Childhood, education and distribuendum gaps

ABSTRACT The state can act in ways that cause injustice between children, but the standard opportunity accounts of the distribuendum fail to explain how this can be the case. Such accounts have a problem of distribuendum gaps. First, they fail to identify the locus of injustice between children, as they must explain such injustice in terms of inequalities between adults. Second, they have an inability to identify cases of injustice where adulthood is not affected. In order to solve these problems, while retaining the insights of the standard accounts, the distribuendum must include some goods appropriate for children and others for adults. G.A. Cohen’s theory of access to advantage can solve these problems of distribuendum gaps, and this speaks in favor it being the correct distribuendum of justice.


Introduction
This paper concerns equality of education. It takes as its starting point that the state, through the system of education, can act in ways that cause injustice between children, if it brings about unjustifiable inequalities between them. A theory of justice must consist of two things: a principle of distribution and an outline of the goods that should be distributed according to that principle. The latter is an account of the distrbuendum. The standard opportunity accounts of the distribuendum, or metric, of justice, such as resourcism, opportunity for welfare or the capability approach, sometimes fail to explain cases of injustice. Since they assume an account of agency that fits adults, but is unsuitable for children, they have a problem identifying injustices that obtain between children. These theories have problems with distribuendum gaps; they are susceptible to the problem that the theory of justice fails to explain cases of injustice, due to the construction of the distribuendum. These problems are especially salient in the area of education. In order to remedy such shortcomings, this paper argues that we should turn to G.A. Cohen's equal advantage to access, which combines considerations found in the standard opportunity approaches with some additional ideas. This theory is able to identify injustices that other theories of the distribuendum fail to detect, while taking into account the central lessons of these theories.
The paper has the following structure. Section 2 presents the debate on the distribuendum of justice. The next section develops an argument that the standard opportunity views misidentify the locus of injustice between children. In the fourth section, a further example is used to show that there are cases where the standard opportunity accounts fail to identify obvious instances of injustice between children. This is followed by a section that aims to explain the demands that these two problems of distribuendum gaps make on a theory of the metric of justice. Section 6 argues that access to advantage meets these demands and that it should, therefore, has a strong claim to be accepted as the correct account of the distribuendum. The last section sums up.

Theories of the distribuendum
Every theory of distributive justice must include two things. One of these is a principle of distribution, such as strict equality, prioritarianism or sufficiency. The topic of this article is the second one: that which the theory aims to distribute according to the principle of distribution. This is the distribuendum of justice. The present section will give an overview of the theories of the distribuendum from the literature. This will show that the standard opportunity views take responsibility as a fundamental value and how this, in turn, indicates how these accounts may fail to take children into account.
The debate on the distribuendum started as an attempt to find alternatives to welfarism. Welfarism is the view that happiness in some form is what is ultimately and intrinsically important and should therefore be the distribuendum of justice. There are different versions of welfarism (Griffin 1986). Hedonists believe that happiness should be understood in terms of mental states. To have welfare is to experience pleasurable mental states. Other welfarists think of welfare in terms of getting what one desires. This view is preferentialism and claims that welfare should be understood as having one's preferences satisfied. A third position is objective list welfarism, which says that there are several aspects to a happy life, and that we need a list of valuable things, including relationships, knowledge and experiences to make sense of welfare. A life where these goods are instantiated is a life that goes well.
However, few contemporary egalitarians hold welfarist views. Dworkin (2000) argues that the distribuendum should be resources, rather than welfare. The reason is that welfarism fails to handle the value of responsibility, and that it, therefore, mandates unfairness. Dworkin's argument revolves around the problem of expensive tastes. These are tastes that it costs more than average tastes to satisfy. If one needs champagne to achieve the level of welfare that other people get from drinking beer, then one has an expensive taste. Imagine a society that has achieved equality and a person, Louis, who finds that he is missing something in his life. He sets out to develop a taste for pre-phylloxera claret and plovers' eggs.
Since these goods are so expensive, Louis' equal share of resources will not provide him with very much of them and his welfare will be lower than that of other people. The implication of equality of welfare would be that we should redistribute resources to Louis; but why should others subsidize Louis' acquired new taste if he is responsible for his ambitions? On a resourcist theory, Louis would support the cost for his new expensive taste, since, on this account, he is owed an equal share of resources and not an equal level of welfare. Welfare is, hence, the wrong distribuendum for grown-ups, since it does not register responsibility.
Dworkin was not the first to argue for resources over welfare. Rawls (1971) is well known for favoring what he calls primary goods: (i) the basic rights and liberties, (ii) freedom of movement and free choice of occupation against a background of diverse opportunities, (iii) the power and prerogatives of offices and positions of authority and responsibility, (iv) the all-purpose means of income and wealth, and (v) the social bases of self-respect (Rawls 2001, 58-59).
In Rawls's earlier work (Rawls 1971), the argument for this list is that these are goods that any rational agent would need in order to carry out their specific individual projects. Moreover, they are compatible with the ideal of neutrality, which requires states not to promote any specific conception of the good but remain neutral among them. In the later Rawls (2001), this ideal of neutrality has been afforded an even more prominent role within the theory, and the justification of primary goods have been recast. In order to develop a theory of justice that can serve as an overlapping consensus between different comprehensive views of the good, the theory starts from the ideal of free and equal citizens. Primary goods are now defended as the distribuendum of justice because they are of the kind that such agents need to exercise what is called the two moral powers, which define free and equal citizens. The two moral powers are the rational, which is the ability to have a conception of the good, and the reasonable, the capacity to act from justice. Arneson (1989) has showed that resourcists have overlooked an important possibility when rejecting welfarism. Dworkin's argument implies that responsibility is important, but this does not in itself necessitate the move to resources. Instead, Arneson argues, we could opt for the theory of equal opportunity for welfare. This is the view that justice is achieved when each person faces equally valuable decision trees, so that their sets of alternatives have equal value in terms of expected welfare. What level of welfare a person achieves will then be dependent on the choices he or she makes. In this way, equality of opportunity of welfare incorporates the concern for responsibility. Arneson's theory is not the only opportunity approach to the distribuendum. There are also the capability approaches of Nussbaum (2000) and Sen (1999). On such views justice should be concerned with capabilities. To explain this concept, it is helpful to start with the distinction between functionings and capabilities. A functioning is something one can be or do, like being nourished or to read. A capability is an ability to achieve a functioning. The capability approach, then, says that the distribuendum should not be thought of as functionings, but as capabilities. People are responsible for their own ends, and, hence, should be free to choose them.
In the following, I shall call these theoriesresourcism, opportunity for welfare and the capability approachthe standard opportunity accounts of the distribuendum. They share the view that responsibility is of paramount importance for the development of an account of the distribuendum of justice, and put forward, as alternatives to welfarism, theories that revolve around the notion that autonomous agents are responsible for their choices. The goods that make up the distribuendum on these accounts satisfy two conditions. They are both desirable and appropriate for distribution among responsible agents. The goods of the distribuendum are designed to be useful and desirable for autonomous agents. The value of neutrality also tends to play an important role for these accounts, since it should be up to autonomous agents to choose their own conception of the good. However, children are not yet autonomous agents. In the following two sections, I will discuss two problems that this focus on autonomy and responsibility creates for the standard opportunity accounts when one turns to questions of injustice between children.

Distribuendum gap 1: the misidentification of the locus of injustice
Jack and Jill are both young school-age children. However, the state has decided that it will only fund Jack's education, leaving Jill without schooling. There might be all things considered reasons that justify this decision, but these reasons must show why it would be right to override the clear injustice of denying schooling to Jill. Regardless of why the state has decided to do so, this is, I take it, an obvious example of a pro tanto injustice. Moreover, denying a child education is instantaneously unjust. It is unjust the moment that Jill is denied schooling. In this section, I shall attempt to show that the standard opportunity accounts fail to explain this intuition of instantaneous injustice.
Starting with resourcism, the motivation for why resources are the appropriate distribuendum is that they make room for autonomous and responsible choice. However, Jack and Jill are school children. The concept of childhood is contested (Cf. Gheaus, Calder, and De Wispelaere 2019), partially because childhood is period of development so that there are clear and important differences between toddlers and adolescents. However, for the purposes of the issue that is being investigated in this article, only one aspect of being a child plays a core role in the argument. Children have yet to become adults, i.e., they have yet to become autonomous and responsible agents. If resources are goods owed by justice to the kind of agents that Jack and Jill have yet to become, it follows that resources are not yet this kind of goods for them. Rather, resources will become goods for Jack and Jill at a later stage, when they become adults. Education is a resource that autonomous agents can use to decide about how they want to live their lives. This means that inequality in the case of Jack and Jill must be explained in a way that refers to inequality between autonomous and responsible agents, since the distribuendum is defined in a manner to capture exactly those kinds of inequalities. This misidentifies the locus of the injustice. An injustice occurs instantaneously between the two children. The policy choice in this example can cause an injustice between adult Jack and Jill, but even before that happens there is the immediate injustice between childhood Jack and Jill that consists in one of them being denied schooling.
Can the opportunity approaches regarding welfare of capabilities do better? As with resourcism, what motivates the focus on opportunities or capabilities is a concern with responsible choice. Jack and Jill are not at that stage of development where they are responsible and autonomous agents and the injustice must be that adult Jack and Jill have different opportunities due to the policy of not giving Jill an education. Opportunities for welfare and capabilities are valuable for adults, but it seems clear that Jill has been unjustly treated qua child, and that instrumental connections to adulthood are insufficient to explain this. The problem here is not epistemological, it is not that it is it is difficult to observe inequities between children, but it appears at the level of basic theory. There is a misidentification of the locus of injustice.
The standard opportunity accounts share a problem of a distribuendum gap: clear cases of injustice fail to register in the appropriate way due to their accounts of the distribuendum. For these accounts, an injustice is an inequality in the ability to choose a path in life. Such choices are demanding and can only be responsibly made by adults. This means that if we are going to identify something as just or unjust, we must investigate its connection to autonomous choice. For Jack and Jill, the implication is that the injustice will take place at a point where there are differences in how they can take autonomous choices, i.e., when they are adults. This leaves a distribuendum gap and leads to a misidentification of the locus of injustice.
Many resourcists, and others, are luck egalitarians, and that principle may seem to solve the problem of distribuendum gaps, since it says that a distribution is just if it is the result of responsible choices, and inequalities that are not the result of such choices are unjust. Now, there is no responsible choice in the Jack and Jill case, which seems to imply that goods should be distributed equally between the two children. There may be a solution after all to the distribuendum gap problem. However, if this solution works, it works in the wrong dimension, since it attempts to solve the problem through the distributive principle rather than the distribuendum. The redistribution implied by luck egalitarianism is by the same problematic distribuendum. Moreover, if the inequality between Jack and Jill does not register as an injustice directly at the time, but only through the instrumental connection to adult Jack and Jill as autonomous agents, then there is no case for redistributing any goods on the basis of Jill's interests qua child. The difference will only appear once they are adult responsible agents. We have made no progress. The cases will still be based on the inequality between adult Jack and Jill.
It is not surprising that such theoretical problems can appear. They express an underlying assumption that seems common when we think about childhood. This is the thought that childhood is a preparation for adulthood. In one sense this is obviously the case, we learn during childhood and this learning makes us prepared for the challenges of adulthood. However, childhood is not only a preparation for a later stage in life, it is also a part of life. At least 20% of a human's life is spent in various stages of childhood. It would seem odd if this much of life only has instrumental value. It also seems counterintuitive that the things that make for a happy childhood, e.g., unstructured play or a sense of wonder before the world, gain their value exclusively from the usefulness of these experiences to the adult version of the person (Cf. Brennan 2014; Gheaus 2015; Brighouse and Swift 2014). Childhood is, like all other parts of a human life, intrinsically valuable. The preparatory view of childhood also often plays a role in how we think about education. It is not uncommon to think that the value of an education is the preparation for adulthood that it affords. Again, part of what is important about education is indeed this preparation, but this cannot account for all that is valuable in schooling. The joy of understanding, the fun of break time, play or the community among school friends also carry value. At a general level, this preparatory view of education seems to be what causes the problem in the Jack and Jill case, but looked at more specifically there appears to be another, related, assumption that causes the problem for the theories of the distribuendum that we have exanimated. These theories make what Colin Macleod (2010) has dubbed the Agency Assumption: First, in thinking about what constitutes justice-salient advantages we assume that persons have and can exercise the two moral powers. Second, in virtue of their possession of the moral powers agents must assume responsibility for their ends. Third, persons are able and expected to interact with others in ways that respect the agency of fellow participants in social cooperation. (Macleod 2010, 179) This is phrased in terms of Rawls's theory (Rawls 2001), but it generalizes. The agency assumption in a more general form, says that persons have the ability to exercise responsibility, that they must assume this responsibility and that they must act responsibly towards others. The problem for the views we have investigated is that since the account of the distribuendum is designed for adults, and children are not adults, cases of injustice will not register directly when the parties involved are children. To handle this distribuendum gap and the problem of the misidentification of the locus of justice, we need an account of the person that is applicable to whole lives, and not only adulthood. 4. Distribuendum gap 2: the failure to identify injustice Now imagine two other children, Gina and George. The state has decided to afford Gina an education, but not George. The reason for this is that George is terminally ill and will not survive until adulthood. The implications of thinking about childhood in terms of preparation should be obvious. If education is merely preparation for adulthood and George will never reach adulthood, there seems to be little reason to afford him this kind of goods. If there is nothing that George can be prepared for, then he will have no claim to goods that are valuable to adults. Even if there are instrumental reasons to educate Gina, that kind of argument cannot justify giving George an education. There will never be a situation where goods or opportunities will be of the right kind of value, since he will not become the kind of autonomous agents for which such goods are of value. If this is so, then it seems to follow that what seems a clear case of injustice is in fact not an injustice. For there to be an injustice, there needs to be two, or more, autonomous persons between which the injustices obtain. But the example obviously contains an injustice.
The problem for standard opportunity accounts is that they imply that education is provided only for the sake of autonomous agents, but not for children qua children. Since George is not, and will not be an adult, his claim for education does not register. And since, at the time when education becomes a good for Gina, i.e., when she becomes an adult, there is no one to compare her distribution to, there will be no inequality and hence no injustice. In this case, as opposed to the case of Jack and Jill, there is not even an instrumental relation to adults gaining goods that could explain the injustice between the children. Similarly, for such theories opportunity matters for autonomous agents, and inequalities only count if they are differences in opportunity sets between such agents. If George is not around until adulthood, there will be no point when such a comparison can be coherently made. This is a second distribuendum gap.
The conclusion to draw from this second distribuendum gap must be that the standard opportunity accounts of the distribuendum fail to identify cases of injustice. This might seem an overly hasty conclusion. Couldn't there be a way to derive an account of the distribuendum based on the choice-based theories? This is trickier than it might appear. In order to do so, one need to get around the problem that Macleod (2010) calls incomplete derivation. He explains the issue in terms of Rawls's primary goods. The problem is that not all that is important about childhood can be cashed out in terms of primary goods. To see how this is a problem, compare two schools. One has a great program for extracurricular activities and the other does not. But both are equally successful in providing the pupils with primary goods. Is this difference unfair? Intuitively, we would say that children of the second school have a valid complaint. However, this complaint cannot be cashed out in terms of primary goods. Macleod goes on to say: 'Yet surely the difference is one that is salient from the point of view of justice since it is unreasonable to hold the children responsible for the significant differences in the quality of their childhoods.' (Macleod 2010, 182-183) If this is correct, then we need an account of the distribuendum for children that does not rest on the agency assumption. This conclusion generalizes beyond primary goods. If resources and opportunities are goods owed to people because of their value to autonomous adults, then a solution to the problem of distribuendum gaps would, it seems, have to find a way of taking the characteristics of childhood and children into account. Therefore, a derivation of goods appropriate for children from an account developed for adults will be incomplete.

The problem of distribuendum gaps
We have identified two distribuendum gaps. The first is that the standard opportunity accounts of the distribuendum misidentify the locus of justice. They seem committed to understanding injustice between children in terms of inequalities between adults. The second distribuendum gap is that these theories of the distribuendum fail to identify clear cases of injustices, in cases where there is only one adult and therefore the required comparison cannot be performed. In this section, we shall try to identify the characteristics that a theory of the distribuendum must have in order to close these two gaps.
The general problem that must be handled is that the accounts of the distribuendum that we have looked at are based on an ideal for adults, but children and adults differ in characteristics in a way that makes the theory unsuitable for children. This also brings to the fore the problem of incomplete derivation; one cannot get from an ideal for adults to an ideal for children. In order to handle the gaps, I shall argue, the distribuendum must include specific goods in the distribuendum for both adults and for children.
If the distribuendum should have this kind of structure, along what dimension should it be developed? The agency assumption is plausible for adults, since it makes room for both considerations of responsibility and neutrality, but it is not suitable for children. This would mean that not everything can be opportunities, there must be some outcomes. Since resources are a part of the distribuendum because they make the theory of justice responsibilitysensitive, it will not do to think of the solution to this problem solely in terms of resources. In order to close the distribuendum gaps, we need a good as a part of the distribuendum that is directly good for children.
What could these goods for children be? There are several things that Jill and George are deprived of in relation to Jack and Gina. Learning is obviously an important aspect of education, as will be discussed below. Another important aspect has to do with the social relationships with classmates and the fun of, at least, break time. These are the kinds of values illustrated in Macleod's thought experiment above. If you are not allowed to go to school, these are valuable things that you will miss out on. Of course, school-life can be unhappy, but in general it is probably a source of positive experiences. It seems straightforward to characterize what is at stake here as a kind of welfare. We started out this paper by illustrating why welfare has been rejected as a distribuendum; have we come to a contradiction? Not necessarily, we could have a view where welfare is appropriate for children, but not for adults. And if, as is the case, the reason for rejecting welfare is that it is inappropriate for responsible agents, then this argument gets no foothold for the part of the theory where the agency assumption is inapplicable. Welfare could be a part of the distribuendum for children. Macleod (2010) suggests that in order to make sense of his results we should investigate whether there are intrinsic goods of childhood, but notice that if the important difference between the two schools is that one is more fun than the other, then welfare seems to do the trick nicely. A happy childhood is valuable, and it contains the happy experiences of play and wonder. The issue of intrinsic goods of childhood is a rapidly growing field that has given rise to many interesting suggestions on how to think about the distribuendum (Cf. Lindblom 2018). However, it seems to me that the value of goods like unstructured play, quite straightforwardly reduces to a perfectionist kind of welfare (Cf. Mill 1957Mill [1861). A perfectionist theory of welfare would say the following: to have welfare is to have pleasurable mental states brought about by the experience of valuable goods. Such a view would combine the notion from objective list theories that there are some values that must be instantiated in a good life, with the hedonist point that pleasurable experience is important. Indeed, it seems that we have reason to accept Anthony Skelton's view that welfare for children, 'consists in being happy in what is worthy of happiness' (Skelton 2015, 98).
Again, another important aspect of education that Jill and George are deprived of is learning. The core of education is not play and hanging out with friends but gaining knowledge. How should we conceive of this value of education? One approach would be to think of this learning in instrumental terms, and another to say that there is a distinct category of preparatory goods, which are such that they prepare the person for future stages of life, and that education is valuable in this vein. This would allow us to say that there is an injustice in the Jack and Jill case. However, it is not clear that these approaches would help us make sense of the George and Gina case. If there are no future stages of the relevant kind, then there seems to be no value to preparatory or instrumental goods for Gina.
How should we, then, conceive of the value of learning? It cannot be thought of as only a resource, capability or an opportunity for welfare, for the reasons of responsibility that showed that resourcism is unsuitable for children. One approach would be to take learning to be a functioning in the vein of the capability approach. Nussbaum suggests that functionings could be a suitable good to focus on for children, at least for preparatory reasons (Nussbaum 2011, 26) This is a promising approach, but I shall argue that learning is a kind of welfare for children, even if it is also a resource for adult. Since having welfare is having pleasurable mental states brought about by the experience of valuable goods, we could say that the childhood value of learning is consists of being happy in having the experience of learning about and understanding the world. This would combine the insight from objective list theories as well as the capability approach, with what is important in hedonism. If we think of welfare in this way, we can achieve several things. First, we retain the intuition that a happy childhood is a very important goal. Second, we can do this, while also being able to say that there are essential insights in, e.g., Nussbaum's list of fundamental capabilities, which includes play and practical reason as well as imagination and thought (Nussbaum 2000, 33-35). These capabilities, or rather functioning for the case of children, lead to welfare to children when they are being happy in exercising them.
Some may worry that this welfarist account of the distribuendum for children could give rise to a problem of adaptive preferences. What if children achieve welfare through experiences that do not seem valuable, such as playing pointless games like Cookie Clicker on their phones? This is where the perfectionism of the account of welfare plays an important role. If welfare as a part of the distribuendum has to do with experiences of the intrinsic goods of childhood, then the possible well-being derived from, e.g., idle games will not register as the kind of welfare that should be pursued. However, another worry may be that to explain the value of learning in terms of welfare could provide a too narrow account of this value. Surely there are other aspects of learning that are important than that it makes the person learning experience welfare? There is, indeed, more to learning, and this can be explained by how education is also a preparation for adulthood. In the sense learning also delivers preparatory goods for the child; it is a resource for adult life.
The conclusion of this section, then, is that in order to solve the problem of the two distribuendum gaps we need an account of the distribuendum that combines goods that are suitable for children with an opportunity-based account for adults. More particularly, the distribuendum should make room for welfare for children, as well as an appropriate standard theory of the distribuendum for adults. Moreover, it should combine direct having of goods for children with an opportunity account concerning goods for adults.

Access to advantage as a solution to the problem of distribuendum gaps
There is a theory of the distribuendum of justice that contains the tools to handle the problem of distribuendum gaps. G.A. Cohen's theory of the distribuendum proposes that what justice should be concerned with is equal access to advantage (Cohen 1989). Advantage is the combination of both resources and welfare. The reason that this is the appropriate distribuendum, argues Cohen, is that welfare deficiencies and resource deficiencies are distinct forms of unjust disadvantage. An egalitarian would help both a person in pain (even if he has access to resources) and a poor person (even if she is happy). The term advantage may give the impression that this theory is concerned with those aspects of social life that enables one to get a head of others, but Cohen's theory is egalitarian and advantage in this context refers, as a technical term, to the combination of welfare and resources. What is important is that this account of the distribuendum makes room for welfare. By access Cohen means to include both the usual meaning of opportunity and 'anything which a person actually has as something to which he has access' (Cohen 1989, 917). This stipulation is needed because one may be unable to make use of an opportunity, and this inability can also be a kind of injustice. This aspect of the theory allows us to combine considerations of opportunity with the notion that children should have outcomes directly and not contingently on choice.
In the Jack and Jill case, the problem is that the standard opportunity theories of the distribuendum misidentify the locus of injustice. That Jill is denied an education is an example of instantaneous injustice, and not only one of injustice in terms of opportunities between adult Jack and Jill. Access of advantage bridges this gap in two ways. First, since access includes not only opportunities but also the notion of directly having a good, it provides a way of going beyond explaining the problem in terms of opportunities. Second, since this distribuendum contains the direct having of welfare, and the theory of welfare can be interpreted in a way that makes sense of the experiences both of fun and of learning, it provides a way of explaining the inequality between Jack and Jill that does not only revolve around their later adulthood. If Jack is given education, but not Jill, this causes an inequality of welfare between them, in addition to the one in terms of resources that will affect their adulthoods. This implies an instantaneous injustice. Access to advantage can solve this problem of a distribuendum gap.
Access to advantage also handles the case of George and Gina. The distribuendum gap here was that the standard opportunity views failed to identify obvious cases of injustice. With welfare as a part of the distribuendum, it is straightforward to explain the injustice of providing only Gina with education. George has less welfare than he is entitled too. In this way, access to advantage solves both of the problems of distribuendum gaps, and this, in turn, indicates that this theory should be preferred as the account of the distribuendum of justice.
We have been concerned with finding the appropriate distribuendum for children, but the distribuendum of justice should also be suitable for adults. Cohen's access to advantage contains both welfare that helps us account for the distribuendum gap cases, and the resources that we may find necessary for adults for the reasons given by Dworkin and Rawls. With the help of access to advantage, we could say both that resources are important for adults and that welfare is important for children. On Cohen's own view, both welfare and resources are goods owed to adults, and in this sense the theory is not structured for children and adults respectively. There are two ways to go. Either one could, if one has resourcists leanings, interpret access to advantage as a structured theory that retains the insights of Dworkin and Rawls, or one could understand it in accordance with Cohen's intentions. In the first case, resources accrue to adults and welfare to children, whereas in the second case, no such structuring of goods is provided. Since both alternatives solve the problems we are concerned with in this article, I shall not take sides regarding this issue, but only note that either view seem preferable to the standard opportunity views.
Children will become adults and an important part of their upbringing is to prepare them for this. Focusing only on happiness during childhood would not be a feasible method of preparation. There is a trade-off to be made between childhood happiness and preparation for adulthood, even though some level of happiness in childhood is probably a precondition for successful preparation. At times, the demands of welfare and preparation will come into conflict, even if one should not exaggerate the frequency with which this will happen. Moreover, there is another trade-off. If welfare is understood along perfectionist lines, but resourcism for adults is preferred for reason of neutrality, then there is a second dimension of conflict between childhood and adulthood goods (Cf. Fowler 2014). In one way, it seems to favor of access to advantage that this conflict is made explicit. It makes sense of the choices parents often face. However, the trade-offs must be made for policy purposes. There is a solution to making this trade-off that departs from the fact that perfectionistic welfare is pluralistic and that it often supports, as in the case with learning, the pursuit of resources or other opportunity goods. However, the conflict of values to solve is that perfectionism for children may undermine neutrality on the adult level. If perfectionism allows that one raises a child in a way that guarantees that he or she will have a particular conception of the good as an adult, then the ideal that autonomous agents should be free to choose their own conception of the good would be severely undercut. The obvious solution is to let neutrality constrain the pursuit of welfare. This does not have to mean that what must be constrained is the level of welfare. Instead, the trade-off can be made concerning what kinds of preparational values get to play a role in the conception of welfare. Childhood goods such as learning and play need not be in conflict with neutrality. This means that the trade-off need not imply less welfare for children, even it may lead to different kinds of welfare.

Conclusions
This article has presented the problem of distribuendum gaps for the standard opportunity accounts of the metric of justice. These gaps lead such theories to both misidentify the locus of injustice and to fail to identify clear instances of injustice between children. The analysis of these problems showed that to solve them the theory of the distribuendum must include goods that are appropriate for both adults and children. Moreover, it indicated that opportunity goods may be suitable for adults, but for the case of children the direct having of goods is the correct approach. In particular, it has been argued that G.A. Cohen's theory of access to advantage can take these points into account and thereby solve the problems of distribuendum gaps. This speaks in favor access to advantage being the correct distribuendum of justice.