{'fraction_non_alphanumeric': 0.022061914610973784, 'fraction_numerical': 0.004203870924347139, 'mean_word_length': 5.192211578508955, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Can schools fairly select their students?

Selection within the educational domain breeds a special kind of suspicion. Whether it is the absence of transparency in the selection procedure, the observable outcomes of the selection, or the criteria of selection itself, there is much to corroborate the suspicion many have that selection in practice is unfair. And certainly as it concerns primary and secondary education, the principle of educational equity requires that children not have their educational experiences or opportunities determined by their postcode, their ethnic status, first language, or family wealth. Indeed educational opportunities determined by unearned advantage or disadvantage offend against basic notions of fairness. But are public schools even permitted to select their students, and if so, how can selection procedures used by schools be best structured to achieve equitable ends? In this article we delineate, describe, and defend what we believe are the essential features of selection and also why we need to pay equal attention to both the outcomes and the processes leading to those outcomes. Provided the selection is motivated and guided by the right reasons, as well as appropriately monitored, we argue that selection can be equity promoting.

difficult to understand why. Indeed, many variables potentially contaminate the integrity of the selection procedure. Money, doping, nepotism, and prejudice are but a few of the reasons why many of us remain skeptical about the integrity of selection, even when the criteria for the selection appear fair. Moreover, insiders know that a variety of internal mechanisms rely on less publicly acknowledged factors that are taken into consideration in the selection, not all of them discernible to the casual observer. Selection for jobs is often based on the testimony of a known colleague or friend, for instance, rather than credentials that can be objectively assessed (Granovetter, 1974(Granovetter, /1995. Selection within the educational domain breeds a special kind of suspicion. For instance, selection policies used in elite college admissions are often based on a range of non-academic factors such as legacy status, parental employment at the institution, athletic ability, or institutional interest in managing gender, race, or ethnic composition (Fullinwider and Lichtenberg, 2004;Karabel, 1972;Stevens, 2006). Whether it is the absence of transparency in the selection procedure, the observable outcomes of the selection, or the criteria of selection itself, there is much to corroborate the suspicion many have that selection in practice is unfair. Selection policies used by primary and secondary schools are particularly contentious, given that they are believed to have a unique institutional role to play in providing, shaping, and either expanding or restricting opportunity to large numbers of citizens at a very early stage of their lives and development (Downey and Condron, 2016;Schmidt et al., 2015). 1 Whatever opportunities and rewards may be merited by talented, motivated, and hard-working adults, the reasoning goes, the same standards appear unduly harsh and unwarranted when applied to children and adolescents. We can identify several reasons for this: family backgrounds are grossly unequal, a motivation to learn is not fixed, and both talent and hard work can be cultivated. In any case, educational equity requires that children not have their educational experiences or opportunities determined by their postcode, their ethnic status, first language, or family wealth. Indeed, educational opportunities determined by unearned advantage or disadvantage offend against basic notions of fairness.
In reality, of course, unearned advantage and disadvantage have long influenced the unequal educational opportunities that children receive. Consider, for instance, the enormous variation present at birth owing to genetic inheritance, geographic location, and socialization; furthermore, parenting style, place of residence, peer group, and how one wishes to spend one's free time all profoundly influence the interests, preferences, and choices of children in many domains (Duncan and Murnane, 2014;Simpkins et al., 2015). One would have to eliminate the family system altogether if one wanted to achieve a truly equitable distribution of educational opportunities, since nourishing and conferring advantages on one's children is at the very core of the aims and functioning of the family unit (Blau and Duncan, 1967;Lareau, 2003). Furthermore, as we have seen, school systems have long been known to reproduce these inequalities, dispensing opportunities and rewards to those best positioned to seize them (Bourdieu, 1977;Raftery and Hout, 1993;Schmidt et al., 2015), or whose family and social class backgrounds favorably dispose them to the institutional norms of the school.
One way that we might address these sobering facts might be to eliminate completely institutional selection from primary and secondary education as a matter of principle and offer all children of roughly the same age the same kinds of challenges or opportunities to learn. Yet, notwithstanding South Korea's experimentation with an equalization policy, expunging selection from modern educational systems is at best highly improbable. First, beyond perhaps the earliest grades of primary school, selection is necessary. Regrettable though it may be, in a world of scarce resources and limited opportunity, there always will be a need to sort, rank, and exclude in all but the earliest and most rudimentary of opportunities. If selection does not occur across schools (Alon, 2015;Fuller and Elmore, 1996;Stulberg, 2008), selection occurs within schools or classrooms. For example, students are selected into differentiated curricular tracks (Gamoran and Mare, 1989;Lucas, 1999) or the instruction in classrooms is personalized (i.e. the curriculum is selected for individual students). Accordingly, a variety of assessment criteria and instruments will be necessary to determine eligibility, to facilitate admission or assignment, to determine rank or priority, and to reward effort. Even the staunchest defenders of a high-quality education for all children (among whom we count ourselves) acknowledge that a one-size-fits-all approach to education will be inequitable for its failure to take into account the relevant differences in the pupil population, inter alia with respect to aptitude, language proficiency, disability, cultural background, and so on (Peacock, 2016;Warnock and Norwich, 2010). Furthermore, without selection schools are unable to promote individual mobility. The upshot is that once personalization of any kind becomes necessary, selection mechanisms are already in play.
Second, and perhaps more controversially, attention to selection will be necessary in order to achieve fairness. Taking fairness seriously means that we ought to try to at least mitigate unfair forms of selection where it is possible to do so. In the subsequent paragraphs, we refer to 'basic equity standards' as shorthand for demonstrating fairness. More controversially, we argue that many forms of selection are able to satisfy equity standards. Of course in order to demonstrate fairness in any selection, relevant and accurate criteria must be devised. Indeed, as we have seen, because selection is vulnerable to morally dubious influences, we must also use criteria that are independently robust yet mutually complementary and reinforcing. Furthermore, these criteria should be amenable to interpretation and application in different contexts. The question motivating this investigation is: how can selection procedures used by schools be best structured to achieve equitable ends?
The structure of the article is as follows. We first examine the de facto norm of selection; in doing so we will demonstrate why selection is not only inevitable but also necessary for equity. Following this we delineate, describe, and defend what we believe are the essential features of selection and also why we need to pay equal attention to both the outcomes and the processes leading to those outcomes. Provided it is motivated and guided by the right reasons as well as appropriately monitored, we argue that selection can be equity promoting. Next, devising three very different but recognizable school typologies, we apply these equity standards to each, testing our criteria against the kinds of selection most commonly associated with each school type. But we do not restrict our attention to typologies. Our final step is to examine an actual case study, which, as our analysis will illustrate, yields less clear-cut outcomes relative to abstract cases. Because schools arguably are the most consequential public institution for facilitating or denying opportunity to so many, in this article we restrict our focus to selection at the institutional level, homing in on the selection mechanisms used for determining public -and hence not private -secondary school attendance.

Caveats
Before proceeding further, we submit the following four caveats. The first is a basic precept in philosophy: an is does not give us an ought, which is to say, the empirical facts about any selection procedure will tell us nothing about what we could, or even ought, to do. For example, policies governing housing, health, and safety are doubtlessly unjust to one degree or another the world over, but this empirical observation does not mean that these policies cannot be motivated by equity standards (Hausman, 2015;Sharkey, 2013). Our second caveat is this: there is much more to school selection than the official formal procedures. In addition to inherited inequalities, other exigencies include district policies, residential choice, application requirements and deadlines, waiting lists, sibling preferences, and social networks: any or all of these may unduly bear upon selection. Even equally well-educated parents may not be able to activate their social capital in the same way if they are not familiar with how the 'field' of school choice operates (Lareau et al., 2016). Relatedly, selection mechanisms are of course not restricted to the institutional norms of any particular school; the extraordinary pluralism within most education systems makes selection both necessary and inevitable.
Our third caveat is this: school selection procedures are not totalizing. Families, but also the communities and social networks in which families are situated, constitute a potent countervailing influence. Thus, while proximity and postcode are commonly used to assign school attendance, in most countries parents also have to a degree the ability to enroll their child in a school of their choice, including schools outside of their district or catchment area. Parents are also at liberty to select private schools (many of which are not selective in the discriminatory sense), or opt for homeschooling. While the laws regulating school variety, quality, and selection vary from one location to another -such as those governing 'open enrollment', homeschooling registration, or graduation requirements -the basic right to make a selection on behalf of one's own child is widely held to be sacrosanct, enshrined as it is in most state constitutions and well as the United Nations Declaration of Human Rights and the European Court of Human Rights. Thus, even critics of selection procedures in education are loath to denounce school selection tout court, particularly as these concern decisions affecting one's own child. As our analysis will show, our point is not that all parents enjoy the same ability to exercise those liberties in ways that advantage their children (Fuller and Elmore, 1996); rather, we simply observe that selection by schools is not the whole story. 2 Our fourth caveat is as follows. Investigating how selection might be structured to achieve equitable ends does not mean that we believe that any system could facilitate fully equitable outcomes. Far too many inequalities are deeply embedded in the structural conditions and organizational and social practices of late capitalism. Even in societies that manage to satisfy equity standards, wealthier and more educated persons still enjoy certain privileges less available to others, such as the ability to live where there are fewer safety risks (e.g. violent crime), or the ability to purchase better healthcare above a minimally acceptable threshold. The point is that in each of these cases, even when the explicit aim is to ensure equitable use of resources, minimal equity standards may only take us so far.
Hence, this is an investigation into the possibilities that schools might exercise equitable selection of students relative to the educational systems that we have, or might devise. Yet given that we are skeptical that the resources, or the political will, exist in a measure sufficient to guarantee excellent schools for everyone, we concern ourselves with designing selection criteria and procedures that can be as fair as conceivably possible. To that end, ours is an argument for mitigating inequality. But what we reject is the suggestion that an educational philosophy concerned with equity must repudiate all forms of selection (cf. Sorokin, 1927).

Is selection morally problematic?
On the face of it, there might appear something morally problematic, if not simply oxymoronic, about selection in a public domain. Indeed in the popular imagination, publicness seems to denote open and unrestricted access to all (Calhoun, 1992;Watson, 2006). Conversely, questions about the propriety of selection in the private domain seem less pressing because, for instance, the owners and/or managers ordinarily determine who is eligible to use that space and broad latitude is granted as long as categories of individuals are not explicitly excluded on a discriminatory basis.
But this is too simplistic an understanding of the public and the private. For instance, public space is not devoid of rules, regulation, and even restricted access. The National Park Service, for instance, may enact and enforce ordinances regulating the access and use of public lands. Public train stations may restrict platform access to ticket holders, public libraries may restrict access to its facilities during operating hours. Nor is the private domain immune to public interest. Child Protection Services may remove children from their families when there is compelling evidence of abuse or neglect. And in the education domain, because liberal democratic states have reasons to foster and enforce non-discriminatory norms, states typically regulate -if only to a minimum degree -what private schools are permitted to do.
However, it does seem intuitively the case that a public domain -by virtue of its simply being public -arguably imposes a more demanding standard of equity. After all, for space to be meaningfully public, it implies universal accessibility. And in any case, where the school is concerned education is considered by most to be a different kind of good -analogous to, say, healthcare -one that is of importance for persons concerning their individual well-being, but also having broader public impact. And thus where selection in a public domain concerns granting access to a (restricted) opportunity, we have reasons to pay close attention to the rationale, procedures, and accountability mechanisms of that selection. Hence the morally problematic nature of selection turns not on its occurring in the public domain but rather on its intended or unintended consequences. In particular, we argue, selection will be morally problematic when it serves to reinforce or aggravate existing modes of unfairness and inequality. More on this in the following section. First, however, we will illustrate how selection in a number of ordinary (public) domains easily satisfies basic equity standards. That is to say, in most cases the following uses of selection are not likely to reinforce or aggravate existing modes of unfairness or inequality.

Selection by means of a lottery
Lotteries are used for distributing a scarce good, where (1) the qualifications of potential beneficiaries are not relevant and where (2) the number of possible beneficiaries exceeds the quantity of the resource available. Hence, a lottery would not be an appropriate selection mechanism for, say, awarding Olympic medals because doing so would entail ignoring important distinctions in performance relevant to the sport in question. However, a lottery might be one way to award children fairly a place in a school that is oversubscribed, given that no child is more deserving of the right to pursue happiness, or to receive a quality education than another. Provided that the lottery is fairly designed and administered, the chances of any one individual being selected by the lottery are roughly equal. That is, because outcomes are completely randomized, the chances of person x receiving the scarce resource are no better than person y. If there is something unfair about a child not being selected for placement in an oversubscribed school, it is because there are simply not enough schools like it to go around and not because the selection mechanism itself is inequitable. As a selection mechanism, then, lotteries do not violate basic equity standards. 3

Selection by means of a hiring decision
Ideally, a hiring decision will involve selecting one individual from a pool of qualified candidates because he or she best matches the stated criteria. However, as is often the case, many hiring decisions involve making a selection from among a pool of candidates, several of whom more or less satisfy the hiring criteria. When this happens, different considerations may come into play. One might consider the relative weight of the qualifications, and come to a decision concerning which combination of them would best serve the needs of the institution. For example, one hiring committee may choose to place greater emphasis on teaching experience, while another may give greater weight to a candidate's publication record or success in procuring research funding. Or a hiring committee may look beyond the stated criteria in order to consider other relevant -though perhaps not explicitly stated -qualifications. For instance, for demographic reasons they may consider it an important asset to select someone able to speak fluent Spanish; meanwhile, another committee, wishing to balance the gender scales, may prefer a female candidate. Whatever the details in each hiring decision may be, so long as the selection is consistent with the advertised criteria, and so long as any non-advertised qualifications taken into consideration do not themselves violate basic equity standards (i.e. they are intended to promote equity), then ordinarily the selection made will be deemed fair.

Selection by means of a school serving special needs
Children who are hard-of-hearing or deaf have strong legal protections in the United States (certainly more than most countries) not only to attend public schools, but also to have their special needs accommodated by the local school district. Accommodations come in different forms. They may include a translator, an FM system, special training for the classroom teacher, assignment modification, and speech therapy, to name a few. Although the enrollment of hard-of-hearing and deaf students in schools established exclusively for deaf students has significantly declined since the 1970s, many countries (and states) continue to have separate schools for the deaf. By admitting only deaf students, Schools for the Deaf are not discriminating against non-deaf persons. Nor is a School for the Deaf being discriminatory by selecting staff already fluent in sign language. Indeed, when the school's explicit mission is to serve the needs of the Deaf community, a community that traditionally has not had its needs satisfactorily met in regular schools, it goes without saying that the selection of deaf and hard-of-hearing persons for its staff and students does not violate basic equity standards. Indeed its preferential selection criteria are geared toward mitigating unfairness, not aggravating it.
As each of these examples illustrate, selection can be structured to achieve equitable ends. In the second and third illustrations, selection may even permit preferential treatment where the aim is to better achieve those ends. By way of contrast, a school that selects or excludes on the basis of criteria irrelevant to the opportunity being offered or on the basis of expanding opportunity to an otherwise privileged group clearly violates basic equity standards. None of this is to say that the motivation of decision-makers is always guided by fairness concerns; they may, for instance, be motivated by convenience or other considerations. The point is simply that even selection to exclude can be motivated by the right concerns and thus facilitate outcomes consistent with basic equity standards.
But an account of equitable selection will need to be concerned not simply with satisfying basic equity standards, where persons selected for an opportunity match the relevant qualifications. Indeed, more than merely the outcomes of a selection, the aims and process that inform and guide the selection are even more consequential. It is therefore apt that we develop an account of selection, one that uses criteria that are both independently robust but also mutually complementary and reinforcing, and furthermore, where the criteria are amenable to interpretation and application in different contexts.

The need for equitable school selection
As our examples of a lottery, hiring decision, and a School for the Deaf illustrate, many ordinary forms of selection are not morally or politically contentious. Yet unlike schools serving children with special needs, most schools that use selection criteria for determining admission seem to require a stronger justification. Indeed, it is reasonable to assume that selection criteria are of paramount importance given their pivotal role in providing, shaping, and expanding opportunity. Articulated differently, education supplies both intrinsic and instrumental benefits that in many ways are constitutive of how well someone's life goes. And the fact is that many of the de facto norms of selection used by schools lack a strong moral justification. As such, they risk running afoul of basic equity standards, indeed many risk being discriminatory and harmful.
For example, selection criteria or procedures that heavily rely upon testing instruments that fail to capture what students know and understand will violate basic equity standards; so too will educational and career options using selection criteria or procedures that rely upon the personal intuitions and preferences of a single evaluator -such as a classroom teacher -without any recourse to other means of assessment, as will selection procedures introduced at too young an age that result in educational and/or vocational careers difficult to alter or escape. Each of these, in our view, fail to satisfy even basic ethical standards.
Defensible criteria for selection must be articulated prior to their being applied, and accountability mechanisms must be informed by the original criteria, as well as ensure that the application of those principles is consistently applied and fair. Accordingly, we will want to use criteria that are both independently robust yet mutually complementary and reinforcing. Furthermore, these criteria should be amenable to interpretation and application in different contexts. Below, we aim to do this by parsing selection at three different levels. In doing so we hope to demonstrate why one should assess the fairness of school selection with reference to the character of the following three analytically distinct, but interrelated, criteria: (1) the intended aims of the selection, (2) the appropriateness of the organizational process, and (3) accountability measures regarding outcomes. Our objective in this section is to show how these three separate features are both analytically distinct and interdependent.

Intended aims
The first criterion is the intended aims of the selection. While intentions are not always observable and in fact often diverge from explicit rationales provided by social actors for an activity, nevertheless, we argue that underlying intentions are one element that can be used to evaluate the category of cases in which selection is purposively pursued not as an end in and of itself, but as a means intentionally designed to allocate individual access to a particular educational opportunity. We recognize, of course, that in the case of education there is considerable disagreement concerning the underlying purpose of the activity. For example, some believe that education should focus primarily on academic achievement or labor market preparation, while others emphasize citizenship or socialization, and still others aspire to equity and social justice. Although these stated purposes differ in their philosophical rationale, as well as the curriculum design required to achieve the specific pedagogical purpose, each of these aims assume a commitment to education being organized and delivered to provide a larger social good to a diverse population.
Selection targeted to allocating educational opportunities is arguably defensible with respect to this first criterion, if the intended aim is to provide a scarce social good to a diverse population. Ideally, the population would be diverse not only in terms of social class, ethnicity, and gender but also in terms of levels of talent, motivation, and effort. This is because talent must be cultivated, and motivation and effort are not fixed. If selection on the other hand is designed not to allocate educational opportunities among individuals with the intention of providing a social good to a diverse population, but is instead intended to exclude educational opportunity from a specific social group or segment of population, it fails to satisfy this criterion. To take a well-known example: de jure segregation during Jim Crow had this character as its intentions were clearly exclusionary in character -denial of access was not an unintended consequence of the pursuit of more universalistic aims, but was itself the intended outcome. A more subtle yet contemporary example might be Christian faith schools in Europe that use criteria (e.g. a baptismal certificate) irrelevant to the educational opportunity to exclude children of ethnic minority background.

Organizational processes
The second criterion to judge the appropriateness of selection requires an evaluation of the organizational processes adopted to enact the educational selection. A fair selection process requires that candidates be evaluated based on factors relevant to the type of educational opportunity being offered. In addition, ideally more than one factor should be considered in the selection, as validity and reliability of educational assessment generally increases with consideration of multiple measures. Selection for advanced educational opportunities could therefore be appropriately based on factors such as academic performance on a standardized test, prior course grades, or a candidate portfolio 4 -as long as these indicators themselves could be demonstrated as relevant and empirically related to success in the educational opportunity offered. A candidate portfolio might include work experience, volunteer service, as well as letters of reference where these could be used to inform more accurately the selection procedure beyond narrower measures of prior academic performance (such as course grades and test scores).
Hence an elite -and thus by definition selective -college that selected a candidate based on his or her legacy status or parent's employment position at the college would be hard-pressed to defend the fairness of the act either as relevant to the educational opportunity offered or on the empirical grounds that the selection was related to the increased likelihood of individual success in the activity. Similarly, a selection made solely on the basis of letters of reference from admired colleagues irrespective of the more objective criteria applied to all other candidates would fall foul of basic equity standards. The perceived fairness of an organizational process, such as educational selection, is greatly enhanced through institutional transparency; when the rules of the game are known and the play on the field is observable, external actors are more likely to endorse the legitimacy of the activity.

Inspection and accountability
The third criterion needed to evaluate selection involves subjecting outcomes to periodic inspection and accountability. Given that education is a social good with both individual and public benefits and, further, that educational selection itself can be judged in part by the extent to which social goods are the intended aim of the activity, the outcomes associated with educational selection require openness to public scrutiny. Even when the selection process is clearly defined and transparent, one cannot assume a priori that good intentions and a process designed in good faith in practice will lead to non-exclusionary ends. The outcomes of selection, therefore, require ongoing monitoring and assessment in order to uncover patterns of disparate impact affecting categories of individuals at risk for social exclusion.
Given that individual selection even with worthy aims and well-designed processes will often lead to group-level differences in outcomes, one requires a mechanism to identify the magnitude and character of the differences. What is critical from our standpoint is that a mechanism is in place to identify the disparate impact. This mechanism then allows societal actors to monitor the level of group-level differences in outcomes that are deemed acceptable or not in the context of the intended aims and organizational practices that were adopted. Because a transparent selection process that is open to inspection and accountability can uncover disparate impact and exclusionary outcomes, we believe that formal selection can be considerably fairer than an educational system in which selection instead occurs using principally informal mechanisms, and as such is likely to reinforce rather than mitigate the implicit biases built into individual judgments, not to mention that are deeply embedded in the inner workings of the educational process. The upshot is that formal selection subject to periodic inspection and accountability creates a bureaucratic process that enables fairness to be institutionally possible.

School selection: A typological sketch
In order to test the three distinct yet interrelated criteria comprising our account of equitable selection, we now test them against three very different school types. We employ typologies for the following reasons. First, the specifics of any given school, including the districts in which they are situated, are continually in flux, with different pupils, teachers, principals, curricula, and testing regimes. Much else besides depends on the state of the economy, the location, learning targets, and modes of governance in play. Second, and relatedly, however instructive specific case studies may be for illustrating the process and outcomes of selection in a particular time and place, extrapolating these unique realities to other contexts will inevitably be problematic. In contrast, the typologies we have invented will be recognizable to an international audience. As with any typology, there is risk of caricature. Yet the purpose they serve is not to capture a specific empirical reality but rather to enable an ethical analysis of selection.
The imagined context of these typologies is a large, shared, urban conurbation comprising great cultural, religious, linguistic, and socioeconomic diversity. Moreover, the imagined context contains a variety of public (i.e. state-funded) school types. All three of our typologies also describe schools that are doing well in terms of academic achievement; that is, each of the schools is performing well relative to other schools in the vicinity. Owing to these positive results and concomitant reputation, each school has reached full capacity; that is, each school has fewer available seats than the number of eligible children or interested parents. Consequently, each of the schools must resort to some form of selection regarding who attends the school. Yet given the unique features, each school uses selection in a different way. Thus in each of the cases we examine, it will not immediately be apparent whether the selection being used is structured to achieve equitable ends.

School A: 'Local Public'
Local Public (LP) is a public school situated within an affluent postcode. Average incomes are well above the national average. The neighborhood is ethnically very homogeneous, though a smattering of professional diversity is on the rise. Rainbow flags and signs saying things like 'No matter where you're from, we're glad you're our neighbor' are prominently displayed in front windows. A popular co-op grocery store enjoys support from the community, and a farmer's market hosting a number of local organic farmers appears on the main boulevard every Wednesday and Saturday morning. Two internationally known museums are close by. Second-hand bookstores as well as fashionable boutiques and restaurants can be found in abundance. Police presence is inconspicuous, although most residents feel perfectly safe. Most inhabitants of the area vote for the center left political party. The school comprises mainly children of the dominant group, with the average home comprising two parents with above average educational attainment. Consistent with the neighborhood, only a small number of minority students are enrolled, though these, too, tend to be children with both parents at home with above average educational attainment. School selection occurs by default as stipulated by zoning regulations. Most parents could easily opt for private education for their child if they wanted to; however, if asked most stress the importance of public education. Indeed, many chose to live in the neighborhood in large part because of the stellar reputation of the local public school.

School B: 'Magnet Public'
Magnet Public (MP) is a highly selective public school. It functions as a 'magnet', where the stated aim of the school is to facilitate the 'integration' of pupils of different backgrounds, and more specifically where talented children from less privileged -and thus often ethnic/racial minority -backgrounds have the opportunity to receive a more challenging and rigorous education. The school is situated in a poor neighborhood, as if to accentuate its raison d'être. There is higher crime in the neighborhood relative to other locations and police vehicles can be seen patrolling the area. There is much evidence of urban decay (e.g. boarded-up windows, vacant lots, loitering), but in part because of the presence of the school, gentrification is occurring rapidly and large numbers of young professionals have moved into the area in recent years. Although ethnic / racial balancing is a core aim, because MP is only one of five such schools in the city, selection is based entirely on the basis of a single test score. The high-stakes test is administered to everyone on the same day, and only the highest scoring students qualify for admission. The student population is mixed, with a slight majority hailing from poor immigrant backgrounds.

School C: 'Alternative Public'
Alternative Public (AP) is typical of the set of public schools that have made a tradeoff with the district offices. In exchange for less funding they receive more autonomy to make decisions with respect to hiring, curriculum, and intake procedures. AP is situated in a low-income working-class neighborhood. Its residents are primarily from historically disadvantaged backgrounds. It must 'compete' with other local publics for children whose parents otherwise will attend ordinary publics. To do this, the school fosters a strong ethnic identity and offers bilingual instruction, drawing its pupils from the local area. As a result, its entire student body comprises poor and minority children. However, given the school's reputation there is a high demand to attend; its strong language programs are also considered attractive by middle-class parents interested in bilingual education. Drawn to the school's offerings, several more affluent families have moved into the neighborhood, producing a 'gentrifying' effect. As a public school, AP may not discriminate against anyone who wishes to enroll; however, owing to the school's popularity there is a limited number of available places, and therefore district rules dictate that selection for enrollment must be determined by an admissions lottery.

Discussion
To the extent that all three public schools engage in some kind of selection, whether at the point of entry, or as it concerns internal selection (e.g. ability grouping), each of the schools is at least equally susceptible to forms of exclusion that may harm. Furthermore, as we have seen there is much more to school selection than the official formal procedures. Hence while our concern in this article is that selection procedures controlling school admission be structured to serve equitable ends, we are not naïve in imagining that any system of school selection could lead to fully equitable outcomes. In each of the typologies we have described, there are legitimate concerns that might be raised concerning why some children rather than others attend those schools, particularly when each of these schools has achieved full capacity, and moreover, owing to this full capacity must resort to some form of selection. That said, each school uses selection in very different ways, and therefore we need to look to the three criteria for equitable selection that we adumbrated above.

Intended aims examined
With respect to the intended aims criterion, all three schools have as their aim to provide a social good, that is, education, to a diverse population. However, only MP and AP purposefully make use of selection with the aim of doing so. Both are situated within less advantaged neighborhoods with the intention of attracting a more mixed student body. Moreover, both schools operate according to guiding principles whose aim is to more equitably provide an important social good, in particular to those most in need of it owing to other disadvantages particular students face. A crucial difference between them is that the MP draws its students from across a wider geographic area. MP also uses a performance-based selection criterion; hence all who score well enough in the entrance exam are accepted, so long as they belong to the greater unified school district. Conversely, AP restricts its student intake to the local neighborhood; its reasons for doing so have to do with its aim of providing high-quality education to the less well-served families in the immediate area.
Meanwhile, LP, with what little diversity it has, depends almost entirely on the ability of its families to afford the cost of living in the neighborhood in which it is situated. Selection at the school level, then, occurs by default rather than by deliberate procedure. However, the effects of this selection arguably have greater implications for the equitable distribution of an important social good than in the other two cases. Indeed the exclusion of so many by virtue of its affluent location means that its ability to satisfy this criterion fails. And perhaps it also should be said that the default position of this local public operates very differently from the default position of most local publics in our large conurbation, a great many of which serve the regular poor kids so often found in large urban districts. Most public schools are only 'selective', then, inasmuch as they draw from the local area, as our LP in this typology does. Yet while LP does not employ selection procedures in the same way as our other two schools do, it does serve to illustrate how the educational market works apart from the fairness of any particular schoolspecific selection process.

Organizational processes examined
With respect to the organizational processes of the selection the LP again fares badly. It 'solves' its oversubscription problem simply by giving priority to families who live the closest. The only additional criterion that it considers for selection concerns family continuity, that is, automatically selecting a younger sibling of an attending student over a child with no sibling. MP, on the other hand, administers an identical high-stakes exam to all applicants. The rules of the game are known and the play on the field is observable. MP may be attended by children across its wide district, yet because its academic standards are particularly demanding, only the highest scoring applicants are selected until all available seats are taken. Because the instrument used to make the selection is not based upon neighborhood advantage, and moreover because the exam is the same for everyone, its selection outcome is fairer than is the case with LP. Yet while in theory anyone with the intelligence, knowledge, and skills can do well in the exam, the fact remains that children whose parents provide them additional learning opportunities (e.g. private tutoring, academic camps, and foreign travel) are likely to do better than those who are not. Not incidentally, too, there are additional difficulties with achieving equitable ends at MP to the extent that some children who qualify for attendance encounter further obstacles with transportation, and therefore must spend a greater amount of time and resources commuting to and from the school.
Meanwhile, owing to the strength of its reputation, AP's admission selection relies entirely on a lottery, conducted publicly before all interested parties. Those whose numbers are randomly chosen are selected with no further discussion. Only if a parent forfeits her right to enroll her child (or is forced to surrender the right owing to other extenuating circumstances) will another child be allowed to take her place. Importantly, given the high level of mobility in the school district, this is not an uncommon occurrence: from time to time other draws by lottery must be made, ordinarily at the end of each academic term. By its very design, the lottery is impartial and hence the possibilities of acceptance are statistically equal for all. However, the lottery outcome is not the only variable in the process; owing to its being purposefully situated to serve a particular demographic, a majority of its children are also ethnic/racial minorities, and poor. While parents whose children are not selected experience grave disappointment, the outcomes of the selection at AP enjoy strong legitimacy in the local community, where no apparent evidence of foul play can be observed concerning who is able to attend.

Inspection and accountability examined
With respect to inspection and accountability, LP satisfies our third criterion only by engaging in no obvious exclusionary selection. On the other hand, as we have made clear, the school's selection mechanisms function by default owing to the property values in the neighborhood in which it is situated. Hence the school's modes of selection better fit what we have called informal processes rather than the formal modes of selection that describe the other two schools. Those neighborhood features, in turn, result in rather striking disparate impacts. Indeed the absence of ill will and discrimination does not absolve the school of producing exclusionary outcomes, even when these outcomes are indirect, and even when most parents in the neighborhood are vocal supporters of 'diversity' and school integration.
For their part, both MP and AP fare better owing to the formal mechanisms of the selection itself as well as the transparency of the process. The standardized exam required for entrance at MP is subject to peer review and periodic inspection as is the lottery used for determining admission at AP. In addition, in both cases a bureaucratic process is in place that facilitates fairness inasmuch as public officials are called upon to inspect both the proceedings and the outcomes in order to determine disparate impacts. With respect to the outcome of the lottery in determining admission to AP, parents are also permitted to be present, further strengthening the legitimacy of the selection procedure.
There are, however, discernable differences between these two schools. Although both MP and AP use formal selection procedures, and though both have mechanisms in place that allow each to do well in terms of transparency, there are more disparate impacts in the former than the latter. First, in terms of the entrance requirements, like the other two schools MP has as its principal aim to provide a high-quality education to all children eligible to attend. However, while there is both consistency and transparency, that is, all children who wish to qualify for attendance must take the same test, 'eligible' here can only be understood in the narrow sense of the ability to do well in a standardized test. And thus, while MP hosts a much more diverse cross-section of the metropolitan area's population -indeed more than 50% of its student intake is minority -the selection mechanism used arguably favors those with more social capital, notably those with more strategies at their disposal for taking high-stakes tests, those whose parents are able and willing to pay for expensive test prep courses, and whose parents go to the trouble of applying for admission in the first place. This is not to say that one is unable to observe inequitable impacts with respect to selection procedures at AP. While unlikely, it is for instance conceivable that a lottery might be corrupt. More likely, however, is that some parents are not adequately informed about the school and its entrance procedures; consequently, even if the majority of parents live below the poverty line, only the best informed and most 'involved' parents may apply for admission to the school in the first place. Be that as it may, the disparate impact of the selection is low. Compared with the other schools, AP serves the most disadvantaged and diverse student body and, largely owing to its exclusive local student intake, succeeds at selecting the greatest number of students in need of better educational opportunities. In other words, its selection procedures are best structured to achieve equitable ends.

Case study: Stuyvesant High School
We now subject our equity framework to a critical test by moving from abstract discourse focused on a typology of schools to an empirically challenging and difficult case: Stuyvesant High School, a specialized math and science public school in New York City, where selection criteria by state law is restricted solely to consideration of an entrance exam. The selection process has been subject to extensive criticism. For example, the National Association for the Advancement of Colored People (NAACP) Legal Defense and Education Fund filed a Civil Rights complaint about the selection process in 2012 (NAACP Legal Defense and Educational Fund, 2012), and the current mayor of New York City, Bill de Blasio, has asserted that 'we have to get rid of that test' as 'a matter of fairness' (Shapiro, 2018). We briefly explore the fairness of the selection process at Stuyvesant by applying our three criteria: (1) the intended aims of the selection, (2) the appropriateness of the organizational process, and (3) accountability measures regarding outcomes.
Tests have long been used as proxies for talent, motivation, and effort. Stuyvesant High School began to use standardized testing for the admission process simultaneous with the need to divide the student into double and then triple sessions to accommodate the growth of student demand for the rigorous coursework they were offering. Stuyvesant's reliance on a standardized test for selection was codified into New York state law in 1971 by the Hecht-Calandra Act.
While we will discuss the limitations to the use of standardized assessments for selection below, one can grant that the intended aims of the process are to allocate scarce positions in a rigorous academic program to individuals with exceptional demonstrated levels of talent, motivation, and effort. Critics might assert that standardized assessments were introduced with the unstated intention of excluding immigrants and later native non-White students from accessing these opportunities (Lemann, 2000). This challenge though requires one to assume that educators who promoted this form of selection have for the past century been acting in bad faith and that these social actors had overlooked more direct ways to exclude such populations.
The organizational process Stuyvesant has adopted to enact its selection is considerably more problematic. Stuyvesant relies solely on one instrument, a 3-hour exam -the Specialized High School Assessment Test (SHSAT) -administered to students only one time per year (New York City Department of Education, 2018). The reliability and validity of the process is undermined by relying solely on one performance-based measure, rather than considering multiple indicators, such as talent, motivation, and effort (cf. McCrickerd, 2012); the process may be further compromised to the extent that highstakes testing instruments fail to rely on cognitive models that are better suited to assessing meta-cognition and sound reasoning (Norris et al., 2004). Furthermore, relying solely on a single standardized assessment is problematic given that social science research has demonstrated that this form of testing is subject to multiple forms of bias including cultural sensitivity of content, stereotype threat, and inequitable distribution of the opportunities for test preparation (Jencks and Phillips, 2011).
Finally, one can also assess Stuyvesant's selection process on the basis of admission outcomes. The outcomes of the selection process at Stuyvesant are public and appropriately open to inspection, critique, and accountability. The most recent data on demographic characteristics of Stuyvesant students (New York City Department of Education, 2017) indicate that 74% are Asian, 18% White, 2% Hispanic, 1% African American, 1% Pacific Islander, and 4% mixed race or other. In all, 36% of Stuyvesant students self-report speaking a language other than English at home, and in terms of class background, 32% of students are defined as demonstrating economic need (originating from families that have incomes below the federally defined poverty rate, eligible for food assistance, or are in temporary housing) and close to half are eligible for government-supported free lunches.
These outcomes are striking in a number of ways. First and foremost, in a city that is 53% African American or Hispanic, students from these backgrounds are vastly underrepresented. This racial disparity is associated with fewer students from these backgrounds taking the admission test, scoring high enough on the test to gain entry, or choosing Stuyvesant in Manhattan (as opposed to another selective public high school in the Bronx or Brooklyn). 5 Second, Whites too are underrepresented in relationship to their population in the city where they comprise 32% of the population. Third, Asian students, many of whom are from immigrant families, are overrepresented relative to their presence in the general population of the city (14 %). Finally, large numbers of students are from economically disadvantaged backgrounds. While the school (together with the entire school district) as a whole can be justifiably criticized for failing to serve African American and Hispanic students, there is little evidence that Stuyvesant serves as a bastion of White affluence, such as one finds, for instance, in European gymnasia (Bourdieu, 1998;Weenink, 2005). Instead, the school's predominant character is that it serves aspiring immigrants. As a whole the outcomes are mixed.

Conclusion
In this article we have asked whether, and if so how, selection at the school level might be structured to achieve equitable ends. We have argued that selection in one form or another is required and potentially can either enhance or undermine fairness. Furthermore, many forms of selection are able to satisfy what we have called basic equity standards so long as the aims, procedures, and accountability mechanisms are structured to achieve equitable ends. In order to assess the fairness of the selection, one must also take into account the dynamics of the larger education market, the particular challenges schools face, and the populations they serve. Opposition to selection for admission to an oversubscribed secondary public school may evince a failure to consider these variables seriously. However, as the Stuyvesant case study suggests, even when the selection aims, organizational processes, and accountability procedures are motivated by equity concerns, the outcomes can indeed be unpredictable, even disappointing. Each case will be different, in terms of the parents involved, the demographics of a given neighborhood, competition from nearby schools, opportunities for test preparation, and perhaps most importantly of all, the specific school district rules that guide (or, as the case may be, fail to guide) the selection procedures.
Although we have argued that selection can be structured to achieve more equitable ends, we are skeptical that any selection procedure -no matter how just -can promise fully equitable outcomes given the vast extent of inequality independent of even a more just school selection. We also acknowledge that improvement in the fairness of the selection process could lead to the growth of alternative parallel education markets, where economic capital becomes more important. However, in the absence of a more just school selection procedure, such as what we have delineated, we believe that we end up with a much more pernicious and unchecked form of inequity within the educational domain. Our argument for more equitable selection procedures, then, is aimed at mitigating inequality.
There are, however, two difficulties that our article does not resolve. The first difficulty concerns the reason that different societies allow for institutional distinctionhence selection -in the first place. Here we observe a discrepancy between the justification of, say, a magnet public school, where the aim arguably has less to do with what may be good for individual learners than with what the courts and policymakers believe is good for the broader society. This is not to say that the two necessarily clash; a school that uses technology or science as its 'magnet', for instance, may be established in order to serve the interests of the larger economy and still be good for the individual learners attending the school in terms of the moral, intellectual, and social outcomes derived from learning alongside others different from themselves. Since technology and science have emerged in most advanced societies as sacred commitments, broader societal goals are typically judged as self-evident; the religious orientation of some schools, however, is increasingly subject to public scrutiny. But the fact that schools are designed with specific social aims in mind does mean that it may at times operate at cross purposes to the expectations concerning what may or may not be equitable.
Another difficulty that our article does not resolve -certainly in the case of the MP and AP -concerns when a particular selection ought to take place given different rates of development, especially if the difference in rates of development is a matter of 1-2 years, or even a matter of months. As we have seen, selection between children is in some sense regrettable given the biological and sociological factors that lie beyond a child's control, and given the scarcity of educational opportunity available to a smaller number of children than would profit from it. Hence if a child performs poorly in, say, an entrance exam because of the absence of an adequate opportunity to learn something, or a slight delay in brain development, such that 6 months later the same child would -as one would expect -perform very differently, then a case can be made that the selection mechanisms are arbitrary in character and thus unfair.
Correcting for developmental differences will be very difficult indeed to achieve without far-reaching and intrusive social engineering of the sort unlikely to enjoy widespread legitimacy for what it portends for privacy and for family life, but also for what it putatively implies about 'normal functioning'. Moreover, children perform poorly in exams for a variety of reasons, not all of them developmental: being tired, not having eaten breakfast, possessing a thinking style that does not conform well to the design of the exam, and so on. Furthermore, as we saw with our case study, there also may be evidence of test bias, stereotype threat, or inequitable access to test preparation. In any case, it seems to us improbable that we might be able to predict a child's intellectual potential beyond a particular moment in time without introducing even more controversial mechanisms into the procedure. Notwithstanding these difficulties, our ethical analysis suggests that inequities in selection procedures can be significantly mitigated by looking at aptitude in more complex ways, and by incorporating self-correcting mechanisms into the process. Multiple forms of assessment, too, may be used, and the more frequent the better, in order to capture important developmental changes as well as make the appropriate adjustments to the educational opportunities a child receives. including policies -for example, Affirmative Action -aimed at rectifying historical injustice. But whether such policies will aid the disadvantaged versus benefit the already better off members of certain minority groups, too, remains unclear (Slater, 2013). A more promising strategy, one we briefly reference in our discussion of the Stuyvesant case, would be to use tests based on cognitive models that theorize the content and capabilities of children's minds (Norris et al., 2004). 5. In addition to Stuyvesant, there are eight specialized high schools in NYC that use the admission test to allocate admission. The NAACP Legal Defense and Educational Fund (2012) reports that at the time of filing the legal challenge: 319 out of 6382 African American students who took the exam were offered admission to one of the specialized high schools; 414 of 6143 Hispanic student test takers were offered admission; 2490 of 7119 Asian-American student test takers were offered admission; and 1253 of 4101 Whites were offered admission. Considered in terms of the distribution of admission offers: 7% went to African Americans; 9% went to Hispanics; 56% went to Asian Americans; and 28% went to Whites.