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# Prioritarianism

## Summary and Keywords

Prioritarianism is a principle of distributive justice. Roughly, it states that we should give priority to the worse off in the distribution of advantages. This principle has received a great deal of attention in political theory since Derek Parfit first introduced the distinction between egalitarianism and prioritarianism in his Lindley Lecture, published in 1991. In the present article, prioritarianism is defined in terms of a number of structural features of the principle. These structural features are also used to distinguish between this principle and other distributive principles such as utilitarianism, egalitarianism, and leximin. Prioritarianism is mostly discussed as an axiological principle that orders outcomes with respect to their (moral) value, but it is also clarified how it can be incorporated in a criterion of right actions, choices, or policies. Furthermore, different aspects of the principle that need to be further specified to arrive at a full-fledged distributive theory are discussed, including the weights that give priority to the worse off, currency (what kind of advantages should be distributed), temporal unit (the temporal span in which one has to be worse off in order to be entitled to priority), scope (whether the principle applies globally or only domestically, and whether, for example, future generations and non-human animals are covered by the principle), and risk. For each aspect, different possible views are distinguished and discussed. Finally, it is discussed how prioritarianism may be justified, for example, by outlining and discussing the argument that, unlike certain other distribution-sensitive principles such as egalitarianism, prioritarianism is not vulnerable to the so-called “leveling down objection.”

# Introduction

Prioritarianism is a principle of distributive justice that gives priority to the worse off in the distribution of advantages. Roughly, it states that advantages matter more the worse off the individual is to whom they accrue. This means that prioritarianism is a distribution-sensitive principle, that is, it is sensitive to the way in which advantages are distributed among individuals rather than just concerned with the overall level or sum of them. In this respect, prioritarianism is similar to, for example, egalitarianism, but different from utilitarianism.

The term “prioritarianism,” or rather the “priority view,” was coined by Derek Parfit (1991) in his seminal Lindley Lecture, titled Equality or Priority?1 Here, Parfit distinguished between egalitarianism and prioritarianism and argued that, while they have often been confused, they are in fact distinct principles in that they have distinct implications and justifications and are susceptible to different objections. To exemplify how egalitarianism and prioritarianism may easily be confused, Parfit considers a case from Thomas Nagel, where Nagel imagines he has two children, one healthy and happy and the other painfully disabled. Nagel considers whether he should move to a city where the disabled child can get special treatment or move to a suburb in which his other child will thrive. Furthermore, he imagines that his healthy child will benefit more from moving to a suburb than his disabled child will benefit from moving to the city. Nagel writes:

If one chose to move to the city, it would be an egalitarian decision. It is more urgent to benefit the second child…. This urgency is not necessarily decisive. It may be outweighed by other considerations, for equality is not the only value. But it is a factor, and it depends on the worse off position of the second child. An improvement in his situation is more important than an equal or somewhat greater improvement in the situation of the first child.

(Nagel, 1979, p. 124)

While Nagel here appeals to the value of equality, Parfit (1991, p. 19) points out that he in fact gives prominence to another concern, namely that it is more urgent to benefit the child who is worse off. And as Parfit argues, these are separate concerns. Equality consists in a relation between different individuals, and to know how important it is to benefit, for example, the disabled child according to egalitarianism, we need to know what levels other people are at. In this sense, egalitarianism is a relational view. Prioritarianism is not in this sense relational. To know how important it is to benefit the disabled child, we need only know how badly of he is.

Why might we think that in distributive justice we should be concerned with priority rather than with equality? One reason could be that there are certain objections to which only egalitarianism is vulnerable. I shall discuss one such objection later. However, for now, consider instead the following from Joseph Raz, in which he suggests that the idea of giving priority to the worse off has a certain intuitive plausibility that the idea of equality lacks:

What makes us care about various inequalities is not the inequality but the concern identified by the underlying principle. It is the hunger of the hungry, the need of the needy, the suffering of the ill, and so on. The fact that they are worse off in the relevant respect is relevant. But it is relevant not as an independent evil of inequality. Its relevance is in showing that their hunger is greater, their need more pressing, their suffering more hurtful, and therefore our concern for the hungry, the needy, the suffering, and not our concern for equality, makes us give them priority.

(Raz, 1986, p. 240)

According to this line of thought, the concern many of us may feel for Nagel’s imagined disabled child is a worry about how badly he fares rather than a concern with whether he is worse off than his sibling is, or for that matter worse off than (most) other people are.

The list of theorists that have been attracted to prioritarianism, in one form or another, includes Adler (2012), Arneson (2000), Holtug (2006, 2010, 2015), Hooker (2000, pp. 55–65), Hyams (2015), McKerlie (2006), Nagel (1991, pp. 63–74), O’Neill (2012), Parfit (1991, 2012), Scanlon (1982, p. 123), Scheffler (1982, p. 31), Segall (2016), Temkin (1993, pp. 247–248), Tungodden (2003, pp. 23–32), and Williams (2012). Critics, on the other hand, include Broome (1991, pp. 216–217), McCarthy (2008a, b), Ord (2015), Otsuka and Voorhoeve (2009), and Tännsjö (2015).

# Structure

I need to be a bit more precise regarding the formal statement of prioritarianism. Prioritarianism comes in different versions, but I shall mostly be concerned with axiological prioritarianism: an outcome is noninstrumentally better, the larger the sum of weighted individual advantages it contains, where advantages are weighted such that they gain a greater value, the worse off the individual is to whom they accrue. More formally, axiological prioritarianism (henceforth prioritarianism) can be represented as follows:

$Display mathematics$

where a1 is the level of advantages of the first individual, a2 the level of the second individual, etc., and f is an increasing and strictly concave function of these individual advantages (see Figure 1). Since the function is increasing and strictly concave, it assigns greater weight to individual advantages the worse off the individual to whom they accrue is (or, more precisely, would otherwise be). A different way of stating this is that according to prioritarianism, advantages have diminishing marginal moral value (which is not to be confused with the claim that, for example, money has diminishing marginal utility).

Figure 1 Moral Outcome Value

Prioritarianism thus resembles utilitarianism in being an additive function of individual advantages but differs in that it weights advantages according to how badly off the beneficiary is. This is what makes prioritarianism a distribution-sensitive principle, whereas utilitarianism is distribution-neutral (as it is only concerned with the overall sum).

Nevertheless, given the structural similarity between prioritarianism and utilitarianism, they share a number of structural features. Both satisfy the Pareto principle, according to which an outcome is better than another if it is better (holds higher levels of advantages) for some and worse for none, whereas they are equally good if they are equally good for everyone. Compare two outcomes, (2, 1) and (1, 1), where the numbers refer to individual levels of advantages. (2, 1) is a Pareto-improvement on (1, 1), and prioritarianism implies that (2, 1) is better because it holds a higher sum of weighted advantages.

Furthermore, both prioritarianism and utilitarianism satisfy strong separability. A distributive principle gives rise to a strongly separable ordering if and only if it implies that the ordering of the advantage level of any subset of individuals is independent of the levels of others (Broome, 1991, p. 69). Roughly, the intuition captured by the separability requirement is that the ordering should not be impacted by unaffected individuals. That is, when comparing two outcomes, we should not allow the levels of individuals who do not have a stake in which outcome comes about to affect the ordering of them. To illustrate, compare the following four outcomes:

$Display mathematics$

Again, the numbers refer to individual levels of advantages. Here, strong separability implies that A is better than B if and only if C is better than D. After all, only the first two individuals are affected in the move from A to B and from C to D, and their advantages in A and C are identical as are their advantages in B and D. Utilitarianism straightforwardly implies that B is better than A and that D is better than C, because B has a higher total of advantages than A and D has a higher total than C. According to prioritarianism, the relative ordering of A and B and of C and D will depend on the exact weight function. However, prioritarianism straightforwardly implies that A is better than B if and only if C is better than D. This is because given the prioritarian function, only the contributions of the first two individuals differ when comparing, respectively, A and B and C and D.

However, prioritarianism and utilitarianism differ in that only prioritarianism satisfies the Pigou-Dalton principle of transfer, according to which, if the sum of advantages remains constant, an outcome is improved by a transfer from a better off individual to a worse off individual, as long as their relative positions are not reversed. Thus, a change from (5, 1) to (4, 2) is a change for the better. What the Pigou-Dalton principle does, then, is to introduce a concern for distribution in the ordering of outcomes, as opposed to the indifference between different distributions of a fixed sum of advantages we find in utilitarianism. Prioritarianism, of course, satisfies the Pigou-Dalton principle, since the gain to the second individual is more important than the loss to the first individual in the example above.

Like prioritarianism, egalitarianism also satisfies the Pigou-Dalton principle. However, the manner in which egalitarianism introduces distribution sensitivity is different, as also pointed out above. Egalitarianism is a relational view in a way that prioritarianism is not. Consider the question of whether an increase in an individual’s level of advantages from n to n+1 increases the value of an outcome, holding everything else constant? According to prioritarianism, it does. Indeed, this is implied by any distributive principle that satisfies the Pareto principle. However, to know whether an increase in advantages is also an increase in equality, we need to know what levels other people are at. If, for example, everyone else is at n+1, then clearly equality is increased, whereas if everyone else is at n, there is rather a reduction in equality. According to egalitarianism, then, we cannot assess the value of an increase in individual advantages independently of the advantage levels of others. This is also why egalitarianism does not satisfy strong separability.

Note, however, that while the concern for equality satisfies neither strong separability nor the Pareto principle, egalitarians may have other concerns in virtue of which their all-things-considered principles may satisfy either or both. Indeed, equality cannot plausibly be one’s only concern since there would then be no reason to prefer (2, 2) to (1, 1)—both are perfectly equal. Minimally, then, egalitarians should also be concerned with efficiency and some combinations of these two concerns, equality and efficiency, satisfy both strong separability and the Pareto principle. Indeed, some combinations may be extensionally equivalent with prioritarianism in the sense that they generate the same orderings (Fleurbaey, 2015, pp. 207–208; Holtug, 2010, p. 177; Jensen, 2003, pp. 101–103; Tungodden, 2003, pp. 30–31). However, even so, egalitarianism and prioritarianism are still distinct theories in that they are committed to different reasons for endorsing this ordering. For example, only egalitarians are committed to the value of equality (Adler, 2012, pp. 364–365; Holtug, 2010, pp. 204–209; but for a different view, see Fleurbaey, 2015).

An important aspect of prioritarianism is of course the weights assigned to advantages. Prioritarianism applies the same weight function, f, to all individuals, which also means that this principle satisfies an important requirement of impartiality, namely anonymity. Anonymity implies that the value of an outcome is not affected by the permutation of advantages over individuals. This means that, for example, (2, 1) is equal in value to (1, 2). Anonymity thus rules out a number of views that would be unacceptably partial, such as the claim that we should attach extra weight to advantages to kings or the aristocracy.

Since the prioritarian weights are what give priority to the worse off, the weights also fix how much priority. We can imagine many different kinds of prioritarian functions. One example is square root, resulting in the following prioritarian principle:

$Display mathematics$

This function assigns a value of √1 = 1 to the first unit of advantages that accrues to an individual, a value of √2 = 1,41 to the first two units, a value of √3 = 1,73 to the first three units, etc. As we can see, the contribution of each further unit is smaller than the contribution of the previous unit, and so advantages have diminishing marginal moral value. Prioritarianism can be seen as a family, or spectrum, of views that all have this structure of gradually assigning less value to further benefits to an individual. At one end of the spectrum, such views can get infinitesimally close to utilitarianism, in that they assign almost no extra weight to individuals who are worse off, and at the other end of the spectrum, they can get infinitesimally close to leximin, which assigns all the weight to the very worst-off individual (and in case the worst-off individual in one outcome is equally as well off as the worst-off individual in another outcome, all the weight is assigned to the second worst-off individual, etc.). Thus, the prioritarian spectrum harbors views that differ considerably regarding levels of priority to the worse off.

This characterization presupposes that leximin is not itself a version of prioritarianism, even though there is a perfectly clear sense in which it assigns priority to the worse off. Further similarities are that, just like prioritarianism, leximin satisfies the Pigou-Dalton principle, the Pareto principle, and strong separability. Nevertheless, there are two respects in which leximin differs from prioritarianism (Hirose, 2015a, pp. 95–98). First, it is not a strictly concave function, as it does not allow for trade-offs between the worse off and the better off. Second, leximin has a relational feature that prioritarianism does not. According to prioritarianism, the value of an advantage to an individual depends only on that individual’s level of advantages. According to leximin, the value of an advantage to an individual depends on the relational question of whether she is worst off, second worst off, etc.

Since prioritarianism covers a wide range of views that differ in the weights they assign to the worse off, there is an issue of how to select a particular weight function. Most prioritarians seem to hold that the weights must be fixed intuitively (Parfit, 1991, p. 20), for example, by reaching a reflective equilibrium between a particular version of prioritarianism and considered moral judgments about cases. Nevertheless, some may object that this particular manner of arriving at a distributive view is too unprincipled. Here, prioritarians may offer either of two answers (or both). First, they may argue that it is a general aspect of distributive views that they cannot be justified independently of the intuitive support they may have. Consider, for example, utilitarianism. Utilitarianism also has a weight function, namely a function that assigns equal weight to equal advantages, no matter the level at which they fall. This function is no more natural or less in need of justification than a particular prioritarian function, and somewhere along the line a justification of either function will have to appeal to intuitions about their implications. Second, perhaps there are independently plausible restrictions that may be imposed on the prioritarian function that favor a particular subset of prioritarian functions. For example, Matthew Adler (2012, pp. 383–399) argues that any such view should satisfy the Atkinson social welfare function.

So far, prioritarianism has been presented as an axiological view that orders outcomes. However, in itself, such a view does not tell us anything about how to act, either as individuals, states, or as some other unit of agency. And indeed, there are a number of different ways in which prioritarianism may be included in a full moral theory. For example, prioritarianism may be part of a criterion of rightness that tells us how to distinguish right acts from wrong. Alternatively, prioritarianism may be considered a specification of the virtue of fairness in a theory of virtue ethics. Even if we restrict ourselves to criteria of rightness, there are different ways in which prioritarianism may be integrated. The (perhaps) simplest version would claim that an act is right if and only if it brings about an outcome with at least as much prioritarian value as any other available act would. This is a consequentialist criterion of rightness, and it simply tells us to bring about as good an outcome as possible, where the value of outcomes is assessed according to axiological prioritarianism.

However, there could also be other ways of including prioritarianism in a criterion of rightness. For example, such a criterion may imply that we should promote prioritarian value, except insofar as doing so would involve violating an agent-relative constraint, for example, killing someone. This would be a deontological criterion of rightness that includes axiological prioritarianism as part of its value theory. Alternatively, a criterion of rightness may conceive of priority in a different manner. Thus, Parfit (1991, p. 20) distinguishes between what he calls “telic” and “deontic” prioritarianism. Telic prioritarianism coincides with what I have called axiological prioritarianism above and concerns the goodness of outcomes. Deontic prioritarianism, on the other hand, assumes that injustice necessarily involves wrongdoing. Thus, it is only when individuals are worse off as a consequence of agency that they can be entitled to priority. On at least one version of this view, being worse off because of one’s natural endowments would not qualify for prioritarian concern (Parfit, 1991, pp. 3–19; see Lippert-Rasmussen, 2006).

# Currencies and Temporal Units

So far, I have been speaking rather loosely about the distribution of advantages. However, prioritarians may differ regarding the currency of prioritarian justice. Most prioritarians seem to consider welfare the appropriate currency, so that we should give greater priority to additional units of welfare to one individual than to another insofar as the former individual has a lower welfare level than the latter (Adler, 2012; Holtug, 2010; McKerlie, 2006; Parfit, 1991). However, this is of course not the only option. In fact, prioritarians may adopt many if not all of the currencies that have been discussed in relation to egalitarianism, such as resources (Dworkin, 1981; Rawls, 1971), access to advantage (Cohen, 1989), capabilities (Sen, 1980), and opportunity for welfare (Arneson, 1989; Vallentyne, 2002).

It may be considered whether each and every currency would render the prioritarian ordering distinctive from that of utilitarianism (Greaves, 2015, p. 4). Consider, for example, money. Assuming that money has diminishing marginal utility, it may be argued that utilitarians would be happy to accept the prioritation function. However, on further reflection it seems implausible to hold that monetary prioritarianism and utilitarianism would generate identical orderings. Consider Sen’s (1997, pp. 16–17) case of a disabled person who, because of a reduced range of opportunities, is less capable of transforming income into welfare than another, able-bodied person is. Because of this difference in their utility functions, utilitarianism implies that it is better to allocate more money to the able-bodied than to the disabled person. Monetary prioritarianism, on the other hand, would not have this implication.

Some of the currencies listed above focus only on the distribution of, for example, money or welfare, whereas others are also sensitive to responsibility. For example, Dworkin’s equality of resources aims to hold individuals responsible for their choices, and resourcist prioritarianism may do the same. Likewise, Arneson’s equality of opportunity for welfare aims to compensate individuals for being worse off than others only insofar as they are worse off through no responsibility of their own, and again, priority of opportunity for welfare may do the same. In fact, Arneson has later come to think that prioritarianism may be superior to egalitarianism as a distributive principle and has developed a version of luck prioritarianism inspired by luck egalitarianism (Arneson, 2000). Luck prioritarianism claims that we should give priority to advantages to the worse off, but only insofar as they are worse off through no responsibility of their own.

The reasons for preferring a particular currency qua prioritarian will often mirror the reasons for preferring a particular currency qua egalitarian. Consider, for example, an egalitarian argument for preferring welfare to income. Suppose two individuals have equal income but one of them has a disability that requires her to buy expensive medicine. Welfare egalitarians will here argue that, while equal in income, these two individuals are likely not to be equally well off in the relevant sense. After all, the disabled individual will have much less money to spend on housing, food, leisure, etc., and so will have worse options and will experience less satisfaction of her preferences, everything else being equal. Therefore, according to welfare egalitarians, we should focus on the distribution of welfare rather than on the distribution of income. The point is that prioritarians may favor welfare for the exact same reason. They may hold that while these two individuals are equal in income, it is more urgent to benefit the disabled individual who has worse opportunities and experiences less satisfaction of her preferences because she is worse off in terms of welfare. Likewise, some prioritarians may want to hold individuals responsible for their choices for the same reasons (some) egalitarians do.

A further question pertains to what may be called the “temporal unit” of prioritarian concern. This is the question of when, exactly, one has to be worse off in order to be entitled to priority. According to time-slice prioritarianism, we should give priority to individuals who are worse off at particular points in time. This implies that, for example, if an individual is now worse off than others, it is more urgent to now benefit this individual than it is to now benefit others. However, suppose that this individual is not now worse off, but was so only five minutes ago. Would she not still be entitled to priority? To cater to this view, we might adopt simultaneous segments prioritarianism, according to which we should give priority to individuals who are worse off in particular temporal segments. Since such segments have a temporal extension that exceeds points in time, this view is compatible with the claim that she is entitled to priority. Nevertheless, however we fix the temporal segments, she may have been worse off at the very end of what is now the previous segment, where we are now at the very beginning of the new segment.

To entertain the view that she may still be entitled to priority, we may instead adopt whole lives prioritarianism. According to this view, we should give priority to individuals who are worse off over their lives taken as a whole. Most political philosophers concerned with distributive justice have assumed that whole lives are the appropriate temporal unit (see, e.g., Rawls, 1971, p. 78). This assumption reflects the view that compensation is possible within an entire life. That is, even if I am worse off at some earlier time in my life, this may be compensated by my being better off at some later time. What matters for the level of priority to which I am entitled is how I fare over my life taken as a whole.

Dennis McKerlie (1997, pp. 296–302; 2013) has nevertheless argued that rather than simply accept whole lives prioritarianism, we should combine this principle with time-slice prioritarianism. He argues that whole lives prioritarianism responds to the overall unity that we find in whole lives. Since individuals are psychologically connected and continuous over time, their lives have an overall unity that make them appropriate temporal units of prioritarian concern. However, since the psychological relations (memory, plans, etc.) that make up this unity hold to a higher degree at a time than over time, McKerlie argues that points in time nevertheless have a special distributive significance. Therefore, he proposes a combination of whole lives and time-slice prioritarianism.

Nonetheless, it has been suggested that this combined principle does not fully capture McKerlie’s point about the weakening of psychological relations over time. Suppose an individual is now suffering and we can compensate him in either five minutes or five years. The psychological relations that unify him over time will be stronger between him now and in five minutes than between him now and in five years. Therefore, arguably, benefiting him in five minutes will provide better compensation. However, neither time-slice prioritarianism nor whole lives prioritarianism implies this, and so neither does the combined view. This suggests that if we are concerned with the degree of psychological unity instantiated in a life, we should rather opt for a prioritarian principle that accommodates the point that compensation gradually decreases as the sort of psychological relations that make up the unity in a life weaken (Holtug, 2010, pp. 308–325).

# Scope

In order to arrive at a full-fledged prioritarian principle, one will need to specify not only the weight function, the currency, and the temporal unit but also the scope of prioritarianism in a number of respects. First, there is the question of whether prioritarianism has global scope or domestic scope only. While many political philosophers have proposed distributive principles for the domestic case (see, e.g., Rawls, 1971), others have argued that our basic principles of justice have global scope. One reason for making the latter claim could be that the reasons that motivate a particular principle of justice in the first place may actually drive us toward global scope (Caney, 2005). Suppose, for example, that we hold a version of luck prioritarianism. If what turns an individual’s being worse off into an injustice, or something that merits compensation, is that this individual is not responsible for being in this state himself, then it would seem that our prioritarian principle should have global scope, everything else being equal. After all, being worse off through no responsibility of one’s own is not a property that applies only to members of one’s own society.

In his Lindley Lecture, Parfit considered the question of whether egalitarianism and prioritarianism differ as to whether they have domestic or global scope. Parfit (1991, p. 17) believes that, unlike egalitarianism, prioritarianism “naturally has universal [i.e., global] scope.” He continues: “if it is more important to benefit one of two people, because this person is worse off, it is irrelevant whether these people are in the same community.” Here, Parfit seems to be making the kind of argument referred to above, according to which the rationale for the principle drives us toward global scope. If what makes it more important to benefit one of two individuals simply is that this individual is worse off, this is a rationale that does not distinguish between the domestically and the globally worse off.

However, arguably, the question of the scope of prioritarianism is more complicated (Holtug, 2009). First, this argument does not explain the alleged difference between egalitarianism and prioritarianism. Thus, by analogy, it may be argued that if inequality has non-instrumental disvalue, then since this relation may apply not only domestically but also on a global scale, egalitarianism has global scope. Second, the claim that what entitles an individual to priority is being worse off may not be the whole story about prioritarianism. Consider again, for example, luck prioritarianism. According to luck prioritarianism, we should give priority to the worse off only insofar as they are not themselves responsible for being worse off. One way of construing this claim is that an outcome in which a worse off individual is benefited is better than an outcome in which a better off individual receives an equal benefit, conditionally on the worse off individual not being responsible for his situation. But if priority can be conditional on (non-)responsibility is this manner, why could it not also be conditional on community? This is not to suggest that prioritarianism is more plausible if it has domestic scope only, but merely that any restriction of prioritarianism to the domestic domain would have to be assessed on its own merits.

A second question of the scope of prioritarianism pertains to future generations (Adler, 2009; Arrhenius, 2017; Holtug, 2010). Does prioritarianism apply to individuals who will, or may, exist in the future? Like many other distributive principles, prioritarianism seems to generate counterintuitive judgments if applied to future generations or, more specifically, to outcomes that hold different population sizes. To see this, consider first a well-known implication of total utilitarianism, namely what Parfit (1984, p. 388) has labeled the “repugnant conclusion.” According to the repugnant conclusion, a world, A, populated by individuals, all of whom have a life barely worth living, would be better than a world, B, populated by, for example, 10 billion individuals, all of whom have very worthwhile lives—as long as the former population is sufficiently large. Total utilitarianism implies this conclusion because, if there are enough individuals in A, this world will hold a higher total of advantages than B, even though each individual is much worse off. If prioritarianism is applied to different population sizes, it will likewise imply the repugnant conclusion. In fact, it will even imply what has been labeled the “super-repugnant conclusion” (Holtug, 2010, p. 254), according to which A may be better than B, even if A has a somewhat lower total of advantages. This is because the advantages that accrue to people in A on average fall at lower levels and so on average have a higher moral weight than the advantages that accrue to people in B. After all, since everyone has a life barely worth living in A, all the advantages that accrue to people here fall at very low levels.

This leaves prioritarians with three possibilities. One is to simply bite the bullet and accept the implications of prioritarianism for comparisons of different population sizes. But, as illustrated by the super-repugnant conclusion, this may be hard to swallow. A second possibility is to claim that prioritarianism applies only to same-number comparisons (that is, the comparison of outcomes that have equal-sized populations). In that case, prioritarianism implies neither the repugnant nor the super-repugnant conclusion. However, this renders prioritarianism a severely incomplete theory. After all, many of the choices we make have implications for how many people will exist, not least some of the morally most important policy choices that pertain to, for example, global warming and global poverty. Finally, one may hope to revise prioritarianism such that it can be applied to populations of different sizes, for example, by restricting the scope of the principle to some modal class of individuals, such as necessary or actual individuals, or by only assigning positive value only to advantages that fall above some critical (above zero) level of advantages (but for a critical appraisal of these and other ways of revising prioritarianism, see Holtug, 2010, pp. 259–280). While each of these three possibilities faces difficulties, perhaps prioritarians may take some comfort in the thought that other distributive principles seem to face similar or equally troubling problems in the sphere of population ethics (Arrhenius, 2017).

A third question of the scope of prioritarianism concerns whether this principle applies only to humans or also to (at least some) non-human animals. Most distributive principles are applied only to human beings, where utilitarianism is an exception in that many utilitarians believe that this principle applies also to sentient non-human animals. On the one hand, if prioritarianism is applied only to human beings, this may lead to the worry that prioritizing human over non-human animals in this way cannot be justified in a non-speciecist manner, where speciecism amounts to a particular form of arbitrary discrimination (Singer, 1993). On the other hand, if prioritarianism is applied to sentient non-human animals, this may seem to have the implication that we should massively redistribute advantages from human to non-human animals (Holtug, 2007, 2010, pp. 238–242; Vallentyne, 2006). At least if we assume that, on average, non-human animals are significantly worse off than humans are. And one reason for thinking they are worse off is that humans on average have much longer lives (although the exact implications of prioritarianism here depend on how we answer the currency question and the question of the temporal unite of prioritarian justice referred to above). Of course, the implication that such massive redistribution is warranted will be welcomed by some, but it is worth pointing out that prioritarianism is in this respect more demanding than utilitarianism, which is by many considered rather demanding when it comes to the interests of non-human animals. Again, however, prioritarians may point out that the demandingness objection will also pertain to other distribution-sensitive principles such as egalitarianism, insofar as they are applied to non-human animals.

# Justification

Some theorists seem to have become attracted to prioritarianism roughly on the basis of the following argument. Suppose we find utilitarianism implausible because of its lack of distribution sensitivity. Thus, according to utilitarianism, (9, 1) is equal in value to (5, 5). For example, we may share Rawls’s (1971, p. 27) concern that utilitarianism violates the separateness of persons. While it may be reasonable to maximize benefits in cases of intra-personal trade-offs, this is not so in cases of inter-personal trade-offs because the satisfaction of one person’s interests does not compensate another person for the frustration of hers. If, for example, we move from (5, 5) to (9, 1), the gain to the first individual does not compensate the second individual for her loss, and, indeed, she may now be very badly off.

Both egalitarianism and prioritarianism provide an explanation of what, more precisely, is wrong with utilitarianism. According to egalitarianism, utilitarianism ignores the disvalue of inequality. It ignores that in (9, 1), there is gross inequality while in (5, 5) there is perfect equality. According to prioritarianism, on the other hand, what utilitarianism inappropriately ignores is a concern for the worse off. We should give priority to the worse off individual in (9, 1) and for this reason prefer (5, 5).

However, egalitarianism is vulnerable to the leveling down objection (Parfit, 1991, p. 17). Compare (10, 5) and (5, 5). Since, unlike (10, 5), (5, 5) is perfectly equal, egalitarians must claim that (5, 5) is in at least one respect non-instrumentally better than (10, 5). They need not claim that (5, 5) is better all things considered, since they may have other concerns than equality. But the non-instrumental concern for equality implies that (5, 5) is in one respect better. But how can (5, 5) be in even one respect better, when it is better for no one, not even the worse off? Indeed, egalitarianism implies that (0, 0) is in one respect better than (10, 5), and that so is (−10, −10) (where the latter outcome assumes a currency that can have negative values, such as welfare).

Arguably, there are two sources from which the leveling down objection derives its force (Holtug, 2010, pp. 181–201). The leveling down objection may point out to us that a certain concern that we have, that has motivated us to be egalitarians, is really not captured all that well by egalitarianism. We may have been attracted to egalitarianism because we are concerned about how the less well-off members of society fair. But egalitarianism does not capture the concern for the worse off. After all, even though egalitarians may have other concerns, their distinctive concern for equality implies that (0, 0) and even (−10, −10) is better than (10, 5), whereas obviously the worse off are much better off in the latter outcome. So even though egalitarians may hold, for example, the Pareto principle, and so claim that (10, 5) is better all things considered, the distinctively egalitarian component in their theory is a concern that only contingently, and only sometimes, coincides with a concern for the worse off.

The other concern from which the leveling down objection derives its force is a person-affecting principle, according to which (roughly) an outcome cannot be better (worse) than another in even one respect, if there is no one for whom it is better (worse). This is a principle that stipulates a necessary connection between betterness and individual advantages. It states that good-making properties of outcomes have to somehow benefit individuals. This, it may be argued, is why for example (0, 0) cannot be in any respect better than (10, 5). (For further discussion of, and opposite views about, whether the leveling down objection can be justified on the basis of a person-affecting principle, see Holtug (2010, pp. 181–198) and Temkin (1993, pp. 245–282).)

Nevertheless, some theorists have argued that it is not only egalitarianism that is vulnerable to the leveling down objection, but also prioritarianism. For example, John Broome (2002; see also Fleurbaey, 2015; Persson, 2008) shows that prioritarianism can be represented by:

$Display mathematics$

where T is total advantages and I is a measure of the badness of inequality. Broome argues that since decreases in I imply increases in G, everything else being equal, prioritarianism is indeed vulnerable to leveling down. For example, in the move from (10, 5) to (5, 5), I decreases, which increases the value of G. Of course, T also decreases, and so G is reduced, all things considered, but since the drop in I adds to the value of G, there is at least one respect in which (5, 5) is better than (10, 5).

However, why believe that any possible split of G into separate components will tell us anything interesting about the value commitments of prioritarians? Consider, for example, the fact that total utilitarianism can be represented by:

$Display mathematics$

where n refers to the number of individuals in an outcome and A refers to their average level of welfare. Now consider the move from (−10, −9) to (−10, *), where * refers to the fact that the second individual does not exist in the second outcome. Might it be argued that, according to total utilitarianism, (−10, −9) is in one respect better than (−10, *), since A is higher (−9.5) in the former outcome? This does not seem to be a plausible way of capturing the value commitments of total utilitarians. Presumably they would argue that there is no respect in which (−10, −9) is better than (−10, *) as the total of welfare is much lower in the former outcome. By parity of reasoning, prioritarians may argue that there is no respect in which (5, 5) is better than (10, 5) and more specifically that the way of structuring the prioritarian function suggested by Broome does not tell us anything important about the value commitments of prioritarians. If so, it has not been shown that prioritarians are vulnerable to the leveling down objection.

Thus, prioritarians may argue that not only do they accept distribution sensitivity and respect the separateness of persons, but that, unlike egalitarianism, they also avoid the leveling down objection and, indeed, they accommodate both the sources from which this objection derive its force. Thus, clearly they capture a concern for the worse off. And they respect the person-affecting principle. After all, the prioritarian function implies that we cannot have an increase in the value of an outcome in the absence of an increase in advantages, as the goodness of an outcome is an additive function of (positively) weighted such advantages.

Nevertheless, it may be objected that while prioritarianism does capture a concern for the worse off, it does not capture this concern in its most plausible form. This is because of the aggregationist nature of prioritarianism (Hirose, 2015b). Like utilitarianism, prioritarianism implies that a large loss for a worse off individual can be counterbalanced by a small gain for a sufficiently large number of better off individuals, no matter (1) how small the benefits to the better off individuals are, (2) how large the loss to the worse off individual is, (3) how well off the better off individuals are and (4) how badly off the worse off individual is. Thus, it may seem that prioritarianism gives insufficient protection to the worse off.

A non-aggregative principle that avoids this implication is leximin. Leximin simply does not allow for trade-offs between the worse off and the better off. Therefore, it may be argued, leximin is superior in the manner in which it exhibits concern for the worse off. However, the non-aggregative nature of leximin seems to raise problems of its own. Thus, consider that leximin refuses to trade off a benefit to the worst-off individual for a benefit to the second-worst off individual, no matter (1) how small the benefit to the worst-off individual, (2) how large the benefit to the second worst-off individual, (3) how small the difference between the level of the worst-off and the second worst-off individual, and (4) how badly off the second worst-off individual is. In fact, leximin refuses to make this trade-off no matter how many individuals at the level of the second worst-off individual we could greatly benefit instead of slightly benefiting the worst-off individual. On this basis, prioritarians may argue that leximin does not, after all, exhibit superior concern for the worse off. Furthermore, as already pointed out, prioritarianism can get infinitesimally close to leximin, depending on how the weight function is fixed.

When we look at arguments for prioritarianism in the literature, we can see that they proceed from different types of value claims. For example, Matthew Adler defends prioritarianism on the basis of a claim-based approach to justice. More specifically, he appeals to what he calls a “claim-across-outcome” approach, according to which individuals have claims vis-à-vis pairs of outcomes, where the strength of these claims depend on these individuals’ levels of advantages in each (Adler, 2012, p. 365). Furthermore, he argues that the strength of this claim for a given individual will be sensitive both to the difference in advantages that accrue to her in these two outcomes and to her level of advantages in them (the worse off she is, the stronger the claim). He argues that this approach supports a ranking that satisfies the Pareto principle, the Pigou-Dalton principle, and strong separability.

As pointed out above, egalitarians may also hold all things considered orderings that satisfy the Pareto principle, the Pigou-Dalton principle, and strong separability, but Adler stresses that their justification for doing so will be different from that of the prioritarian. Thus, Adler contrasts the claim-across-outcome approach and what he calls a “claim-within-outcome” approach, where the latter orders outcomes in terms of how individuals fare relative to each other in each outcome (Adler, 2012, p. 313). So when egalitarians, such as Larry Temkin (1993), suggest that individuals have complaints in virtue of being worse off than others in particular outcomes, they are assuming a claim-within-outcome approach. The claim-across-outcome approach Adler uses to defend prioritarianism, on the other hand, does not rely on this approach and does not attach value to equality or more generally to relations between individuals in outcomes.

However, prioritarians need not commit themselves to a claim-based approach and may, for example, defend prioritarianism on the basis of claims about non-instrumental value instead. Thus, it has been suggested that what prioritarians ascribe non-instrumental value to are compound states of affairs, each consisting of the state that a benefit of a given size accrues to an individual and the state that this individual is at a given level of advantages, where this value increases when the size of the benefit increases but decreases when the level of advantages increases (Holtug, 2010, p. 204). Unlike a commitment to the non-instrumental value of equality, this value commitment is not vulnerable to the leveling down objection. In the move from (10, 5) to (5, 5), we do not have an increase in such compound states (we have a reduction), and so there is nothing of what prioritarians ascribe non-instrumental value to.

# Risk

So far, the version of prioritarianism I have primarily been discussing is axiological or, more specifically, a view about the value of outcomes. I have also said a little about how such a view may be incorporated in a criterion of rightness. However, there is a further question of what we are to do when facing choices where we do not know what outcomes will result from the available actions, that is, choices that involve risk. What does prioritarianism imply regarding such choices? While Broome (1991), McCarthy (2008a, 2008b), and Rabinowicz (2002) eloquently addressed this question in earlier stages, it is Otsuka and Voorhoeve (2009) that have sparked most of the recent debate. Otsuka and Voorhoeve have argued that, not least when applied to risky choices, we can see some deficiencies in prioritarianism.

One way in which to render prioritarianism relevant to risky choices is to develop a probabilistic version of prioritarianism. Probabilistic versions weight the different possible outcomes of an act or choice (or policy) according to their probabilities. There are two standard ways in which this can be done. According to ex post prioritarianism, we weight the prioritarian value of each possible outcome of an act according to that outcome’s probability and then add up these weighted values. Here, the prioritarian value of an outcome is the value assigned to it by axiological prioritarianism. In other words, ex post prioritarianism assesses acts in terms of their expected prioritarian value. According to ex ante prioritarianism, on the other hand, acts should be assessed on the basis of the prioritarian value of the expected individual advantages to which they give rise. That is, instead of first determining the prioritarian value of each outcome and then weighting it for its probability, we first determine each individual’s advantages in each outcome, weight these individual advantages according to the probability of each outcome, and then apply the prioritarian function to such expected advantages.

In most discussions, it is assumed that ex post prioritarianism is the version prioritarians will want to adopt. However, it has been argued that ex post prioritarianism is implausible. Thus, ex post prioritarianism may drive a wedge between prudence and justice, even if only the interests of a single individual are at stake (McCarthy, 2008b, pp. 19–22; Ord, 2015; Otsuka & Voorhoeve, 2009). Consider a case in which an individual will develop either a slight or (equiprobably) a severe disability and where we need now to decide whether to give him a treatment for one or the other of these disabilities. If he is treated for the severe disability and it turns out that he has this disability, it will give rise to a slightly smaller benefit than if he is treated for the slight disability and it turns out that this is the disability he has. Here, ex post prioritarianism implies that he should be treated for the severe disability because, even though the treatment of this disease gives rise to a smaller benefit, he will be much worse off if he has the severe disability and so this benefit will receive extra weight. However, the objection goes, we will thus be acting contrary to his prudential interests, because prudence requires maximizing his expected benefits and this we do by treating him for the slight disability.

Here, Otsuka and Voorhoeve (2009) add a further twist to the objection by claiming that in ignoring the significance of prudential justification, ex post prioritarianism is violating a certain aspect of the separateness of persons. Thus, Rawls argued that intra-personal conflicts are unlike inter-personal conflicts in that prudential justification applies (only) to the former; only in intra-personal conflicts can an individual be compensated for a smaller loss by a greater gain. This may seem to be a particularly damaging objection since, as we have seen, at least some prioritarians will argue that prioritarianism is superior to utilitarianism precisely because the latter violates the separateness of persons.

To further explain the objection, Otsuka and Voorhoeve (2009) compare this first, one-person case to a two-person case in which one individual will develop one of these disabilities and the other will develop the other, but where we can only treat one of them. Here, ex post prioritarianism will again tell us to treat for the severe disability. Thus, ex post prioritarianism considers these two cases relevantly similar. However, according to Otsuka and Voorhoeve, this principle thus ignores that a prudential justification can be given in only one of them. In the two-person case, if we treated the individual with the slight impairment, we could not give the individual with the severe disability a prudential justification for this. In the one-person case, on the other hand, we can give the only individual involved a prudential justification for treating for the slight disability, even if it turns out that he develops the severe disability. After all, we maximized his expected benefits by doing this. Thus, ex post prioritarianism ignores the difference between such one- and two-person cases regarding prudential justification (Otsuka, 2012, p. 368). More specifically, such prioritarianism ignores the difference between intra- and inter-personal conflicts, where the unity of the person suggests in the intra-personal conflict that we should maximize expected advantages, whereas the separateness of persons suggests that in the inter-personal conflict we should favor the less well-off individual.

Unlike ex post prioritarianism, ex ante prioritarianism does not drive a wedge between prudence and justice in single-individual cases. Since, in the one-person case, ex ante prioritarianism applies the prioritarian function to his expected individual advantages and these are higher if we treat for the slight disability, this is what we should do. The prioritarian value of a higher expected benefit will always be higher than the prioritarian value of a lower expected benefit. Nevertheless, ex ante prioritarianism has for many seemed a dubious view for other reasons, which is why many have assumed ex post prioritarianism in their discussion of the implications of prioritarianism in cases involving risk. Consider, for example, a version of the two-person case in which we do not know who will develop the slight and who the severe disability (but we know that one will develop the slight and the other the severe). Furthermore, for each, it is equiprobable that he will develop them. In this “risky two-person case,” ex ante prioritarianism implies that we should treat both for the slight impairment. However, since we know that one of them will end up with the severe impairment, this may seem unfair (Otsuka & Voorhoeve, 2009, pp. 195–198).

Otsuka and Voorhoeve (2009) argue that there is also a second respect in which ex post prioritarianism violates the separateness of persons, namely competing claims. Compare again the one-person and the two-person case. By making the same judgment in these two cases, ex post prioritarianism ignores that (only) in the two-person case, two individuals have competing claims for the benefit in question (Otsuka, 2012, p. 371). That is, it does not attach intrinsic significance to the fact that in the two-person case, one individual will be worse off than the other. Unlike the first respect in which Otsuka and Voorhoeve claim that ex post prioritarianism violates the separateness of person, this respect does not pertain specifically to risk. Thus, even axiological prioritarianism is vulnerable to this objection. Thus, as transpires from the prioritarian function, the moral value of a benefit to an individual depends only on that individual’s level of advantages, and this is so independently of whether one or two individuals are present. This, then, seems to be a complaint about the lack of relationality in prioritarianism.

Many theorists have responded to Otsuka and Voorhoeve’s objections by modifying prioritarianism in various respects. For example, Williams (2012) suggests that prioritarianism is a conflict resolution principle that applies only to inter-personal trade-offs, Parfit (2012) combines ex ante and ex post versions of prioritarianism, and O’Neill (2012) suggests that prioritarianism should be combined with other concerns such as autonomy and equality, such that, for example, autonomy considerations may outweigh prioritarian concerns in single-person cases. However, it is worth exploring how ex post prioritarians may respond to the objections without modifying their principle.

In the case of prudential justification, it should first be noted that it is not only ex post prioritarianism but a larger group of distributive principles that is insensitive to it. Consider again what I referred to as the “risky two-person case” above. Here, for example, ex post egalitarianism also implies that we should give the treatment for the severe disability, even though we can provide a prudential justification to both the individuals involved for providing the treatment for the slight impairment instead (by providing the latter treatment, we maximize the expected benefits for each of them). In fact, as we have also seen, Ostuka and Voorhoeve themselves believe that in this case, we should provide the treatment for the severe disability, thus setting aside prudential justification.

Second, prioritarians may argue that it is in fact a virtue of prioritarianism that it provides a symmetrical treatment of the one-person case and the risky two-person case. After all, the risky two-person case is just an extension of the one-person case in which a further individual is added who is in the exact same situation as the first individual. Arguably, what we do for the individuals in question should not be affected by whether there are one or two individuals in the exact same situation (Parfit, 2012, pp. 413–416).

In the case of competing claims, since this objection does not rely on risk, prioritarians of different kinds may give the same answer. First, as we have seen, prioritarians need not be committed to a claim-based account of justice. They may, for example, defend prioritarianism in terms of non-instrumental value. Nevertheless, even if we do adopt a claim-based account of justice, we should be careful not to conflate what are in fact two different distinctions, namely that between claim-based and non–claim-based accounts and that between relational and non-relational accounts, of fairness (Holtug, 2015, p. 281). Thus, prioritarians may invoke a claim-across-outcome account of fairness in their defence of prioritarianism. In fact, as we have seen, this is exactly what Adler does. Unlike the claim-within-outcome account, this account does not define individual claims in terms of how their advantages compare to those of others but in terms of each individual’s advantages vis-à-vis pairs of outcomes. This is a non-relational claim-based account of justice, and at the very minimum, it is compatible with prioritarianism (in fact, Adler uses it as a premise in his derivation of this principle).

When stating their concern for competing claims, Otsuka and Voorhoeve write: “one must justify any claim on resources in light of the comparative strength of the claim of others. Those who are relatively worse off have stronger claims to a given increment of improvement simply in virtue of the fact that it is, other things equal, harder to justify improving the situation of someone who is better rather than someone who is worse off” (2009, pp. 183–184). However, both the claim-within-outcome and the claim-across-outcome accounts can explain why the “relatively worse off” have stronger claims in virtue of it being “harder to justify improving the situation of someone who is better rather than someone who is worse off.” According to Adler’s claim-across-outcome account, a worse off individual will have a stronger claim to a given benefit than a better off individual, because an individual’s claim vis-à-vis a particular pair of outcomes is greater the worse off she is in the for her worse outcome. So not only is prioritarianism compatible with a claim-based account of justice, prioritarians may argue that it is compatible with the very notion of competing claims that Otsuka and Voorhoeve take to be important.

Let me finally point to a different way in which prioritarians may deal with choices under risk that, for some reason, has not received any attention in the literature. Both ex post and ex ante prioritarianism are probabilistic principles. Probabilism should be contrasted with factualism, where factualist principles assess acts or choices not in terms of the outcomes that could possibly result from them but in terms of the outcomes that will in fact result from them. So even if we do not know when making a choice what outcome will in fact result, it is nevertheless the value of this outcome that determines the value of the act. Factualist prioritarianism will thus assess acts on the basis of the prioritarian value of the outcomes to which they will in fact lead. One interesting implication of factualist prioritarianism is that it does not ignore prudential justification. In the one-person case, it implies that we should provide the treatment for the severe disability if and only if the individual will in fact develop this disability. This, of course, coincides with this individual’s prudential interests. More generally, factualist prioritarianism will always recommend the act that maximizes an individual’s benefits in single-person cases, and so there is no gap between the recommendations of such prioritarianism and of prudence. Of course, it may be objected that factualist prioritarianism does not tell us how to decide what to do in the one-person case (or in other cases), since we do not know which outcome will in fact come about. But factualists argue that a criterion of rightness need not settle this issue, as this is rather a question that should be settled by a decision procedure (Bales, 1971; Hare, 1981).

As transpires from the discussion in this section, a full-blown prioritarian theory will have to settle questions not only of weights, currency, temporal unit, and scope but also of how to apply prioritarianism to choices involving risk.

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## Notes:

(1.) The lecture, which is difficult to come by, is reprinted in Clayton and Williams (2000).