Tag Archives: aggregation

Outline of a taxonomy of approaches to aggregation



Gloomy gardens then went by, one by one: gloomy houses.

Mr Power pointed.

– That is where Childs was murdered, he said. The last house.

– So it is, Mr Dedalus said. A gruesome case. Seymour Bushe got him off. Murdered his brother. Or so they said.

– The crown had no evidence, Mr Power said.

– Only circumstantial, Martin Cunningham said. That’s the maxim of the law. Better for ninetynine guilty to escape than for one innocent person to be wrongfully condemned. (Joyce 1993 [1922], 96).


What limits, if any, to the moral standing of the individual are morally permissible, and under what circumstances? This depends on what sort of approach to aggregation is in question. At its simplest, aggregation in moral reasoning is the procedure by which different entities are added together and then “weighed” against other similarly attained aggregates in order to arrive at decisions on what it is morally right to do. I’ll discuss only interpersonal aggregation, i.e. aggregation of and between different persons, or of and between things that affect different persons. I’ll overlook intrapersonal aggregation (aggregation within the same life), and non-moral uses of aggregative reasoning.


The four approaches to aggregation can be thought of as lying on the same continuum. Non-aggregation denies the moral permissibility of interpersonal aggregation, and lies at the negative extreme of the continuum. Asymmetric aggregation is at the opposite extreme: according to this view, interpersonal aggregation is morally permissible in almost any situation. Symmetric aggregation comes close to the asymmetric end of the continuum: here aggregation is broadly applicable, but with some constraints which I’ll discuss later in this section. Weak aggregation comes somewhere between symmetric aggregation and non-aggregation on the continuum.


I’ll outline each of these, illustrating the distinctions by reference to Joyce’s maxim: Better for ninety-nine guilty to escape than for one innocent person to be wrongfully condemned. Detailed discussion of the approaches and a defence of weak aggregation, must be left to another time.




It’s possible to argue that interpersonal aggregation is not morally permissible under any circumstances. This approach rules out the pursuit of any aggregate good that would restrict individual autonomy, or otherwise conflict with individual interests in any way. Such an extreme position does not have many philosophical defenders. John Taurek’s ‘Should The Numbers Count?’ remains the best-known espousal of it. If one is forced to choose between helping one person or many others, Taurek ‘cannot see how or why the mere addition of numbers should change anything’ (1977, 306). He concludes that the decision to help either the one or the many should be left to chance, by flipping a fair coin. A revamped and moderated version of Taurek’s non-aggregation has been proposed by Jens Timmermann (2004).


Applied to the Joyce example, non-aggregation would entail that it’s wrong to sacrifice one innocent person in order to convict ninety-nine guilty, and — at least in its most absolute form — it wouldn’t matter how serious the wrongdoings of the ninety-nine were. They could be ninety-nine Genghis Khans, but it would still be wrong to sacrifice one innocent person in order to bring the ninety-nine to justice, even if this were the only possible way of doing so. It also seems that from a non-aggregationist position, the leniency or severity of the sacrifice imposed on the one innocent person would have no bearing on the question of whether to use the one as a means to the end of convicting the ninety-nine: if the rule is an absolute one of “do not aggregate, no matter what”, then even wrongfully condemning the innocent person and sentencing him to a day’s imprisonment, if this would somehow help in securing the conviction of the ninety-nine guilty, would be morally wrong. On this view it thus makes no difference how serious the guilt of the ninety-nine is, nor how small is the sacrifice imposed on the one innocent person. Such an approach to aggregation such only seem plausible from an extreme libertarian standpoint, itself a wildly implausible position.


The examples just mentioned make it sufficiently clear that no serious moral theory can prohibit interpersonal aggregation altogether. But even subtler approaches than Taurek’s to the rejection of interpersonal aggregation fail to answer the simple but profound objection made by Derek Parfit in a response to Taurek: ‘Why do we save the larger number? Because we do give equal weight to saving each. Each counts for one. That is why more count for more’ (Parfit 1978, 301, his emphasis). Non-aggregationism is simply too restrictive, too rigidly libertarian, to ever be even minimally adequate in deciding what is morally right or wrong to do.



Asymmetric aggregation

At the opposite extreme lies asymmetric approach, which holds that interpersonal aggregation is morally permissible in any circumstance in which it would produce a benefit that would outweigh the aggregate harm involved. So it would be morally permissible to sacrifice (convict and punish through law) one innocent person if this were necessary for the conviction of ninety-nine others who have committed serious crimes, even if they were ninety-nine atrocious criminals. But the non-aggregationist position would also entail that an innocent person could be sacrificed if this would lead to the conviction of ninety-nine others who were guilty of lesser crimes, no matter how trivial: other things being equal, it would be morally permissible on this view to send one innocent person to prison as a means of convicting ninety-nine university students who violate copyright law by photocopying books without the written authorization of the publisher, or ninety-nine smokers who light up in a No Smoking area. Moreover, it follows from the non-aggregationist position that provided it’s necessary for the conviction of the ninety-nine, there is no limit to the severity of the legal punishment that could be inflicted on the one innocent person. He or she could be sentenced to life imprisonment, or, in legal systems that allow it, to death, if this were all that could secure the conviction of the ninety-nine, regardless of how serious or trivial their crimes were. Of course, when the level of asymmetry between the more serious and less serious considerations is very large, ninety-nine of the latter type would hardly be enough; the asymmetric aggregationist response is simply to adjust the number accordingly. Thus according to act-utilitarian Alistair Norcross (1997, 135), ‘there is some finite number of headaches, such that it is permissible to kill an innocent person to avoid them’. Norcross believes that the principle sanctioning such a choice is ‘not particularly unpalatable’, and that most people in practice accept at least some views that are close to it’ (ibid., 159).


What matters for the asymmetric aggregationist view is the relative “weight” of each opposing set of aggregated values, or sources of value. If one aggregate outweighs another, then that is the one that should be chosen, regardless of the relative significance of each individual value or source of moral value in each set. The aggregate good of convicting an even greater number, say one million unauthorized photocopiers, could on the asymmetric aggregationist view make it morally permissible to sentence one innocent person to death, if for some even stranger reason this were the only way of bringing the million to justice.


Peter Singer writes (1997, 277-8):

In a society in which the narrow pursuit of material self-interest is the norm, the shift to an ethical stance is more radical than many people realize. In comparison with the needs of people starving in Somalia, the desire to sample the wines of the leading French vineyards pales into insignificance. Judged against the sufferings of immobilized rabbits having shampoos dripped into their eyes, a better shampoo becomes an unworthy goal. The preservation of old-growth forests should override our desire to use disposable paper towels […] all these [luxuries] become disproportionate to people who can shift perspective long enough to take themselves, at least for a time, out of the spotlight.


Asymmetric aggregationists, like anybody else, could not reasonably dispute Singer’s assumption that the value of sampling fine wines is tiny alongside the value of preventing the suffering that starvation involves. As he noted many years earlier (1972, 231): ‘People can hold all sorts of eccentric positions, and perhaps from some of them it would not follow that death by starvation is in itself bad. It is difficult, perhaps impossible, to refute such positions, and so for brevity I will henceforth take this assumption as accepted’. But acceptance of the gross disparity in value here is consistent with holding that the value of sampling fine wines is not infinitely trivial; that could only mean that it had no value at all, and the principle of transitivity — if A is better than B, and B better than C, then A must be better than C also — would not apply to it.


It’s implicit in the passage just quoted than even Singer accepts that the enjoyment of fine wines does have some value. With asymmetric aggregation, this is all that’s needed: we have a situation with more than one source of value, from which it follows that the transitive relation “better than” necessarily applies. For brevity I’ll call the value of being able to live a life the quality of which is above subsistence level Life, and the value of being deprived of the fine wine Château Pétrus. Assuming for present purposes that the principle of transitivity is universally valid, it follows that although a single instance of Château Pétrus is vastly outweighed by Life, given a sufficiently large quantity of the former the opposite would be true. So if we assign Life the value of 1 and Château Pétrus the value of 0.000001, then 1,000,001 instances of Château Pétrus have an aggregate moral value that outweighs one instance of Life. To call such a conclusion repugnant, as Derek Parfit has labelled a similar conclusion (e.g. 1986, 148-64), is putting it mildly. This mechanical application of simple addition to moral reasoning is absurdly crude, but some, such as Norcross (1997), don’t see it that way. On the asymmetric aggregationist view, the only way to avoid this repugnant conclusion is to show that experiences such as drinking wine have no value at all. One can justifiably think that this can be shown without having to go as far as Roger Scruton, who seems to ascribe a moral value to wine: ‘the path to meditation, and the harbinger of peace’ (Scruton 2009, 5). The best hope of avoiding the repugnant conclusion is to argue that radically different kinds of value, such as those represented by Life and Château Pétrus, cannot be compared. But this line of argument could only succeed, it seems, in circumstances in which the “better than” relation is intransitive.[1]



Symmetric aggregation

This third approach permits interpersonal aggregation when the individual considerations being aggregated and weighed against each other are of equivalent moral importance, but involve different numbers of people. This equivalence or symmetry of the considerations being weighed against each other is what distinguishes symmetric from asymmetric aggregation. What the asymmetric and symmetric models share is that they are both maximizing approaches. The simplest example of symmetric aggregation in practice might be the familiar thought experiment of letting one person die (or even killing him) when this is the only available, or at least most likely to be successful, means of saving the lives of a greater number of others. (“Simple” is a misleading word here, of course, given the controversy over the question of what, if any, moral difference there is between killing and letting die, or more generally, between acts and omissions. But I’ll set that aside here). Symmetric aggregationism holds that it could be morally permissible to inflict some burden on one or more persons if only this could secure some benefit for a greater number of others. There would have to be some minimum standard, some lower limit on what counts as a sufficiently morally significant reason for imposing the burden in question on the smaller number of persons. It is in this respect that the symmetric aggregationist answer to what it is morally right, or at least permissible, to do in a given case differs most clearly from the asymmetric aggregationist answer: there are no limits on what can be aggregated in the asymmetric aggregationist model, whereas the symmetric model does involve some limits, of the following individualist sort.


In the asymmetric model, it is morally permissible to do whatever course of action will be most likely to secure the greatest aggregate benefit, irrespective of the level of moral significance of the individual benefits involved in the aggregation, and irrespective also of the level of moral significance or seriousness of the individual burdens involved in the aggregation. With symmetric aggregation, by contrast, the burdens imposed on each individual have to be equivalent in moral significance to the benefits accruing to each individual. This requirement of symmetry makes a significant difference between what’s morally permissible under the asymmetric model and what is so under the symmetric model.


Recall Joyce’s maxim: the symmetric aggregationist response would be that under certain conditions it’s possible to find a way of “rightfully condemning” the one innocent person if this is the most effective, or only, available means of convicting the ninety-nine. But it would be wrong on this view to impose a severe burden, say a jail sentence, on the one innocent person if the crimes of the ninety-nine, taken individually, were relatively minor, e.g. misdemeanours such as petty theft and being drunk and disorderly in a public place. The asymmetric aggregationist, unlike his symmetric counterpart, would see no obstacle to adding together the crimes of the ninety-nine to determine what size of aggregate burden would be needed to outweigh the benefit of convicting the ninety-nine guilty. If the aim were to bring ninety-nine misdemeanants to justice, the asymmetric aggregationist would have to show how it could be justified to imprison one innocent person in order to bring about this benefit to society. (I’m assuming throughout that for whatever reason, no other means of bringing about this aggregate benefit is available or would be as likely to work). The symmetric aggregationist doesn’t face the same requirement, since his line of reasoning doesn’t involve this procedure of “blind” aggregation of benefits and burdens that are then weighed against each other to yield an answer as to what course of action is morally permissible to take. Instead, for the symmetric aggregationist the first step comes prior to the aggregation procedures: the individual benefits and burdens must be compared to each other. This being done, it’s clear that in the example at hand, imprisoning the one would outweigh the benefit obtained, and so would be morally wrong.


The symmetric model, at its simplest, proceeds along these lines: if it would be morally impermissible to imprison one innocent person to secure the conviction of one misdemeanant, the requirement of symmetry at the individual level entails that the numbers would not count: it would still be morally impermissible to imprison one innocent person if this would lead to the conviction of more than one misdemeanant. There is nothing in this idea to suggest that there could be a cut-off point beyond which the individualist restriction (i.e. the requirement that the burden to each person cannot be larger than the benefit to each person) no longer holds. That is to say, the model offers no point at which one decide that although the conviction of one misdemeanant is of less moral significance than the imprisonment of one innocent person, the benefit to society of securing the conviction of, say, ninety-nine drunk and disorderly unauthorized photocopiers would be of such moral significance as to outweigh the harm to the one innocent person of imprisoning him.


In the previous two paragraphs I have discussed the lower limits on how aggregation can be carried out for it to be morally justified in terms of the symmetric model. What about upper limits – what restrictions, if any, are there within the symmetric model on what burdens it is morally permissible to impose in order to bring about some greater benefit? Here the greatest flaw of the symmetric aggregationist approach to moral reasoning is revealed. Recalling Joyce’s maxim again, if the imposition of burdens is morally permissible as long as these burdens are at least equivalent in moral significance to the benefits that imposition would be justified in bringing about, it follows from the symmetric aggregationist view that it would be permissible to impose an equivalent burden on the one innocent person, if this would secure the conviction of the ninety-nine. The problem, in short, is that according to the symmetric aggregationist model there is no upper threshold on what it is morally permissible to do. The severity of burdens is simply tied or indexed to whatever wrongs are to be offset or prevented by the course of action under consideration. So despite being a less expansive approach to aggregation than asymmetric aggregation, symmetric aggregation allows a smaller number, like Joyce’s one innocent man, to be subjected to potentially unlimited burdens if this were the only or most effective available means of bringing about a greater good; I consider this a serious flaw. The last approach in the taxonomy might be better.



Weak aggregation

Asymmetric and symmetric aggregation are both maximizing positions, but otherwise they don’t recognize any restrictions as absolute; in their different ways, they both allow potentially unlimited burdens to be imposed on an individual or small number if this would benefit a larger number of others. Weak aggregation differs from these two in that it involves two sorts of limitation that are absent from those other two approaches in the taxonomy that permit interpersonal aggregation. Unlike asymmetric aggregation, approaches to aggregation are “weak” when they involve placing limits on the types of considerations that can be aggregated and weighed against each other. So even if imprisoning one innocent person were the only possible way of bringing ninety-nine drunk and disorderly unauthorized photocopiers who smoke in a No Smoking area to justice, it would be morally impermissible. This is the first limit, which is shared with symmetric aggregation. The second limit, which is absent from both the asymmetric and symmetric approaches, is the upper threshold on the severity of the burdens that can be imposed on any individual person or persons in order to bring about a benefit for some greater number.


Specifying what form these two restrictions take and how they can be justified are difficult tasks outside my present scope. But one notable attempt to develop an approach to aggregation that includes both restrictions should be mentioned. The best-known, and also most promising exemplar of weak aggregation that I’m aware of is the individualistic approach to aggregation defended by Thomas Scanlon (1998). On this view, aggregation is morally permissible only to the extent to which the reasonable interests of each individual person whose interests are at stake in a given situation are taken into account in such a way that the person could not reasonably reject this outcome if her or she he had to bear the cost of bringing about some greater benefit (Scanlon 1998, 229-41). This principle of ‘reasonable rejectability’, which is central to Scanlon’s contractualist alternative to consequentialist moral theories, is what entails and justifies the two limitations I mentioned.[2]




Of the four types of approach outlined I consider weak aggregation to be the most defensible, although in saying this two qualifications apply. First, it has not been my aim in this paper to provide a detailed defence of weak aggregation; given the force of some of the objections that have been made against Scanlon’s form of it,[3] any such defence must be left until a later paper. All I’ve tried to do here is to sketch out rough characterizations of the various possible approaches to interpersonal aggregation. Second, to claim that the weak approach to aggregation is the most defensible one is not to claim that it is ideal. Interpersonal aggregation is essentially a form of compromise; and there can be better or worse, even rotten compromises (Margalit 2010), but no “ideal compromise”. This would be a contradiction in terms.




Hooker, Brad (2003) ‘Contractualism, Spare Wheel, Aggregation’, in Matravers (ed.) (2003), 53-76.

Joyce, James (1988) [1922] Ulysses (1922 Text), Ed., Intr., Annotated Jeri Johnson, Oxford: Oxford University Press.

Margalit, Avishai (2010) On Compromise and Rotten Compromises, Princeton: Princeton University Press.

Matravers, Matt (ed.) (2003) Scanlon and Contractualism, 53-76. London: Frank Cass.

Norcross, Alistair (2002) ‘Contractualism and Aggregation’, Social Theory and Practice 28 (2), 303-14.

–––– (1997) ‘Comparing Harms: Headaches and Human Lives’, Philosophy and Public Affairs 26 (2) (Spring), 135-67.

Parfit, Derek (1986) ‘Overpopulation and the Quality of Life’, in Singer (ed.) 1986, 145-64.

–––– (1978) ‘Innumerate Ethics’, Philosophy and Public Affairs 7 (4) (Summer), 285-301.

Pogge, Thomas (2001) ‘What We Can Reasonably Reject’, Noûs 35 (1), 118-47.

Scruton, Roger (2009) I Drink, Therefore I Am: A Philosopher’s Guide to Wine, London: Continuum.

–––– (1997) [1993] How Are We To Live? Ethics in an Age of Self-Interest, Oxford: Oxford University Press.

Singer, Peter (ed.) (1986) Applied Ethics, Oxford: Oxford University Press.

–––– (1972) ‘Famine, Affluence, and Morality’, Philosophy and Public Affairs 1 (1) (Spring), 229-43.

Temkin, Larry (1987) ‘Intransitivity and the Mere Addition Paradox’, Philosophy and Public Affairs 16 (2) (Spring), 138-87.

Timmermann, Jens (2004) ‘The Individualist Lottery: How People Count, But Not Their Numbers’, Analysis 64 (2):106-12.




[1] But for a defence of intransitivity see Temkin 1987.

[2] For Scanlon’s development of the idea of reasonable rejection see Scanlon 1998, especially Chapters one and five. Scanlon’s idea of ‘reasonable rejectability’ has received an enormous amount of critical attention; for a forceful objection to it see Pogge 2001.

[3] See for example Hooker 2003; Norcross 2002; Timmermann 2004, 107-8.