Section 1

Apples have been left on the road. A car is approaching. You can either save (a bag of) five apples or, if you turn the other way, you can save a single apple. There are no relevant differences between these apples. They are of the same type, Braeburn, and similar in size. None of them will be a cure for cancer nor does any of them host deadly bacteria. They are all just apples. Apples, we agree, are a good thing. They are healthy; they taste nice. You and yours like apples. If one apple is a good thing, five apples are an even better thing. (There are limits. 500 apples are hard to carry and would create problems of storage and distribution. No such issues arise in our case.) All clear. You save the five. You achieve something that, in some sense, has higher value or higher value for you and yours than any alternative. Once saved, you can peel the apples and slice them, you can put them into boiling water or into the oven at 200 degrees. You can make apple strudel or apple compote. You saved them. They are yours.

The number of apples counts but the number of people should not count. Why not? Wouldn’t it be better to save more rather than fewer? We said that apples are a good thing. Aren’t humans, who are more interesting and more lovable than apples, also, in some sense, good things so that saving more of them would preserve more of value than saving fewer?

We have to relate to people differently than to objects. For me, this is the core insight of Taurek’s paper – people should not be treated like objects. Utilitarians treat people as if they were things, much more valuable things than apples, no doubt. They save the larger group of people on grounds similar to why you saved the larger group of apples. For Taurek, this is demeaning and wrong. To use strong terms, the objectification of human beings dehumanizes them. Taurek tells us that objects and people demand different responses from us. Why is this and what does it mean to relate to people differently than to objects?

One important question in moral deliberation – not the only one – is how events affect people. Events that matter either harm people or benefit them. They may be good for them or bad for them. This idea does not yet lead us beyond what is true for objects. Objects can be harmed or benefited. Being run over by a car is bad for a person but, I think, it is also bad for an apple: it destroys it. The crucial difference between harming an apple and harming a person is that the person minds and the apple does not. It does not mind, because it can’t. We can try to imagine what it is like for a person to be hit by a car. If, in contrast, one would shudder at the thought of watching an apple being peeled, one’s attitude is comical. (Remember “Annoying Orange”? “Hey apple!”)

This first point is about the focus of moral thought: people. However, it is not what we focus on but how we do so which is important for ethics. Only the latter generates a difference to utilitarian thinking. Beings who can register their own evaluative condition are objects of moral concern. (Things which cannot register their own evaluative condition can only be the object of moral concern indirectly. The Grand Canyon, philosophers have pointed out, would not mind being filled with concrete.) People as well as animals register their condition by noticing harms and benefits. They see things as being good or bad for them. Empathy with such beings will take the form of seeing things from their point of view. What matters is not what is good or bad in an impersonal sense – such notions, if important at all, will enter moral theory only at a later point – what matters is that things can be good or bad for people and that, via the faculty of empathy, we can see things from their side. Using empathy, we encounter a conflict in situations in which we can save some but not all. Saving the few is good for each of them but bad for each of the many; saving the many is good for each of them but bad for each of the few. So, there are considerations on both sides, and there is not yet a way to negotiate the conflict.

Building on this point, Taurek wants to exclude considerations from moral thought that characterize utilitarianism. People and other animals are able to register harms and benefits. Groups of people do not experience what is good or bad for them in the same way. The threat to the many is a set of threats, one to each of the many. If each of a group of five might suffer, let us say a broken arm, there is no one who would suffer five broken arms. The first point – our moral concern focusses on people via empathetic engagement – should make the second point plausible. Individuals count, groups of individuals don’t.

We are at the crucial point of Taurek’s anti-utilitarian ideas, the exclusion of sums of suffering. I emphasized the claim that moral thought as far as it deals with harms and benefits starts with empathy. I can imagine what it would be like to suffer a broken arm. However, I cannot imagine (in the same way) what it would be like to be a group of five and suffer five broken arms. If seeing things from another person’s point of view is essential to moral thinking, we have motivated the idea that sums of suffering are not part of moral thought.Footnote ¹

There are two ways to support this view further. One is metaphysical, the other normative. The first idea denies that there are sums of sufferings. Taurek was attracted to this idea. In his reply to Parfit, he writes, “I suspect the presence of a metaphysical fiction. To me pain and suffering are magnitudes that cannot be added or summed across individuals’ (Taurek Reference Taurek2021, 313). I find this move less persuasive. If I have a headache on Monday, Tuesday, and Wednesday, there is a sum, the three headaches all had by me at various times. (Summing across a person must be allowed as a person is a proper object of empathy and a person’s sum of suffering matters.) If three of my colleagues have a headache on Monday, there is, I would like to say, a sum, three headaches all on Monday suffered by three people. So, I do not think there are strong reasons to deny sums of harms when they affect different people given that we allow sums of harm when they affect one person at different times. We can, however, deny that such sums are morally relevant. This brings me to the second, normative, point raised by Taurek: allowing sums of harms to matter morally would lead to implausible moral conclusions. Think of a situation in which the sum of small harms, were it morally relevant, would outweigh a big harm. In the following quote, Taurek sees himself as part of the bigger group and you, in this example, would suffer the big harm. “… to my way of thinking it would be contemptible for any one of us in this crowd to ask you to consider carefully, ‘not, of course, what I personally will have to suffer. None of us is thinking of himself here! But contemplate, if you will, what we the group, will suffer. Think of the awful sum of pain that is in the balance here! There are so very many of us’. At best such thinking seems confused. Typically, I think, it is outrageous” (Taurek Reference Taurek1977, 309).

In calling this way of thinking “outrageous,” Taurek appeals to our moral sensibilities. Not everyone might share them, and even if everyone did, this would not be the end of the debate. A utilitarian could, for example, capture the normative implications of this sensibility in axiological terms. The value of sums could increase with increasing numbers of sufferers and it could approach asymptotically a fixed value which might well be smaller than the value of the big harm.Footnote ² (The same harm would then differ in its moral significance depending on how many other people are already suffering it.)

Taurek objects to utilitarianism as far as it supports moral aggregation, i.e. morally relevant sums of harms or benefits. He argues that ethical thinking (as far as well-being is concerned) does not start with impersonal value but with the empathic engagement with people and with what is good or bad for them. This, he thinks, supports the idea that only individuals and not groups count morally. He supports this view further by showing how moral aggregation might lead to implausible normative claims, like that one person ought to take on a big burden so that many others do not have to take on much smaller burdens. If ethical reflection started with impersonal value, we would treat people as if they were valuable objects. Such an approach, he argues, fails to capture what moves us morally. What difference would it make in a world like ours which is full of people already if he saved one or five? “If it were not for the fact that these objects were creatures much like me, for whom what happens to them is of great importance, I doubt that I would take much interest in their preservation. As merely intact objects they would mean very little to me, being, as such, nearly as common as toadstools” (Taurek Reference Taurek1977, 307).

I have outlined Taurek’s negative claim, the denial of moral aggregation. In a slogan, sums of harms and benefits don’t count (if they range across more than one person). There is conceptual space between the claim Taurek is famous for, namely that numbers don’t count, and the claim I have outlined here, namely that sums don’t count. Numbers may count, even if their sums do not, if we look at them from a different perspective.

Before I come to Taurek’s positive thesis – decide conflict cases by a lottery – it might be worth looking at instances of views which support his negative claim. I will look at three prominent supporters: Rawls, Korsgaard, and Scanlon.

Rawls famously objected to utilitarianism that it treats groups as if they were one person, thereby violating what he called the separateness of persons. This aligns with Taurek’s claim that individuals and not groups have a morally significant point of view. To use one’s membership of a group and its constructed point of view – we would lose five times what you would lose – is, both Rawls and Taurek agree, morally dubious. Taurek’s point, moral thinking needs engagement with how things register from people’s perspective and there is only a constructed but not a phenomenal point of view for groups, provides some justification for the idea he shares with Rawls.Footnote ³

Ethical thinking, Taurek said, does not start from what is good or bad, it needs to start from what is good or bad for people. Korsgaard has argued for a similar view. “I believe,” she says, “that nothing can be important without being important to someone – to some creature, some person or animal” (Korsgaard Reference Korsgaard2018, 9). Things gain moral significance because they matter to beings with a point of view. Taurek’s point – think about how things affect people – is presented as the axiological idea that goodness needs to be built on what is good for creatures. “I think there are things that matter because there are entities to whom things matter: entities for whom things can be good or bad, in the sense that might matter morally” (Korsgaard Reference Korsgaard2018, 16.f).

Taurek’s negative thesis is a central feature of Scanlon’s contractualism; he calls it the individualist restriction. “The justifiability of a moral principle depends only on individuals’ reasons for objecting to that principle” (Scanlon Reference Scanlon1998, 229). It does not depend on aggregated harms or benefits. Scanlon’s justification of the individualist restriction is normative rather than metaphysical. This matches how I presented Taurek’s claim; it also shadows one of Taurek’s reasons for adopting this restriction. “A contractualist theory, in which all objections to a principle must be raised by individuals, blocks such justifications [which would appeal to sums of benefits or harms] in an intuitively appealing way. It allows the intuitively compelling complaints of those who are severely burdened to be heard, while, on the other side, the sum of the smaller benefits to others has no justificatory weight, since there is no individual who enjoys these benefits” (Scanlon Reference Scanlon1998, 230).

People are, no doubt, important. If we understand this importance in terms of value, in particular, in terms of value to be promoted, there won’t be a sharp distinction between how we treat objects and how we treat people. In my view, Taurek rightly observed that thinking of people as valuable objects does not match our moral sensibilities. The importance of people needs to be understood differently. They are owed respect and concern. Their value, if we want to talk like this, needs to be honored and not promoted. This breaks the uniform consequentialist line and delineates people and all creatures who have a point of view, as playing a different role in ethical thinking than if they were regarded as valuable objects.Footnote ⁴

Section 2

Taurek makes a tentative suggestion what he would do when faced with the choice of saving the many or the few. Empathizing with each of them, “perhaps,” he says, “I would flip a coin” (Taurek Reference Taurek1977, 303). Why? Because “… it would seem to best express my equal concern and respect for each person” (ibid.). I have removed his hesitation and call this Taurek’s positive thesis.Footnote ⁵

In this section, I will set out Taurek’s positive claim – we should use a lottery – within the framework of an Aristotelian theory of distributive justice which I will call a theory of fairness. In Book V of the Nicomachean Ethics, after introducing general justice as lawfulness, whereby the scope of law extends to all the virtues, Aristotle turns to special justice which concerns matters of distribution. He tells us that a just or fair distribution is such that the value of what is distributed will be proportional to the value or moral worth of those who receive the good. “What is just will also require at least four terms, with the same ratio between the pairs since the people A and B and the items C and D involved are divided in the same way. Term, C, then, is to term D as A is to B, and taking them alternately, B is to D as A is to C” (NE 1131b, 5-8). For people of equal worth, fairness requires that they receive goods of equal value. John Broome (Reference Broome1984 and Reference Broome1990/91) has developed this idea. Instead of moral worth, he uses the strength of people’s claim to a good which, for a distribution to be fair, require proportional satisfaction. In the special case we are interested in, everyone has a claim of the same strength on being saved, and his principle of fairness is simply to treat equal claims equally. Broome claims that the main argument for his theory of fairness is that it can explain when and why we should distribute goods by lotteries.Footnote ⁶ Taurek’s positive thesis thus finds a natural home in Broome’s theory of fairness. Let us see how this justification of lotteries works.

If a good is indivisible and there are two people with equal claims on it, the only way to treat them fairly is not to distribute the good. Equal claims would then be treated equally as both claims remain equally unsatisfied. However, we see that distributing the good would be a Pareto improvement, i.e. it would be better for one person without making anyone worse off. Being concerned about each of the people involved, Taurek would save someone. “I would not like to see any of them die” (ibid.), he says. A lottery brings some fairness into a situation which, if we save someone, will be inherently unfair. The lottery is not ideal in terms of fairness – saving no one would be – but it is fair to an extent because it means treating people equally in the sense that each gets the same chance of being saved. In such conflict situations, lotteries express positive concern (one should not withhold the good) whilst also being second best in terms of fairness: they treat people equally in a sense. Admittedly, they also treat people unequally as far as they bring about an unfair distribution of the good.

We have been talking about a situation in which one can save either one out of two. An equal chance lottery shows equal respect. It is the best thing we can do as long as we distribute the good, which is something we should do for fairness-independent reasons. At this point, Broome and Taurek part company. Broome brings in a utilitarian account, according to which more people count for more. By seeing unfairness as a bad thing for each person he suggests a weighing procedure between well-being-related considerations on the one hand and fairness considerations on the other. The fairness of holding a lottery will then be weighed against the expected loss of life that holding a lottery will bring about when compared with saving the bigger number. The bigger the number difference between the groups the bigger this loss will be. There will be a point at which well-being considerations outweigh the fairness a lottery would bring with it. For Broome, it has already been reached when we compare a lottery between saving one and saving five.Footnote ⁷ This lottery has an expected value of three lives saved, two fewer of what we could achieve by saving the five. This advantage of saving the bigger number compensates, he thinks, for the fairness loss that arises because we denied people an equal chance.

Taurek, we know, rejects these utilitarian considerations. But we can use Broome’s theory to explain his intuition why an equal-chance lottery “seems best to express equal concern and respect.” Holding a lottery is fair to an extent; it gives everyone the same chance. It is also unfair to an extent as the resulting distribution in which one person has the good and the other does not violates the principle to treat equal claims equally. We could satisfy the fairness requirement only by withholding the good. This violates the equal positive concern Taurek has for the people. Taurek told us that sums of losses are morally irrelevant. If this is so, then increasing the number difference between the groups will not change his support for distributing the good by a lottery on grounds of fairness. When asked whether he would flip a coin when he could save either one or fifty, he says, “I cannot see why and how the mere addition of numbers should change anything” (Taurek Reference Taurek1977, 306). He continues, “It seems to me that those who, in situations of the kind in question would have me count the relative numbers of the people involved as something in itself of significance, would have me attach importance to human beings and what happens to them in merely the way I would to objects which I valued” (ibid.). He could not see why and how increasing number differences changes anything. In the next section I want to explain why and how it might change things.

Section 3

There are two ways in which fairness matters in the saving-from-harm scenarios we are considering. One is, do we give each person an equal chance of being saved? Fairness requires equal treatment of equal claims and giving them the same chance would be a way of treating them equally. The other is, do we give each person an equal amount of the good that we distribute? Fairness would require us to do this in equal-claims cases. When we considered saving one of two and we could save either, but not both, the second question is answered negatively. They do not get equal amounts; one gets the good and the other does not. The unfairness is the same whether we save one or the other. This is why the first aspect, giving them the same chance, is decisive. The unavoidable unfairness which comes in equal measures whoever we save is mitigated by giving each of them the same chance and, thereby, satisfying the fairness requirement to an extent.

When we look at the few and the many things stay the same in one respect but change in another. Giving everyone the same chance remains a relevant way of treating them fairly. However, when we look at the distribution of the goods achieved, it might matter whether we save the few or the many. Fairness might require us to prefer one distribution over another. The more equal a distribution is in equal-claims cases, the fairer have we distributed the good.Footnote ⁸

Measuring inequality is a highly technical area.Footnote ⁹ My aim here is to explain how plausible measures of inequality will favor saving the many. It is not my aim to defend the ways of measuring which provide this result rigorously. However, I want to show that widely used and plausible measures will have this result. I will consider a case in which one can either benefit one person or a group of five people.

The basic idea can be explained as follows. If I save the one, we have a distribution in which one person gets a benefit and five get nothing. Let me write this down as [1,0,0,0,0,0]. If I save the five, the resulting distribution would be [0,1,1,1,1,1]. According to some measures, the inequality in these distributions is the same. Take, for example, the sum of the squared distances to the average, i.e. the variance. The average in the save-one distribution is one-sixth and the distance from this average is five-sixths for the person saved and one-sixth for each of the people not saved. In the save-five distribution, the average is five-sixths. One person is at a distance of five-sixth from this average whereas the five others are at the distance of one sixth. So, we have the same set of distances in both cases and if we square the distances and sum the squares we get the same value for both distributions. Other measures look at the two distributions differently. We ask for each situation, what is the total amount of good in this distribution, and how much of it goes to each person. In the save-one distribution, one person gets all the good. We can write this as [100%, 0%, 0%, 0%, 0%, 0%]. If, however, we save the five then there are five people who benefit. We can write it down as [0%, 20%, 20%, 20%, 20%, 20%]. In this way of looking at inequality, saving the five is fairer than saving the one because it leads to a more equal distribution of benefits.Footnote ¹⁰

More generally, we can visualize distributions in terms of a Lorenz curve. The horizontal line orders the people from those who have the least of what is distributed to those who have the most. The vertical line represents the accumulative wealth (wealth, again, in terms of the good distributed). Zero percent of the population will have zero percent of the wealth, whereas all the people will have all the wealth there is to be had in this distribution. If the bottom 10% of the population have 10% of the wealth and the bottom 20% have 20% of the good and so on, then we have a straight line from (0%/0%) to (100%/100%). This is the line of equality: everyone has the same amount of good. If the bottom 10% have less than 10% of the wealth, the distribution curve will, for the first segment, be below the line of equality. If the lowest 10% have 0% of the wealth, the curve stays on the x-axis, thus being the furthest from the line of equality. The further away we get from the line of equality the bigger inequality is. The Gini coefficient tells us how much of the total area below the equality line is covered by the area between the line of equality and the distribution line.Footnote ¹¹

If we save the one person, five-sixths of the population have 0% of the wealth, i.e. the distribution line stays on the x-axis for five-sixths of its length. If we save the five, the distribution line stays on the x-axis for one-sixth of its length and then gradually moves up. The bottom one-third of the population have 20% of the good. The bottom two-thirds have 60% of the good. The Gini index will thus be lower if we save the five than if we saved the one. A lower Gini-index means that the distribution is more equal. Therefore, in equal claim cases, it is fairer (in one sense) to save the many than to save the few.Footnote ¹²

Fairness requires to treat equal claims equally. We said that giving everyone the same chance is a way of treating people equally. This way of satisfying fairness to an extent will be decisive if no fairness difference arises by holding a lottery. We have learnt, however, that if the numbers in the groups we can save are unequal, the lottery may result in distributions that vary in how equal they are. With increasing number differences, this fairness difference increases as well. Think of a distribution in which 100 people have each one percent of the total good, and one person has nothing. This is very close to the line of equality, whereas 100 people having nothing and one person having all of the good has a Gini index of close to 1, a distribution unequal as it gets. This explains the widespread intuition that increasing the number differences diminishes the attractiveness of holding a lottery. If the difference is big, the resistance to a lottery will be strong.

Taurek only recognized one aspect of fairness, namely whether everyone gets the same chance. But his commitment to fairness involves another aspect, namely whether the distribution achievable by the lottery exhibits fairness differences. These aspects need to be weighed against each other. It would be implausible to maintain that only the chance aspect matters. Thus, there is a sense in which the numbers should count for Taurek. We can agree with him that their sums do not count morally, and this was certainly what he wanted to argue for. But his commitment to equal concern and respect is a commitment to saving the bigger number on plausible measures of inequality. We save the bigger number because, given that we do not want to see anyone die, it is the best we can do to treat people with equal claims equally, thereby expressing our equal respect for them. The intuition to save the many is not based on the idea that more of a good must be better than less of it. Taurek would ask, better for whom? The intuition that we should save the bigger number is based on fairness. Why should all the good go to one person when it can be spread more evenly? Given all the good to the one is unfair. True, in the situation we are considering a more even spread can only be achieved because we can choose in a way so that more benefits are available. Nevertheless, it is not the number of benefits that moves us, it is our commitment to fairness.

Section 4

I end by placing this contribution within recent discussions of number skepticism. We should distinguish Taurek’s claim that sums do not count – because if they did, we would treat people like we treat objects – from his denial that we should save the bigger number. The first idea I call anti-aggregationism, sums of harms or benefits are not morally relevant. And in what follows I will use the term “number scepticism” as referring to a denial of the claim that we should save the bigger number.

As I have presented Taurek, he is a limited number skeptic. Sometimes we should save the bigger number for reasons of fairness relating to the final distribution of goods, at other times fairness demands that we hold an equal chance lottery. What we should do depends on which fairness consideration is stronger, the equal-chance aspect on the one hand or the risk of a distribution far from equality on the other when we could achieve a more equal distribution.Footnote ¹³ In this way, Taurek can account for the widespread intuition that with increasing size of numbers their difference matters less. Take a case in which we can save either 100 people from harm or 101 different people from the same harm. Like in the case in which we can save one out of two but not both, there is almost no difference regarding the equality achieved by our two options. (Whereas in the one-out-of-two case both resulting distribution are equally unfair, in the 100–101 case both distributions are almost equally fair.) In such a case, the chance-aspect of fairness will be stronger, and we should hold a lottery.Footnote ¹⁴

Compare this with a different attempt to account for a related phenomenon, namely that in the big-number case, i.e. the case of 100 versus 101, we do not have to save the bigger number as both options are permissible. “It is plausible that it is permissible to save the 100, even though there’s more requiring reason overall to save the 101” (Pummer Reference Pummer2023, 54). For Pummer, what he calls requiring reasons combine, i.e. sums of harms and benefits matter. But there are also what he calls individualist permitting reasons (which, he says, can undermine requiring reasons). “It is plausible,” Pummer says, “that the individualist permitting reason to save each of the 100 together constitute a sufficiently strong permitting reason to save the 100 instead of the 101” (ibid.). Taurek’s explanation of why we do not have to save the bigger number in this case, is simpler and gets by without Pummer’s distinctions between distinct kinds of reasons (which need to be argued for on separate grounds).Footnote ¹⁵

Like me, Lang and Lawlor (Reference Lang and Lawlor2016), see a tension between Taurek’s commitment to holding a lottery and his number skepticism. I said there is a tension because fairness has two aspects and one of them, coming close to an egalitarian distribution, speaks in favor of saving the bigger number on plausible measures of inequality. Lang and Lawlor construct the tension they see differently. They introduce the idea of a “super-subject”, one that would be able to experience sums of harms. Taurek (like everyone else) denies that there is such a super-subject. So far, so good. They then suggest that Taurek’s suggestion that holding a lottery would be fair also requires something like a “super-subject”, or, at least, an “interpersonal perspective”. “Our claim is that the conceptual apparatus that he needs to make EGC [the rule to equalize greatest chances] intelligible and important is exactly the same conceptual apparatus as that which is needed to make SGN [the rule to save the greatest number] intelligible and important” (L&L 2015, 304). I am not convinced: I don’t detect a tension in a view which holds that fairness is important, but sums are not. One can deny moral aggregation whilst making moral judgments, for example, those based on fairness. (In other words, anti-utilitarianism is not contradictory.)

In a recent article Eric Zhang argues that saving the bigger number is compatible with Scanlon’s individualist restriction. We can, he argues, justify saving the bigger number to the one who will not be saved by a principle that cannot be reasonably rejected. The principle is one of equal consideration. Let us apply this principle to cases in which we can either save one person or two other people. Saving the one means giving up saving two people from the same harm, whereas saving the two would mean giving up saving one person. Equal consideration tells us that we should not give up more for one person than we would for any other person. However, saving the one requires a bigger sacrifice than saving the two does. Therefore, equal consideration speaks against saving the one. Each of the two could raise a legitimate complaint. The complaint would be based on the principle of equal consideration. “Why are you willing to save A at the cost of two lives but no more willing to save me at the cost of one life?” (Zhang Reference Zhang2024, 497).

Is there a morally relevant difference between counting costs and counting gains? Whether we say that we produce more benefits when saving the many or whether we say there would be a higher cost when we save the few are two ways of looking at the same thing. Zhang points out that in looking at losses there is a sense in which we satisfy the individualist restriction via the principle of equal consideration. This principle allows for value aggregation. So, Zhang’s position is that value aggregation can be excluded as a direct justifying consideration but is allowed as an indirect adjudicating consideration. “An individualist approach bars aggregation at the level of justification but not at the level of adjudication” (Zhang Reference Zhang2024, 483). Once we admit that saving more lives is better than saving less lives – this is what Zhang calls axiological aggregationism – there is still conceptual space to stop short of utilitarianism. We need to add that, sometimes, we should not do what would have better consequences.

Zhang’s principle of equal consideration accepts axiological aggregation. Taurek rejects any such principle. If the principle to treat equal claims equally cannot be reasonably rejected, and why should it be, Taurek’s limited number skepticism will allow for saving the bigger number when we deem it appropriate. There is no need, then, to let utilitarian thinking in by the back door when one wants to satisfy Scanlon’s individualist restriction.

There is a contribution that, in a way, comes close to what I have been arguing for in this paper. Hsieh, Strudler, and Wasserman (Reference Hsieh, Strudler and Wasserman2006) argue that a commitment to equality supports saving the bigger number. In the cases we are considering, “You should,” they argue “come as close to an equal division as possible. Going to the island with five people brings you closer to equality than would going to the island with one person” (HSW 2006, 353.) They also point out rightly “…that failing to save the greater number is a worse wrong when there is a comparatively large disparity between the size of groups to be saved, for example, that it is a worse wrong when the rescuer chooses one rather than five than when he chooses four rather than five.” I have used the same fact about equality when I said that increasing number differences, for example comparing a 1-or-5 case to a 1-or-50 case, increases the pressure to save the bigger number on fairness grounds.

I agree with the core idea put forward by HSW. My proposal differs in three aspects. First, I explain why relative measures of inequality tell us that the resulting distribution is more equal when we save the bigger the number as compared to when we save the one. Lorenz curves represent the percentages of the overall good that go to the various groups of people. Secondly, this explanation shows a limitation of this approach. Not all measures of inequality will deliver this verdict. Statistical variance was my example of a measure that would violate the axiom of scale invariance which is characteristic of relative measures of inequality. On relative measures, blowing up a balloon, i.e. increasing the provision of some good, will leave inequality the same. On absolute measures, blowing up a balloon will increase inequalities.Footnote ¹⁶ I said that relative measures are plausible and, thus, they should be available to a moral theory which develops Taurek’s view. Thirdly, I embed equality in a theory of relational fairness. This is a significant difference to their proposal.Footnote ¹⁷ HSW limit the concern for equality to the people affected by one’s decision. However, if the concern were simply that of increasing equality in a society, the restriction to those affected by one’s choice seems arbitrary. Furthermore, this broader concern for equality overall might speak against saving the bigger number from a harm. Think, for example, of short-sightedness. If this harm is widespread then increasing the number of perfectly sighted people by protecting people from this harm would increase inequality. Aren’t these broader concerns simply irrelevant for how to decide? Embedding equality in a theory of fairness explains why this is so. The requirement to treat the people one interacts with fairly can neglect the effects of one’s action on overall equality.Footnote ¹⁸

Munoz (Reference Muñoz2024) argues that the basic egalitarian premise, each person counts for one, does neither lead to utilitarianism, as Parfit thought, nor does it support Taurek’s view or the view of HSW. The basic egalitarian premise needs to be supplemented with further claims to deliver normative conclusions. Against Parfit’s move from each counts for one to more count for more, he points out that both a majority rule and a rule requiring unanimity would satisfy the claim that each counts for one. I agree with Munoz. However, once we have embedded a concern for equality in cases of claims of equal strength in a theory of fairness, the foundations for saving the bigger number have been laid. Munoz’s criticism of HSW, namely that the idea of “saving people equally” is not a simple consequence of the basic egalitarian commitment that each person counts the same, does not (and is not meant to) affect the proposal I have offered.

Section 5

Taurek was not a skeptic about morality. He argued that if we take sums of benefits or harms to be morally relevant, we are led astray in our ethical thinking: we would treat people as if they were objects. This criticism, I feel, presupposes that, for him, there are better ways of ethical thinking. The aim of his article was to provide a critique of utilitarianism. In terms of providing a positive ethical theory, we were left with his suggestion that flipping a coin seemed to him to be the best way to show equal concern and respect. In this paper, I pursued this suggestion. The aim of showing equal respect to equally deserving people fits well with the idea of fairness. Fairness requires to treat equal claims equally and, thereby, we show equal respect. Fairness also supports Taurek’s idea of holding a lottery. Giving each person an equal chance is, as I have said, a way of treating them equally. It is not the only or the best way to be fair. Giving everyone no chance to get the good and, thus, withholding the good would satisfy the demands of fairness fully. This would be, however, incompatible with having equal positive concern for each person. Given this concern, we must use and may not waste resources that others need. So, we are left with an equal-chance lottery. In recognizing that withholding the good would be fairer, we recognize that there are two aspects of fairness that need to be considered, the chance aspect and the equality of the final distribution. The former will always speak in favor of holding a lottery. The latter is, given relative measures of inequality, sensitive to differences in the number of people we are saving. We will need to judge which aspect of fairness is more important in any given context. If the number differences are big enough, the second aspect will dominate. Taurek’s suggestion developed into a theory of fairness has the resources to explain why, in some cases (though not, for example, in the big-numbers-small difference case we considered earlier), we ought to save the bigger number: Look at the many people. It would be unfair to leave them with nothing and give all to one person.

I do not know whether Taurek had a mustache, though I doubt it. I know that he thought he had made a strong case for the claim that numbers don’t count. And he might well be right that they don’t count in the only way he considered, namely as sums. Equal respect and concern matters. It might well be how we ought to relate to people who are not closer to us than being contemporaries. Equal respect demands that we treat people fairly. To treat them fairly when they have equal claims and we are concerned, we need to distribute resources as equally as we can. Only if we achieve this, have we been fair or, if you want, fair to everyone involved. A more equal distribution, on plausible measures, is achieved by saving the bigger number. This speaks in favor of doing so. Taurek did not see this; if he had, I think, he would have agreed. It renders his ethical outlook more plausible, and it finally breaks a stick he has been beaten with many times.