This paper was published as a GPI working paper in October 2024.

Abstract

According to Partial Aggregation, a serious harm can be outweighed by a large number of somewhat less serious harms, but can outweigh any number of trivial harms. In this paper, I address the question of how we should extend Partial Aggregation to cases of risk, and especially to cases involving small risks of serious harms. I argue that, contrary to the most popular versions of the ex ante and ex post views, we should sometimes prevent a small risk that a large number of people will suffer serious harms rather than prevent a small number of people from certainly suffering the same harms. Along the way, I object to the ex ante view on the grounds that it gives an implausible degree of priority to preventing identified over statistical harms, and to the ex post view on the grounds that it fails to respect the separateness of persons. An insight about the nature of claims emerges from these arguments: there are three conceptually distinct senses in which a person’s claim can be said to have a certain degree of strength. I make use of the distinction between these three senses in which a claim can be said to have strength in order to set out a new, more plausible, view about the aggregation of people’s claims under risk.

Introduction

Consider the following stylised decision situation.

Deaths vs Risks of Death: There is a one-in-ten-thousand chance that eight million New Yorkers will be killed. One hundred Texans also face certain death. All of these individuals are known to you by name. You can save the Texans or eliminate the risk to the New Yorkers, but not both.^[1]

Nobody will ever actually face this choice, not least because nobody is that good with names. But we do sometimes need to trade off small probabilities of harms to the many against larger probabilities of harms to the few. A government might have to choose between deploying part of its limited budget on the provision of life-saving medical care, or on preparedness for an unlikely pandemic. A philanthropist might wonder whether their money is better spent on relief for an ongoing disaster or on preparedness for future disasters. Voters might ask themselves whether it is worth diverting money that could be used to save lives today towards civil defence measures, given that these could save many lives in the (hopefully) very unlikely event of nuclear war. And so on. The actual decision situations are the ones of practical interest. But cleaned-up cases like Deaths vs Risks of Death can help us identify the morally salient factors at issue.

What, then, ought we to do in cases like Deaths vs Risks of Death? Proponents of “Full Aggregation”—the view that benefits and harms can always be aggregated—have a ready answer available: simply compare the expected numbers of lives saved.^[2]  Rescuing the New Yorkers would save eight hundred people in expectation, while rescuing the Texans would save one hundred. So, on this view, we should save the New Yorkers. At the opposite end of the spectrum, proponents of “No Aggregation” think that the numbers never matter, so that we should prevent a single serious harm rather than any number of less serious harms.^[3] On this view, presumably we ought to save the Texans.^[4]

However, both Full and No Aggregation have implications that many people find implausible. Full Aggregation implies that we should prevent a large enough number of trivial harms rather than save a life, since doing so might prevent greater aggregate harm; and this strikes many people as counter-intuitive.^[5] No Aggregation goes too far in the opposite direction: it prevents us from saying, as we might like, that preventing one million people from having their left legs broken is more important than preventing one person from having both legs broken.

There is a third view which sits between these two extremes. According to Partial Aggregation (also known as Limited Aggregation), large enough numbers of lesser harms can outweigh smaller numbers of somewhat graver harms, but no number of trivial harms can outweigh any number of serious harms. Or, put more simply, losses of limbs can outweigh death, but headaches cannot. Since the verdicts of Partial Aggregation strike many people as extremely plausible, I shall assume this view without further argument. My project shall be to investigate what we should say about Deaths vs Risks of Death, and about risky cases more broadly, if we take Partial Aggregation for granted.

The most popular version of Partial Aggregation is Alex Voorhoeve’s “Aggregate Relevant Claims View”.^[6] This works as follows:

(i) Individuals have claims against being harmed, and the strengths of these claims correspond to the extent to which they would be harmed.^[7]

(ii)  Claims compete when they cannot be jointly satisfied.

(iii)  A claim is relevant if it is strong enough, compared to the strongest individual competing claim. Otherwise it is irrelevant.

(iv)  We should choose whichever action maximises the satisfaction of aggregate strength-weighted relevant claims.

Unfortunately, the Aggregate Relevant Claims View, as specified above, does not yield a useful verdict on whether we should rescue the Texans or the New Yorkers. The problem is that the strengths of claims are taken to be given by the extent to which individuals would be harmed, unless you were to prevent the harm in question.^[8] But the point of Deaths vs Risks of Death is that we don’t know whether the New Yorkers will die if this is not prevented. In order to get a useful recommendation as to what we should do, we must therefore find a way to extend the Aggregate Relevant Claims View to cases involving risk.

At a first pass, the main thing we need to decide is whether the New Yorkers’ claims are relevant. Two ways of thinking about this immediately present themselves. On the first, each individual New Yorker can have only a tiny claim to be rescued, because the strength of their claim against death should be discounted by the improbability that their death would actually eventuate if one were to save the Texans instead. These claims will then be treated the same way as claims against the certainty of a harm one-ten-thousandth the size of death. On the plausible assumption that such harms would be irrelevant to certain death, the claims of the New Yorkers will also be irrelevant, leading us to side with the unopposed claims possessed by the Texans.

The second way of thinking about the relevance of the New Yorkers’ claims is to attend to the fact that, if the one-in-ten-thousand probability does eventuate, the New Yorkers stand to die. Risks of death, one might think, should always count as relevant when they compete with certain death. On this approach, the New Yorkers will have relevant claims to be saved, and the aggregate strength of these claims will presumably exceed the aggregate strength of the claims of the Texans.

I shall argue in this paper that we should take the second view, not the first. I’ll begin by sketching the two most popular approaches to risk in the literature on Partial Aggregation, which are the ex ante and ex post views. The most common versions of these views agree that the claims of the New Yorkers should be considered irrelevant. However, I shall argue that both are unsatisfactory. The main problem with the ex ante view is well-known: it gives implausibly extreme priority to preventing identified over statistical harms. I shall flesh out this objection in §2. The ex post view can be objected to on various grounds, but the objection I shall press in this paper is that it fails to respect the separateness of persons. I shall make this objection precise in §3.

If successful, these two objections to the two standard views do not only show that these views are mistaken. As I shall show in §4, it turns out that avoiding these two objections requires that claims against small risks of serious harms must be relevant to claims against being harmed to the same extent with certainty. Since we should indeed avoid both objections, this answers the question we started with. We should rescue the many rather than the few in cases like Deaths vs Risks of Death, because the claims of the many are indeed relevant.

To help explain how we can reconcile respecting the separateness of persons with taking statistical harms seriously, I shall distinguish between three senses in which a claim can be said to have a certain degree of “strength”. I will use this distinction to present what I shall call the “Ex Ante Claims, Ex Post Relevance” view. I believe that this view brings us closer to getting things right about the aggregation of people’s claims in cases of risk. I shall respond to two important objections to it in §5, and then conclude in §6.

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1. ^{^}

   A structurally similar case has been discussed by Steuwer (2021: 119–120).

2. ^{^}

   Not every fully aggregative moral theory endorses this answer. For example, Ex Ante Prioritarianism, which has been defended by McCarthy (2006, 2008), applies a priority weighting to each person’s expected wellbeing: our reasons to benefit people are stronger, the worse-off these people would otherwise be in expectation. Since the Texans are worse off in expectation if they are not helped, Ex Ante Prioritarians will somewhat prioritise increasing their expected wellbeing, and thus (depending on how heavily the worse-off are to be prioritised) may decide to save the Texans. One could, in principle, also combine Alec Walen (2020)’s “Weak Aggregation” with the view that while claims lose strength at a faster-than-linear rate as they decline in size, they always remain relevant even to much stronger claims.

3. ^{^}

   See Taurek 1977.

4. ^{^}

   Michael Otsuka has pointed out to me that proponents of non-aggregation might be able to justify the social policy of saving the greater expected number on the basis that this policy would be in each person’s interests ex ante. Thus, if the decision in Deaths vs Risks of Death falls to a government, the choice to safeguard New York might be justifiable even if interpersonal aggregation is not, despite the fact that safeguarding New York is unlikely to actually save any New Yorkers. See Taurek 1977: 312–313. Reibetanz (1998: 301) suggests something similar.

5. ^{^}

   See Scanlon 1998: 235.

6. ^{^}

   See Voorhoeve 2014.

7. ^{^}

   One might take the view that claims should also be weighted for additional morally relevant factor such as the importance of prioritising the worst off. Such complications will not matter for my purposes, so I shall set them aside going forward.

8. ^{^}

   That is, on a straightforward reading, the Aggregate Relevant Claims View might be interpreted as what Steuwer (2022: 72) calls “actualist ex post limited aggregation”.