
George Bernard Shaw, The Intelligent Woman’s Guide to Socialism and Capitalism, London, 1828, sect. 84
[T]he Utilitarian cannot confine himself to a single mind; he has to consider what he calls “the total happiness of a collection of minds”. Now this is an extremely odd notion. It is plain that a collection cannot literally be happy or unhappy. The oddity is clearly illustrated if we […] use the analogy of greyness. Suppose that a number of different areas, which are not adjoined to each other, all go through successive phases of greyness. What could we possibly mean by “the total whiteness of this collection of areas”?
C. D. Broad, Five Types of Ethical Theory, London, 1930, pp. 248-249
The Pareto principle is, I think, untrue. It is an ill-begotten hybrid. It tries to link individual preferences with general good. But one should either link individual preferences with what should come about, as the democratic principle does, or individual good with general good, as the principle of general good does. The hybrid is no viable.
John Broome, Weighing Goods, Oxford, 1991, p. 159
Another argument commonly used against aggregationism is also hard to understand (Rawls, A Theory of Justice, p. 27). This is the objection that utilitarianism “does not take seriously the distinction between persons”. To explain this objection: it is said that, if we claim that there is a duty to promote maximal preference satisfaction regardless of its distribution, we are treating a great interest of one as of less weight than the lesser interests of a great many, provided that the latter add up in aggregate to more than the former. For example, if I can save five patients moderate pain at the cost of not saving one patient severe pain, I should do so if the interests of the five in the relief of their pain is greater in aggregate than the interest of the one in the relief of his (or hers).
But to think in the way that utilitarians have to think about this kind of example is not to ignore the difference between persons. Why should anybody want to say this? Utilitarians are perfectly well aware that A, B and C in my example are different persons people. They are not blind. All they are doing is trying to do justice between the interests of these people. It is hard to see how else one could do this except by showing them all equal respect, and that, as we have seen, leads straight to aggregationism.
R. M. Hare, in Helga Kuhse and Peter Singer (eds.), A Companion to Bioethics, Oxford, 1998, p. 83