Never Just Save the Few

Abstract

Most people have the intuition that, when we can save the lives of either a few people in one group or many people in another group, and all other things are equal, we ought to save the group with the most people. However, several philosophers have argued against this intuition, most famously John Taurek, in his article ‘Should the Numbers Count?’ They argue that there is no moral obligation to save the greater number, and that we are permitted to save either the many or the few. I argue in this article that, even if we are almost completely persuaded by these ‘numbers sceptics’, we ought not to just save the few. If the choice is simply between saving the many or the few, we ought to save the many.

1. Introduction

Most people have the intuition that the number of people affected by our actions is a morally relevant factor when deciding what we ought to do. When we can save the lives of either a few people in one group or many people in another group, most people would agree that, when all other things are equal, we ought to save the group with the more people. But there have been several philosophers who have argued against this intuition. They claim that there is no general moral obligation to save the greater number (SGN) and so we are permitted to save either the many or the few. These ‘numbers sceptics’ include John Taurek, G. E. M. Anscombe, Véronique Munoz-Dardé, Tyler Doggett and Kieran Setiya.¹

I will argue in this article that, even if we are almost completely persuaded by the arguments of these numbers sceptics, we should reject the practical implications of their conclusion. Even if we are almost convinced that there is no general moral obligation to save the greater number, so long as we think that there is at least some possibility that the numbers sceptics are wrong, we ought not to just save the few. By this I mean that we should not accept the numbers sceptics’ claim that we should simply pick a group to save. The argument I put forward threatens to undermine the numbers sceptics’ position, not by challenging the arguments they make, but by directly undermining the implications of their conclusion. If I am right, we are never permitted to just save the few, at least when all other things are equal.

The most famous argument against SGN is found in Taurek's article ‘Should the Numbers Count?’.² There is some ambiguity in his article regarding whether he is endorsing a permission to save either group or a principle which requires us to toss a coin when deciding whether to save the many or the few. In Section 2, before outlining my argument against the numbers sceptics’ position, I will address this ambiguity and argue that Taurek is indeed claiming that we are permitted to save either the many or the few. This is important because, as I will explain, my argument against the numbers sceptics’ position only goes through if this is indeed the position they endorse.

In Section 3, I put forward what I call the dominance argument in favour of SGN over the numbers sceptics’ position that we are permitted to save either the many or the few. This argument shows that even if we are almost certain that the number sceptics are right, we ought never to just save the few. And if we are choosing between just two options, saving the many or saving the few, we ought to save the many because this is the only option that is guaranteed to be objectively morally permissible.

In Section 4, I defend the dominance argument for saving the many against two potential objections. First, I address the worry that my dominance argument has implausibly demanding implications when applied in some contexts, and overly conservative implications when applied in other contexts. I argue that we can overcome this objection without undermining my dominance argument against the numbers sceptics’ position. Second, I consider other principles which compete against SGN, such as a principle requiring us to give people an equal chance of survival or to hold a weighted lottery. If an agent has some credence in these competing principles, the dominance argument would not work in favour of SGN. I argue that, though this objection prevents the dominance argument from supporting SGN, it does not prevent it from undermining the numbers sceptics’ position. What the dominance argument ultimately shows is that, even if we are not obligated to save the many, we should still never just save the few. I then offer ways in which an agent with credence in competing principles could go forward.

2. Numbers scepticism

There are several philosophers who argue that we are not morally required to save the greater number, and that instead we are permitted to save either the many or the few, even when all other things are equal. Philosophers who endorse this view include G. E. M. Anscombe, who writes ‘there seems to me nothing wrong with [saving the one] and letting the others die’.³ Véronique Munoz-Dardé also argues, ‘if we have a choice between saving two people and saving one (and we cannot save all three), then, other things being equal, it is permissible to save either side’.⁴ Tyler Doggett also concludes that ‘generally, you can save the few’,⁵ and Kieran Setiya endorses this claim, saying ‘we are justified in saving the one when we could save three’.⁶ As there is no moral obligation to save the greater number, and as it is morally permissible to save either side, these philosophers conclude that when we are faced with a situation in which we must save either the many or the few, we can simply pick any group to save. I will call this view the numbers sceptics’ position.

The most well-known argument in the debate on the moral significance of numbers is given by John Taurek. In his article ‘Should the Numbers Count?’, he argues that there is no general moral obligation to save the greater number. There is some ambiguity as to the correct interpretation of Taurek; some think that he is arguing for the numbers sceptics’ position, while others believe that he is endorsing a different principle on which we are obligated to toss a coin. Before outlining my argument against the numbers sceptics’ position, I will look at Taurek's argument to clarify this ambiguity. If, as I will argue, Taurek is claiming we can save either the many or the few, the argument I present in Section 3 will hold against the most prominent case for the numbers sceptics’ position.

2.1 Taurek's argument against SGN

When we can save the lives of either a smaller group of people or a larger group of different people, and all other things are equal, most people agree that we ought to save the larger group. To draw out this commonly held intuition, Taurek presents the following case:

Drug. I have a supply of some life-saving drug. One of six people needs the drug in its entirety if he is to survive, whereas the other five require only one-fifth of the drug each.⁷

Many people have the intuition that I ought to use the drug to save the five rather than the one in this case, at least if all the people involved are strangers to me.

Taurek claims that this intuition is difficult to reconcile with another commonly held conviction, namely, that we would be permitted to save the one if he or she were someone we knew and liked. Consider an alternative case:

David. I have a supply of some life-saving drug. David, someone I know and like, needs the drug in its entirety if he is to survive, whereas there are five strangers who need only one-fifth of the drug each in order to live.⁸

In this case, most people have the intuition that it would be morally permissible for me to give David the drug. Taurek argues that this view is incompatible with SGN. This is because, if there were a general obligation to save the greater number, an appeal to the partial interests of the moral agent – your special concern for David – would do nothing to override that moral obligation. SGN would be ‘feeble indeed’ if it would be overridden by our personal preference for someone.⁹

Taurek makes the problem clearer with the following example. Suppose that the five strangers had contracted with me in advance to deliver this drug to them. This contractual obligation could not be overridden by the mere fact that it turns out someone I know and like needs the drug also. So, it seems a genuine obligation to save the five cannot be overridden by appeal to the partial interests of the agent. If this is right, then we must conclude that there is no obligation to save the greater number in the original David case, and hence no general obligation to save the greater number at all.

So, in Taurek's opinion, we are left with only two options: either we deny that we are permitted to save David, or we accept that we do not have a moral obligation to save the greater number. Taurek thinks it is intuitively clear that we are permitted to save David and so he concludes that we do not have a moral obligation to save the greater number.¹⁰

2.2 Against the Equal Chances interpretation of Taurek

If Taurek is right, what should we do in a case like Drug? Taurek's article does not give a clear answer. In rejecting SGN, Taurek's argument seems to imply that you are permitted to save either the one or the five. Taurek clearly thinks you ought to save someone; he just thinks it is up to you which group to save. However, Taurek also claims that, when all six are strangers, he himself would toss a coin, saving the one if the coin lands on one side and saving the five if it lands on the other. This, he claims, would best show his equal concern for all individuals.

It is not clear whether Taurek is merely suggesting that we perform this coin toss or, instead, claiming that we are morally required to do so in order to give each person an equal chance of survival. Let us call the latter interpretation the Equal Chances (EC) interpretation. There is disagreement among philosophers as to the correct interpretation. While most philosophers attribute the EC interpretation to Taurek, some philosophers have pointed out the ambiguous nature of his conclusion.¹¹ I will now provide an argument to show why we should reject the EC interpretation of Taurek.

There is strong reason to believe that the EC interpretation of Taurek is incorrect – that Taurek is not making a moral claim when he says that he would toss a coin to give each person an equal chance of survival. This is because, if we take it that Taurek is arguing for a moral obligation to give each person an equal chance, we are faced with the following problem: the David argument that Taurek makes against an obligation to save the greater number can also be levelled at a principle to give each person an equal chance.

Recall that in David, we are permitted to save David over the five strangers because David is someone we know and like. The reason Taurek gives for rejecting SGN is because it cannot be reconciled with a permission to save David. If there were such an obligation to save the many, our special concern for David would do nothing to override that moral obligation. So, we can either say that we are morally obligated to save the many in both Drug and David, or that we are permitted to save the few in both cases. As Taurek thinks it is intuitively obvious that we are permitted to save David, he concludes that we do not have a moral obligation to save the many.

If Taurek is really endorsing a principle of equal chance, this means that in Drug, you cannot just choose to save either the one or the five on a whim. Rather, because you are morally obligated to give each person a fair chance to be saved, you must toss a coin in order to give each person a 50 per cent chance of survival, or use some other equally fair decision procedure. You cannot just decide randomly to save the one or the five, because you have a moral obligation to decide which group to save using a process that ensures each person has an equal chance of survival.

But, if Taurek's argument succeeds, EC similarly cannot be reconciled with our intuitions in David. We would expect that if David is in either one of the groups, you would be permitted to save the group that he is in, without having to toss a coin. Taurek certainly thinks this, as he says he would toss a coin only when he doesn't have personal preferences either way. So, if David is either the one in need of saving, or if he is one of the five in the group which needs saving, Taurek thinks you would be permitted to save either the one or the five, forgoing tossing a coin to give each person an equal chance.

However, if you are permitted to automatically save the group that David is in, rather than tossing a coin to determine which side to save, this would mean that the obligation to give each person an equal chance is, in Taurek's words, ‘feeble indeed’, as it can be overridden by your partial preference for your friend. That is to say, if there is really an obligation to give each person an equal chance of survival, an appeal to the partial interests of the agent would do nothing to override that moral obligation. Using Taurek's own reasoning, this shows that there is no such obligation to give each person an equal chance of survival in the first place.

Some might say that the partial interests of the agent are sufficient to override the EC obligation – that we are only obligated to toss a coin when all other things are equal. In other words, it can be argued that we have only a pro tanto obligation to give each person an equal chance of survival. However, if this were true, it would also undermine Taurek's argument against SGN, for it would be unclear why the partial interests of the agent cannot similarly override a general obligation to save the greater number. If Taurek's argument against SGN succeeds, the same argument also undermines EC.

For this reason, I am persuaded that tossing a coin is merely a suggestion of Taurek, something which he believes reflects his conviction that each individual's claim is equally important. Indeed, the language Taurek uses seems particularly vague and weak to reflect a real commitment to a principle of EC. ‘Why not give each person an equal chance?’ Taurek asks. ‘Where such an option is open to me it would seem to best express my equal concern and respect …’¹² Taurek is ‘inclined to treat each person equally by giving each an equal chance to survive’.¹³ So, although giving equal chances is what Taurek himself would do, Taurek clearly holds back from claiming that giving equal chances is morally required.

Therefore, I conclude that, when Taurek claims that numbers do not count, he is saying that, when faced with the decision to save a single individual or a different group of five people, he is permitted to choose either option. We can save either the one or the five, as both options are equally permissible. As there is neither an obligation to save the many nor an obligation to give each person an equal chance of survival, I can choose to save the one over the five without a second thought; no coin toss is needed to permit me to save the few.

In this section, I have shown that we have good reason to include Taurek as one of the numbers sceptics who claim we are morally permitted to save either the many or the few. Along with philosophers like Anscombe, Munoz-Dardé, Doggett and Setiya, Taurek also holds the position that when we can save either the many or the few, we are permitted to save just the few without appeal to a fair decision procedure like a coin toss.

In the next section, I put forward the dominance argument, which shows that we should reject the conclusion that Taurek and other numbers sceptics draw from their argument, even if we are almost certain that their arguments are right.

3 The dominance argument against the numbers sceptics’ position

Suppose we find Taurek's arguments and that of other numbers sceptics persuasive. What should we do, then, if we are faced with a choice between saving a smaller group of people and a larger group of different people?

It might seem that we should just pick any group to save, considering that, according to numbers sceptics, there is no moral difference whether we save the many or the few. But this conclusion seems to me too hasty. Even if we are almost entirely convinced that Taurek and others are right, unless we believe that their arguments are infallible, we should leave open the possibility that they are wrong. So, even if we are almost entirely convinced that saving the smaller group is morally permissible, we should also leave open the possibility that saving the larger group is the morally better choice. If the numbers sceptics are right, saving the larger group is just as morally choice-worthy as saving the smaller group. If they are wrong, and there is a general moral obligation to save the greater number, saving the larger group is obligatory, and hence more morally choice-worthy. Since there is at least a small chance that saving the larger group is the better moral choice, and no chance that it is the worse moral choice, it seems we should save the larger group, even if we are almost entirely convinced that the numbers sceptics are right.

This reasoning can be applied to Drug as follows. Given that it does not matter whether we choose to save the one or the five under Taurek's conclusion, and bearing in mind that we do no wrong if we choose to save the five, it seems we ought to save the five just in case it so happens that Taurek is wrong and that numbers do count. Whereas we can do no wrong if Taurek is right, it would be morally disastrous if we choose to save the one but it turns out that SGN is right.

To put it another way, it would be wrong for us to take a chance of acting wrongly by saving the one if we can instead guarantee that we act permissibly by just acting to save the five. Saving the five is the only option that is permissible under both Taurek's conclusion and SGN. So, the possibility of SGN being the correct moral principle provides us with a pivotal reason to choose to save the five over the one, even if we are almost positive this principle is false.

The reasoning I have just presented can be supported by arguments put forward by proponents of moral uncertaintism, a fairly recent area of study within moral philosophy that deals with how we ought to act under moral uncertainty. Plausibly, there are at least two different levels of moral ought. At the first level, there is an ought that speaks to the question of what we ought to do when we face a moral problem and we know all the morally relevant details of the situation – this is the question of what we objectively ought to do. At the second level, there is an ought that speaks to the question of what we ought to do when we face a moral problem and we are uncertain about descriptive facts that are morally relevant – this is the question of what we subjectively ought to do. Moral uncertaintism is the idea that there is a third level of moral ought, which speaks to the question of what we ought to do when we face a moral problem and we are uncertain about which moral theory is true. This is sometimes referred to as what we super-subjectively ought to do.¹⁴

Moral uncertaintism holds that we ought to treat moral uncertainty more or less the same way as we treat descriptive uncertainty. A common principle we comply with under descriptive uncertainty is what is called the dominance principle. This principle states that when one available action dominates the other, then one is rationally required to choose the action that dominates.

What does it mean for one action to dominate another? There are two types of dominance: strict dominance and weak dominance. Let me explain this distinction.

If I am uncertain about the state of the world (about what the world is like), but certain that, given any possible state of the world, option A is more choice-worthy than option B, then A is said to strictly dominate B. For example, say that I am uncertain whether it is going to rain today. I have the option of either going to the movies or the beach, but I would much rather go to the movies. In this case, the option of going to the movies strictly dominates going to the beach, as it is the more choice-worthy option in all possible states of the world. If it rains, going to the movies is more choice-worthy as I am saved from getting soaked on the beach, and if it doesn't rain, going to the movies still is more choice-worthy as I prefer watching movies than going to the beach anyway. So, as everyone would agree, I am rationally required to go to the movies rather than the beach.

If I am certain that (i) given any possible state of the world, A is at least as choice-worthy as B, and that (ii) given some state(s) of the world A is more choice-worthy, then A is said to weakly dominate B. For example, if I am uncertain whether it is going to rain and my umbrella is so light that I won't notice carrying it, taking my umbrella weakly dominates not taking it, as taking the umbrella is sure to yield a result that is as good as or better than not taking it. I am certain that given any possible state of the world (rain or no rain) the option of taking my umbrella is at least as choice-worthy as not taking my umbrella, and in the case in which it does rain, the action of taking my umbrella is more choice-worthy than not taking my umbrella. So, as everyone would agree, I am rationally required to take my umbrella.¹⁵

The example above shows that one ought to comply with weak dominance when uncertain about descriptive propositions. It seems to me that, in the same way that we apply weak dominance in cases of descriptive uncertainty, we ought to apply weak dominance in cases of moral uncertainty. I believe that just as we can be rationally required to avoid weakly dominated options in cases where our own interests are at stake, we can be morally required to avoid weakly dominated options in cases where morality is at stake. This is because, morally, it seems you ought to care about doing the right thing, and a morally conscientious agent would act in a way that mitigates moral risk. It would be morally wrong to take the risk of doing something that could potentially be wrong, when instead you could choose to do something that is guaranteed to be morally permissible. So, if there is one option that weakly dominates another in a moral situation, we can be morally required to choose the option that dominates.

If we return to the original Drug case, when we consider the possible outcomes for numbers scepticism and SGN, we see that saving the five weakly dominates saving the one. The options for the agent are given in Table 1.

Table 1. Drug.

The two possible states of the world are either that Taurek and the numbers sceptics are right and numbers are not morally relevant, or that SGN is right and numbers are morally relevant. If the numbers sceptics’ view is right and SGN is wrong, then saving the five is just as morally choice-worthy as saving the one, as both options are permissible. If SGN is right and numbers scepticism is wrong, then saving the five is more choice-worthy than saving the one, as an obligation to save the greater number means that saving the five is permissible whereas saving the one is morally wrong. Thus, saving the five weakly dominates saving the one, as saving the five is sure to yield a result that is at least as choice-worthy or more choice-worthy than saving the one. The option of saving the five yields an outcome that is permissible on both theories while the option of saving the one yields an outcome that is permissible on one theory but prohibited on another. For this reason, we ought, both rationally and morally, to save the five over the one, as it yields the outcome which is either as good as or better in all possible states of the world.

Even if we are almost persuaded by the arguments of numbers sceptics, we should give SGN the benefit of the doubt and leave open the possibility of it being right, especially considering that many people do hold the intuition that we ought to save the many in situations like Drug. Given that we are fallible human beings, to claim full confidence in the numbers sceptics’ view would be an act of epistemic arrogance.¹⁶ But, as I have argued, if we are anything less than certain that numbers scepticism is right, we should comply with SGN, because although the option of saving the many is permissible under both the numbers sceptics’ view and SGN, saving the few would be impermissible under SGN. The rational and morally conscientious person, someone who cares about doing right and refraining from doing wrong, would not save the few. By saving the many, we can ensure that we do what is permissible regardless of which theory is right.

Admittedly, there is an air of paradox surrounding my dominance argument in favour of SGN over the numbers sceptics’ position. If I am right, my argument seems to show that, even if we are almost certain that SGN is false, we should conclude that SGN is true, or at least comply with SGN. But how can we be almost certain SGN is false while also believing that it is true?

We can explain this seemingly contradictory position by returning to the different levels of moral permissibility noted above. There is a sense of moral permissibility that is not sensitive to moral uncertainty, which determines what we are objectively permitted to do. Taurek and other numbers sceptics’ arguments, if successful, show only that saving the smaller group is permissible in that sense – the sense that it is not sensitive to moral uncertainty. My disagreement with Taurek and other numbers sceptics is not regarding the objective permissibility of saving the few. It may well be that the numbers sceptics are right and it is objectively morally permissible to save the few.

But there is another sense of moral permissibility that is sensitive to moral uncertainty. I argue that, unless we are absolutely certain that saving the smaller group is permissible in the first sense, we must conclude that saving the smaller group is impermissible in the second sense. To put it another way, it is super-subjectively impermissible to save the few given our limited epistemic position regarding the objective permissibility of doing so. The numbers sceptics assume that the objective ought is the one that should guide our actions. I argue that at least in cases of weak dominance, it should be the super-subjective ought guiding our actions. So, my argument is against the numbers sceptics’ position that we are morally permitted, in the sense that matters to guiding our actions, just to choose whether to save the many or the few. Given that the option of saving the many weakly dominates saving the few, if we care about doing what is right and refraining from doing wrong, we ought to save the many over the few.¹⁷

To make this distinction clearer, we can say that when two acts are permissible in the objective sense, both acts are equally morally choice-worthy.¹⁸ When one act is permissible in this sense and the other is impermissible in this sense, we can say that the former is more morally choice-worthy, and the latter is less morally choice-worthy. When an act is permissible in the super-subjective sense – the sense sensitive to moral uncertainty – we can say, simply, that it is morally permissible. Then, what the numbers sceptics show is at most that saving the smaller group is equally as morally choice-worthy as saving the larger group. I argue that, unless you are certain that saving the smaller group is equally morally choice-worthy, saving the smaller group is impermissible.

4 Objections to the dominance argument against the numbers sceptics’ position

In this section, I look at two potential objections to my dominance argument against the numbers sceptics and explain how they can be answered.

4.1 The demandingness/conservativeness objection

A potential objection to the dominance argument is that it has implausible implications when applied in certain contexts.

In some cases, it is too demanding. Suppose you can save two people trapped inside a burning building by sacrificing your life to rescue them. You are almost certain that it is permissible to not give up your life, but you also have a small amount of credence in act utilitarianism, which obligates you to sacrifice your life to save the two. Considering that it is at least permissible to sacrifice your life to save two people in all possible states of the world, the dominance argument seems to imply that you are required to give up your life. This seems to be a reductio ad absurdum of the dominance argument, and as the objection goes, it should be rejected because it demands too much of us.

In a similar vein, the dominance principle could be criticised for being an implausibly conservative morality.¹⁹ Suppose that you are almost certain that abortion is permissible. There is a chance that you are mistaken and abortion is, in fact, impermissible. Considering that it is at least permissible not to go ahead with the abortion in all possible states of the world, the dominance principle seems to imply that you should not go ahead with the abortion, just in case it so happens that abortion is morally impermissible.

There seem to be two ways in which we can defend the dominance argument against the demandingness and conservativeness objection.

First, we can say that under moral uncertainty, we ought to consider what the all-things-considered choice-worthiness of an option is. MacAskill and Ord argue that when considering the choice-worthiness of options, we ought to take into account non-moral reasons, such as prudential reasons, as well as moral reasons.²⁰ The agent who refrains from entering the burning building will have reasonable credence in the view that she ought to save her own life. This would be true on the view according to which act utilitarianism is false and there are prudential reasons to keep oneself alive. As long as you have some credence in the view that act utilitarianism is false and there are prudential reasons to save yourself, the dominance argument would not hold up. The dominance argument would only require you to go inside the burning building if there were absolutely no prudential reasons to do otherwise. Similarly, the agent who goes ahead with the abortion will have reasonable credence in the view that she has non-moral reasons to do so. This would be true on the view according to which abortion is permissible and there are prudential reasons to go through with the abortion. So long as you have some credence in this view, the dominance argument would fail.

This response to the demandingness and conservativeness objection shows that in certain situations, there can be prudential reasons which push back against a certain moral theory dominating others and therefore prevent the dominance argument from being overly demanding or conservative. This does not, however, undermine the dominance argument in favour of SGN over the numbers sceptics’ position. For instance, in Drug, there are no prudential reasons to prefer saving the one rather than saving the five. As there are no prudential reasons pushing back against SGN dominating the numbers sceptics’ view when all other things are equal, the option of saving the five will weakly dominate the option of saving the one. This leads us to the result that we ought to save the five just in case Taurek and other numbers sceptics happen to be wrong.

One might be sceptical of MacAskill and Ord's way of defending the dominance principle. If we are truly concerned about mitigating moral risk, it might seem that prudential reasons should not factor into our deliberations about the choice-worthiness of options.

I am sympathetic to this concern, and I critique MacAskill and Ord's defence on these grounds in other work.²¹ But there is another way to respond to the demandingness/conservativeness objection, suggested by Dan Moller.²² On Moller's view, although it is only moral reasons that determine the choice-worthiness of our options, we are not always obligated to avoid moral risk by avoiding dominated options. Some may say we never need to take moral risk into account and that it is always permissible to take moral risks. Others may say that whenever there is the slightest moral risk, we must refrain from acting – that it is never permissible to take moral risks, no matter the personal costs. Both these views seem too extreme. Instead, we can adopt a moderate position, which says we have moral reason to avoid moral risk, variable in its strength, but not necessarily a decisive one, since it may be overridden by other considerations depending on the circumstances. This response entails that in certain situations, prudential reasons may override a pro tanto reason to avoid moral risk. It thereby prevents the dominance argument from being overly demanding or conservative.

Again, this kind of response does not undermine my dominance argument against the numbers sceptics’ position. There are no circumstantial considerations that would override a pro tanto reason to avoid moral risk in a situation like Drug, where all people in need of saving are strangers. Our moral reason to avoid moral risk, then, becomes a decisive one. We ought to save the many just in case the numbers sceptics are wrong.

4.2 Other competing principles

The dominance argument in favour of SGN goes through only when we compare only SGN and the numbers sceptics’ position. There are, however, other competing principles which offer alternative guidance when faced with a situation like Drug, such as giving each person an equal chance of rescue by tossing a coin. Initially, it may seem that comparing SGN and EC would yield the same moral outcome for both options (saving the many or the few) as comparing SGN and the numbers sceptics’ position. This is because both options are permissible under EC as well.²³ However, although both options are potentially permissible under EC, EC implies that it matters how you arrived at a given option. EC is concerned with giving each person an equal chance of survival by tossing a coin, or through some other procedure that ensures fairness. In other words, although both options may be permissible, there is a prerequisite, namely that one arrived at that option through a decision that ensured each individual had an equal chance of survival.

If we simply choose to save the many, although we do rightly by SGN, we do wrongly by EC, because we have chosen to save the many without giving an equal chance of rescue to the few. If, instead, we choose to toss a coin, although we do rightly by EC in giving each person an equal chance of survival, our act could end up being wrong on account of SGN, which holds that we ought to save the greater number regardless of which way the coin lands. There is no option that yields an outcome that is good or permissible on both theories, and therefore, no option that weakly dominates the other. This is why I argued that the EC interpretation of Taurek is wrong before outlining the dominance argument against numbers scepticism.

However, even if we assume that the EC interpretation of Taurek is wrong, the EC view is still a possible view about what one ought, objectively, to do when faced with a choice between saving different numbers of lives. Moreover, it seems that someone who has credence in the numbers sceptics’ view and some credence in SGN should also attach some credence to the EC view as well. Not only that, there are other principles out there, such as determining which side to save through a weighted lottery of some sort.²⁴ One might even have some credence in the view that we are, in fact, obligated to save the few. Given that there exist these alternative competing principles against SGN, the dominance argument seems to fall through. When we apply the dominance argument to any agent who attaches some credence to these other principles, as they should do, the dominance argument doesn't work in favour of saving the many, as it only has application when none of the theories to which an agent attaches credence classify saving the many as impermissible. Under the EC principle and the weighted lottery principle, saving the many without what each principle considers to be a fair decision procedure would be impermissible, and so we cannot say that saving the many ensures that the agent acts objectively in all possible states of the world.

To respond, the dominance argument is intended to be directed against the numbers sceptics’ position that we are permitted to save either the many or the few. Philosophers such as Anscombe, Munoz-Dardé, Setiya, Doggett, and, as I have argued, Taurek, all claim that we are permitted to save the few without an appeal to a fair decision procedure. The dominance argument shows that we should reject the implications of their conclusion, even if we are almost entirely convinced by their arguments. All things being equal, we ought never just save the few. That is to say, we are not permitted to simply choose to save the few without appealing to some other principle in favour of saving the few. Just saving the few should never be an option. If the choice is simply between saving the many or the few – as in a case where we have no time to toss a coin or run a lottery – we ought to save the many, as this is the only option that is guaranteed to be objectively permissible out of the two options. This is the case even if our credence in the numbers sceptics’ position is extremely high.

So, the agent should dismiss the option of just saving the few. However, it still seems that she ought to have some credence in other principles such as the EC principle or weighted lottery principle. What should the agent, having some credence in these competing principles, do?

One way of going forward would be to maximise expected choice-worthiness (MEC), which is a popular theory of decision-making under moral uncertainty.²⁵ It is widely accepted that, in cases of descriptive uncertainty, one should choose the option which maximises expected utility. According to MEC, in situations of moral uncertainty, one should choose the option with the greatest expected choice-worthiness. What you ought to do, then, would depend on the degree of credence you have in each principle and the degree of wrongness that each principle attributes to an action and its possible outcome.

What the agent should do in rescue cases would depend on the degree of credence the agent has in each competing principle and the degree of wrongness each principle attributes to the possible outcomes. If the ratio between the many and the few is small (e.g. 1,000,000:1,000,001), the agent may opt to toss a coin or run a weighted lottery rather than save the many. This is because the degree of wrongness a fair decision principle would attribute to saving the many would be very great, because a large proportion of people are denied a fair chance. If the ratio between the many and the few is very high (e.g. 1,000,000:1), the agent may choose to save the many, as the degree of wrongness SGN attributes to saving the few would be great.

This approach of maximising expected choice-worthiness, though attractive, faces what is known in the moral uncertainty literature as the problem of intertheoretic value comparisons. ²⁶ In order to determine the expected choice-worthiness of an action, there needs to be some non-arbitrary basis for comparing degrees of moral value or disvalue attributed to this option by competing moral theories. But although it is possible to compare value differences within a theory, it seems impossible to do so across different theories, as there is no common scale shared by both. Much of the literature on the topic of moral uncertainty aims to provide a solution to this problem, but so far, all the proposals face compelling objections, and some opponents of moral uncertaintism suggest that the problem is insoluble.²⁷

Another way to go forward would be to go with the principle you have most credence in, as this is the most common way we approach decision-making in ethics.²⁸ Having dismissed the numbers sceptics’ position as a morally permissible option, the following step would be to go along with the next principle you think is most likely to be correct, be it saving the many, tossing a coin, running a weighted lottery, or any other principle. How convincing each principle is and how much credence we ought to assign to them goes beyond the scope of this article, but I assume that most people have a higher credence in the belief that we ought to save the many considering our common-sense intuitions about Drug-like cases. This is especially the case as any sympathy we have towards these alternative principles typically vanishes once numbers are inflated on one side. So, it seems plausible that most people would have a higher credence in SGN than other competing principles. Given this, even if you are almost certain that the numbers sceptics are right, and even if you hold some credence in other competing principles, you ought to save the many.

5 Conclusion

I have argued that even if we are almost completely persuaded by the arguments made by numbers sceptics, we should not accept their stance that we can just pick either group to save. This is because SGN will weakly dominate the numbers sceptics’ view in all possible states of the world. I also suggested that once we reject the numbers sceptics’ position, we go along with the theory in which we hold the highest credence. Given our common-sense intuitions, I hold that most people would lean more heavily towards SGN than any other principle, and so, even if we are almost convinced by the numbers sceptics, we should save the many.