School Choice Algorithms: Data Infrastructures, Automation, and Inequality

Automated decision-making is a process in which an algorithm collects and analyses data, derives information, applies this information, and recommends an action, at times using forms of Artificial Intelligence (Richardson 2021). This paper proposes that we need to locate automated decision-making as part of the history of educational policy and governance, as well as increasingly networked cultural records or digital archives. As such, we explore the history and present of automated decision systems across a range of cultural records spanning several categories: data, algorithm, and AI-based technologies; innovation and industry; philanthropy and funding; policy and legislation; spatiality and socioeconomics; plus, activism, and communities. To do so, we created an interdisciplinary archival heuristic as a research tool to retrace these interrelated cultural records shaping data infrastructure and inequalities. We then tested this tool in the context of the school admission matching algorithm in New York City. Our central aim is to help counter discourses about the newness and efficiencies of introducing automation and algorithms across education reform initiatives. The education counter-archiving heuristic introduced therefore offers a novel research tool to explore the intersecting history, present, and future of automated decision-making systems, such as school choice algorithms.


Introduction
Increasingly education is governed through digital systems in which data, algorithms, make and shape decisions about assessment, resourcing, and provision as part of data infrastructures (Gulson, Sellar, and Webb 2022;. These infrastructures Postdigital Science and Education (2023) 5:152-170 comprise both hardware and software, while also constituting, and being constituted by, social relations (Sellar 2015) that 'establish a set of parameters for what [an] organization will be doing over time' (Easterling 2014: 80). In this paper, we examine the link between automation, data infrastructures, and inequality, in reference to school choice processes in the USA as a way to build upon, and accentuate, existing interdisciplinary research exploring the spatial and racial inequalities associated with school choice and education policy (Gilblom 2022;Gulson 2011;Horsford 2019).
We aim to investigate how the automation of education, manifested through school choice datasets and algorithms, emerges within the historical dynamics shaping educational policy trajectories in the USA. In the early 2000s, a group of US economists began designing automated school choice programs in New York City and Boston based upon matching and mechanism design theory; prior to this, school districts devised 'ad hoc solutions' reliant upon complicated preference lists and simultaneous admissions (Abdulkadiroglu and Andersson 2022). In this paper, we discuss school choice algorithms as automated decision-making, which comprises: any systems, software, or process that use computation to aid or replace government decisions, judgments, and/or policy implementation that impact opportunities, access, liberties, rights, and/or safety (Richardson 2021: 13).
Automated decision-making 'can involve predicting, classifying, optimizing, identifying, and/or recommending' (Richardson 2021), using computing software that implements an automated reasoning or decision-making process, and algorithms rely upon increasingly manipulable and mobile datasets which are collected and deployed in accordance with particular values and assumptions (Whittlestone et al. 2019). Some automated decision-making uses form of artificial intelligence (AI), such as machine learning and related artificial neural networks, which use algorithms and learn from data.
Our reason for framing school choice algorithms as automated decision-making is that they are attempts to replace traditional human focused processes of school admissions. We propose they fit the definition of automated decision systems above (Richardson 2021), as they use computation (whether AI or otherwise), are aimed at aiding decisions about admissions and implementing school choice policies, they change the life chances of students depending on school allocations, are aimed at optimizing the balance between choice and provision, plus make recommendations for school provision. Inequalities associated with the use of algorithms arises when students, parents, and other educational stakeholders highlight the limits of these various mechanisms, such as being viewed as unfair or easily manipulable to 'game' the system or lack of attention to racial diversity (Mennle and Seuken 2017).
We propose that locating school choice algorithms within a broader automated decision-making context can provide insights into the issue of inequality in both the use of algorithms and the policy issue of school choice in two ways. First, there is emerging work in education on bias and algorithms, paralleling more extensive work in other fields. Bias is not necessarily a problem in that it is built into how algorithms operate (Amoore 2021). Rather, our focus is on what these biases are, and 1 3 what they produce in the world, including effects on the groups who are impacted by algorithms, and context in which algorithms are applied (Baker and Hawn 2021;Belitz et al. 2022;Sahlgren 2021). Relatedly, there are calls for bias to be extended to look at 'including descriptions of the kinds of system behaviors found to be harmful, how and why the system behaviors are harmful, who is harmed, and the normative reasons for making these judgements' (Baker and Hawn 2021). Second, school choice is an area of education policy that is deeply racialised, especially around school provision and admissions (Gulson 2011;Yoon 2017). While school choice research is now close to 30 years old, it is worth rehearsing some of the main debates which continue to permeate this particular decision-making context. School choice policies have long been an area where parental and student choice of preferences has been in tension with system level demands. School choice sits within the marketisation of education, broadly understood as the introduction of competition and market-exchange into public education systems (Weiss 1998;Lubienski et al. 2009). These policies guide how 'students submit their preferences over schools to a central placement authority and the authority decides on an assignment (or a matching) based on schools' capacities, schools' priorities over students, and submitted preferences' (Dur, Gitmez, andYilmaz 2019: 1309).
This paper also aims to make a methodological contribution to critical studies of algorithms in education. We see algorithms as sociotechnical that comprise 'an ethicopolitical arrangement of values, assumptions and propositions about the world' (Amoore 2021: 6). As such, algorithms deployed in contemporary data infrastructures in education need to be examined for the possibility that 'baked in' inequalities are reinforcing existing inequalities. For instance, databases, algorithms, and risk models are producing an automated decision-making 'digital poorhouse' (Eubanks 2019) which 'reframes shared social decisions about who we are and who we want to be as systems engineering problems' -that results in poor and workingclass people across the colour line facing 'the heaviest burden of high-tech scrutiny' (12). However, attempting to investigate the ethical, social, and technical dimensions of automated decision-making is difficult, particularly as algorithms are 'made up of a heterogeneous set of relations including potentially thousands of individuals, data sets, objects, apparatus, elements, protocols, standards, laws, etc. that frame their development' (Kitchin 2017: 20).
In this paper, we seek to better understand how the techniques, ethics, and politics of specific algorithms interrelate and adhere over time and, in doing so, exert multiscalar, temporal inequalities which are often hidden from view. In doing this, we agree with Amoore (2021) that we need to look at 'reopening the multiplicity of the algorithm, digging under the stories, and attending to the branching pathways that continue to run beneath the surface' (162). For Amoore, this involves examining how algorithms -especially opaque or 'black-boxed' ones used in some forms of automation -can only ever be partially known; giving accounts of algorithmic reasoning is therefore necessary not to 'fix' algorithms, but rather to enhance understandings of how the segmentation mechanisms of algorithms operate are applied and impact society. The process of revealing 'coded inequity' (Benjamin 2019) not only can raise awareness of the social dimensions of technology, but also help to identify methods that counter assumptions regarding the neutrality of technology.
Postdigital Science and Education (2023) 5:152-170 Our paper provides a possible method -that of 'education counter-archiving'to investigate both the inequalities and inequity raised by Eubanks and Benjamin, as well as the heterogeneity called for by both Kitchen and Amoore. We propose that a cultural-theoretical perspective of 'archiving' (Agostinho et al. 2019) will allow us to examine the multidimensionality of automated decision-making, plus inform growing attempts to expand the methodological boundaries of studying algorithms. To do so, we position algorithms as a 'cultural object' (Mikucki and Manovich 2021) shaping artefacts, actions, and experiences across contemporary society -which can be classified as a new type of 'cultural record' (Chodorow 2006) that documents societal knowledge, beliefs, and change. We combine this focus upon algorithms as cultural records with critical dataset and archival studies, an emerging body of research which examines the politics and ethics of datasets and how these 'historical artefacts' (Thylstrup 2022) shape new forms of digital archives and power. These intersecting logics of datasets and archives can trace not only the provenance of datasets, but also their embeddedness within particular contexts (Gebru et al. 2021). Such multifaceted methods for 'reading' datasets (Poirier 2021) can help to surface the technical, cultural, and political aspects of data in relation to other cultural records.
Against this backdrop, our paper has the following aims: first, to explore the interrelationship between school choice algorithms and data infrastructures and, second, to propose a novel, multidimensional method to investigate how inequalities become embedded within automated decision-making (ADM) systems. To achieve these aims, this paper is structured as follows. The background section outlines the classificatory logics and inequalities embedded into infrastructures upon which automated decision-making systems operate (such as school choice algorithms). Following this, we outline our conceptual and methodological approach to propose education counter-archiving: a novel tool for retracing the cultural records shaping data infrastructures and inequalities in education. We then trial this tool in the context of a particular ADM in education case: the New York City school choice algorithm. To conclude, we explore implications for future research and policy initiatives related to school choice algorithms and ADM.

Background: Data Infrastructures and Inequalities in Education
Data infrastructures and inequalities emerge in relation to the cultural records that signify diverse knowledge, beliefs, and practices ingrained across societal and technological developments over time. This infrastructure line of inquiry draws attention to cultural records and consequences in relation to (i) how knowledge is produced, (ii) the visible and invisible work involved, and (iii) who/what is marginalised, ignored, and silenced in the process (Bowker and Star 1999). For example, the evolution of student information systems shows how administrative systems for managing student records, enrolment, scheduling, and attendance have developed over time (Darby and Hughes 2005). This focus also grounds our study amid the networked 'interplay between platforms, people, and places' (Swist and Collin 2017) of data infrastructures -which not only underpin innovations (such as school choice algorithms), but also have the potential to exacerbate existing inequalities (and create new ones) Anagnostopoulos, Rutledge, and Jacobsen 2013;Hartong and Förschler 2019).
This leads us to focus on the classificatory power of data infrastructures to institute both immediate and longer-term inequalities in the context of school choice. In terms of immediate effects, Star and Bowker (2007) highlight the 'residual categories' of what is silenced, or left out, of existing classifications: in effect demarcating what is 'knowable' and creating a category 'in such a way that no historical or social information can escape from it' (275). Building on theories of 'categorical inequality' in education, Domina and colleagues (2017) draw attention to the 'social processes that produce variation in student experiences within and between schools, as well as the mechanisms through which this variation contributes to social inequality' (313). These processes are embedded in what they term school 'sorting machines' which 'sort children into schools based on a combination of criteria, including their residential location, parental preference, and-in many contextstheir attributes (including measures of their academic skills, maturity, and other cognitive, cultural and socio-emotional characteristics)' (Domina, Penner, and Penner 2017: 315). These sorting functions and reproduced inequalities are applied -and even amplified -across a range of technology applications in education, such as the instructional use of digital technology, school software and student data, plus college admission systems (Rafalow and Puckett 2022).
The use of automated technologies enters a polarised debate about innovation and reform in education that has two key parts: one, policymakers 'suggest that educational systems are sluggish in adjusting to changes and often reluctant to innovation within a subjectively defined, reasonable amount of time' (OECD 2021: 7), and, two, teachers and other education professionals view that 'there are too many -superficial -changes and supposedly innovations that are externally imposed on them in a top-down fashion' (OECD 2021: 7). The use of automated technologies tends to be seen as reinforcing both the idea of top-down change, usually connected to the idea that these technologies are being introduced externally to education, and the idea that technology will solve the problems of inefficiencies in education. However, there is another way to look at this problem, which is that automated decision-making is introducing new ways of thinking and decisionmaking into education policy (Sellar and Gulson 2021). Automated decision-making underpins integrated data infrastructures that are closely connected to the increasing interoperability among technology vendors, education information systems that are rapidly expanding data-driven capabilities, and decision-making for districts which integrate student information and performance management functionalities at new scales (Darby and Hughes 2005). On the one hand, these data infrastructures offer an openness to decision-making, in which data will be more easily shared and stakeholders able to access systems. On the other hand, these infrastructures based on classificatory practices, and with a focus on creating efficiencies, may end up closing down possibilities for thinking about not just how education is done, but what education is for (Gulson, Sellar, and Webb 2022;Edwards 2015).
Linking data infrastructures and inequalities in education aims to foreground the range of cultural records which imbue the logics of school choice and algorithms.
For example, in not only recognising that the central task of schools is to create and populate categories which become the 'raw material' of longer-term social inequalities, but in also understanding that inequalities emerge from a variety of social and technological changes (Domina, Penner, and Penner 2017;Rafalow and Puckett 2022). This raises the following key question for our inquiry: in what ways can researchers and policymakers surface the diverse cultural records shaping data infrastructure and inequalities in education? In the next section, we propose a method to deal with this question.

Methodology: Education Counter-Archiving
We follow Williamson and Eynon's (2020) proposition that examining AI in education should 'trace out the historical processes, conditions, conflicts, bifurcation and con-and disjunctures out which contemporary practices emerged' (2). To operationalise our study of the interplay between school choice algorithms and data infrastructures in education, we propose the following heuristic: education counterarchiving. Through surfacing the histories and uncertainties of knowledge produced with emerging technologies, and focusing on excavating the multiplicity of algorithms (Amoore 2021), our heuristic aims to foreground archival power, especially the role of diverse cultural records. We see the heuristic as enabling collective experimentation with new concepts and methods for research on data infrastructures, automation, and inequality in education.
In contrast to the stability and linearity of archives which impose official or dominant narratives, we locate our approach as part of a growing body of counter-archiving scholarship that disrupts these conventional narratives (Springgay et al. 2020). This perspective is informed by a cultural-theoretical perspective of big data archives (Agostinho et al. 2019) and the notion that new forms of big data repositories are 'uncertain archives' which echo classic archival practices of mapping, detecting, and subjecting. First, the 'unknowns/unknowables' of archives foreground the role of mapping to identify patterns for 'eliminating or colonising unknowns' which are 'no less pertinent to the calculative realm of large data archives' (426). Second, detecting archival 'errors' can be construed in multiple ways (such as the technical, or political), so the interrelated logic and detection of 'errors' becomes a useful 'inroad into critical engagement with big data archives as political sites of information distribution, rather than as objective statements of truth' (433). Third, 'vulnerability' draws attention to the conceptualisation of data subjects, and the ways in which archival subjecting 'does not merely act on a subject but also forms and enacts the subject into being' (435), with digital archives becoming new regimes of 'pre-emptive personalisation' (438). This archival focus is further informed by a growing body of interdisciplinary research which highlights how the contingency, ambiguity, and complexity of the archive is 'shaped by social, political, and technological forces' (Manoff 2004: 12, following Derrida 1995and Foucault 1972; this is evident in not only the dominance of particular interpretations over time, but also the increasing scale and power of digital record gate-keepers shaping the memory of cultural records. Based upon our methodological and introductory framings, we propose the intent of our 'education counter-archiving' (EC-A) heuristic (Fig. 1) to be: a tool for retracing the cultural records data infrastructures and inequalities in education.
We propose that the EC-A heuristic allows us to distil the common, and varying, cultural records from which data infrastructures and inequalities in education emerge in specific contexts. The categories selecteddata, algorithm, and AIbased technologies, innovation and industry, philanthropy and funding, policy and legislation, spatiality and economics, plus activism and communities -aim to highlight a range of cultural records which shape how varying forms of infrastructure and inequalities are produced. To trial the EC-A, we demonstrate a detailed application of the proposed EC-A heuristic in reference to one specific case: the NYC school admissions matching algorithm. This case was chosen for three key reasons: first, NYC is the largest school system in the USA and is seen as a 'policy laboratory' in education (Elwick 2017); second, it was one of the earliest admission algorithms introduced into to a US school district, alongside Boston (Abdulkadiroğlu and Andersson 2022); and, third, the growing introduction of algorithms to reform admission rules across the USA and globally have had varying, yet understudied, impacts (Bonkoungou and Nesterov 2021).

The NYC Algorithm Counter-Archive
This section focuses on the specific case of the NYC school admissions matching algorithm, to trial our counter-archiving tool (Fig. 2: NYC school choice counterarchive). A preliminary collection of cultural records was identified from a range of scholarly and grey literature (including websites, journal articles, reports, blogs, plus newspaper and magazine articles). These records were then briefly described

Data, Algorithms, and AI-Based Technologies
This initial category of our counter-archiving tool aims to identify how specific forms and mechanisms of data, algorithms, and AI-based technologies imbue new forms of automation in education decision-making.

Cultural Record Example: the NYC School Choice Algorithm
The NYC school choice algorithm is now embedded within the largest educational district in the USA. The school choice algorithm is based upon a matching system originally designed in the mid-1990s by Al Roth, a Professor of Economics and Business Administration at Harvard University. The algorithm was originally created for matching medical students with residency programs and has been more broadly applied to inform models for other matching issues, such as kidney donations and Internet auctions (Toch and Aldeman 2009).
The flow diagram of the school choice algorithm (Fig. 3) illustrates the school choice task and process. Dataset inputs utilised are student/family choices, plus school and system preferences, within the Department of Education MySchools portal; the computer code executes the task based upon tentatively matching student with school rankings until a stable match is reached (Marian 2021). This matching system only takes a few minutes, whereas the pre-existing non-automated model took place over several months, three rounds of selection, with multiple offers for many students, with other students missing out (Toch and Aldeman 2009). This cultural record shows how school admissions in NYC are now organised using a matching algorithm so as to assign students to schools more efficiently. Additions to this particular counter-archive category could include other types of cultural records related to school choice algorithms in NYC (e.g. lottery numbers, results).

Innovation and Industry
How cultural records associated with innovation and industry imbue new forms of automated decision-making systems is the focus of this category.

Cultural Record Example: Automate the Schools K-12 Student Information System
While automated decision-making and algorithms in education are becoming more common in the twenty-first century, we start this part of our archiving in the twentieth century. In 1988, funded by the State of New York, a bespoke K-12 Student Information system called Automate the Schools (ATS) was written and initially developed over the course of 6 months using Computer Corporation of America's Model 2014 database management software (Kumar 2000). The ATS system handled high school allocation systems, over 4000 daily administrative operations, and was networked across nearly 1200 official schools. The ATS system included: 'student registration/enrollment, student demographics, parent and home address information, daily attendance, subject class attendance, health and immunization, Title-1 collection (low-income families data), and elementary and middle school report cards' (Kumar 2000). Kumar, the Director of Student Systems Development for the New York City Board of Education (NYCBOE) at this time, describes how, over the 11 years of operation, the application matured into 'a mission-critical tool for The significance of this cultural record is that it begins to surface the scale of infrastructure required to operate increasingly networked school information systems within which automated decision-making, such as school choice algorithms, operates. In particular, the ATS subsystems highlight how different types of data are segmented and stored, to be recalled for specific functions, such as school admission matching algorithms. Future cultural records for this particular counter-archive category could include the role of corporate vendors now play in the NYCBOE student information system.

Philanthropy and Funding
This category aims to foreground the cultural records linked to philanthropy and funding, plus their expanding influence upon educational reform and governance.

Cultural Record Example: Portfolio School District Model
In 2002, on the back of state legislation which provided mayoral control of public schools, the New York Department of Education partnered with private sector and consulting firms to implement a range of new programs, such as the Children First Initiative which led to the creation of over 200 small schools for a 'portfolio' of schooling options (Scott and DiMartino 2009). New York is one of over 20 US districts participating in the 'portfolio school districts' network which aims to erode older 'traditional school districts' in favour of new 'portfolio school districts' (Lake and Hernandez 2022). Decentralization, charter school expansion, reconstituting/ closing 'failing schools', and test-based accountability are key elements of this approach; such 'urban school decentralization' is based on the premise that if 'education vendors compete on the basis of proposed innovations, with a school superintendent monitoring activities, children will receive greater opportunity for academic success' (Saltman 2010: 1). The portfolio agenda has strengthened over time since the early 2000s, with a new range of philanthropic organisations distributing money to push the movement across the USA (Barnum 2017). Notably, this experiment to improve US public education is dominated by business and free-market paradigms -yet there is no substantive or reliable peer-reviewed study about this approach (Saltman 2010).
The value of this cultural record is that it surfaces how philanthropy and funding practices concentrate capital and political power to instil a stock market-inspired style of education reform with closer ties to competing education vendors (Williamson 2018). Future additions could be the grant distribution formulas which allocate federal government funds to assist students in concentrated areas of poverty (Camera and Cook 2016;Camera 2019). These circulations of philanthropy and funding are relevant to the rapid growth of NYC schools over recent years (Scott and DiMartino 2009). Such school developments inform not only the input data for the school choice algorithm (the range of schools available from either being closed down, or starting up), but also the extent to which students and schools in low-income areas do, or do not, benefit from various philanthropic and funding practices.

Policy and Legislation
Surfacing the policy and legislation records which shape education reform and how schools operate is the focus of this counter-archiving category.

Cultural Record Example: 2003 Charter School Initiative
Our key focus here is on policies encouraging school choice, especially charter schools, introduced during the tenure of Mayor Michael Bloomberg, and led by the education Chancellor Joel Klein, from 2002 to 2013. A key policy was the Charter School Initiative in 2003, extending a 1998 Act that had supported the creation of charter schools, and building on the introduction of charters in the USA since 1992. The specific aim of the 2003 Initiative was to enable the creation of 50 more K-8 charter schools, based on ideas of education innovation, 'that could spread and help transform the educational system in New York City'. As [Joel] Klein put it, 'I wanted to make New York the Silicon Valley for charter schools' (Hatch et al. 2021). The introduction of the charter initiative was part of a broader push to connect accountability and autonomy in the schooling system, including creating publicly available data comparing school performance and student outcomes.
The cultural record highlights both how school choice creates forms of comparative data (e.g., on student outcomes) and how school choice algorithms enter heavily racialised choice policies. While over 160 schools were closed in NYC during the tenure of Bloomberg, the charter school initiative was one part of emphasizing choice in the system, as 'small schools of choice' (Elwick 2017). However, the closed schools were mostly large high schools in areas of disadvantage (Elwick 2017) and mostly attended by students of colour. Hence, as the school choice algorithm is about sorting for high school allocation, this artefact highlights how school choice that was expanded in K-8 had an inverse effect on choices for high school. Possible future records could include the following: the 1969 NYC School Decentralization Act that could highlight the historical racial segregation of schooling in NYC and the 1968 Fair Housing Act which sought to foster integration and outlaw housing discrimination.

Spatiality and Socioeconomics
This counter-archiving category highlights the spatial and socio-economic records shaping data infrastructures and inequalities in education.

Cultural Record Example: NYC Income and Racial Makeup Map
The links between demography, geography, and schooling are key to understanding how school choice operates in NYC. While the school choice algorithm only deals with high school allocation, this allocation obviously follows the opportunities provided to students in K-8. While schooling in NYC is formally desegregated, it is common for students in K-8 to attend the school closest to their home in heavily racialised areas, as well as being able to choose other schools (Kafka and Matheny 2021). Hemphill and Mader's (2015) interactive maps suggest there is not always a causal link between school segregation and housing in NYC. One map shows the median income for students attending elementary schools, including those in zones, and other schools such as charters. Analysis using the map 'demonstrates that 124 of the city's 734 neighborhood elementary schools … are substantially poorer than their school zones' (Hemphill and Mader 2015). Another map connects the racial makeup of elementary schools to the people living in each school attendance zone. The findings from this map showed less of a contrast than the income map, in that: 'Some 332 of the city's 734 neighborhood elementary schools have enrollments that are more than 90 percent black and Latino. Most of these are in neighborhoods that are also predominantly black and Latino.' (Hemphill and Mader 2015) The merit of adding this cultural record to the 'counter-archive' is that the authors conclude that the maps suggest parents are utilising school choice. This record highlights some reasons why choice is seen as necessary in NYC and already established prior to high school and the use of a school choice algorithm. Future additions to this counter-archive category could include maps of the connection between high school choices and demographics, including the racial makeup of teachers in NYC.

Activism and Communities
This counter-archiving category calls attention to the role activism and communities play in critically and creatively contesting inequalities in education.

Cultural Record Example: Integrate NYC Hackathon Prototype
In 2019, a group of NYC high school and undergraduate students, part of youthled organisation called IntegrateNYC, joined an all-day hackathon to create an algorithm prototype that could better reflect the city's diversity. The proposed idea from this event was a new algorithm could potentially 'boost disadvantaged students higher up in the matchmaking process, provided they have already passed a school's screening process' with the following features and priorities: highly correlated with race such as a student's census tract, whether they receive free or reducedprice lunch, and whether English is their second language (Cassano 2019). Notably, the students involved recognised other significant factors in the admissions process (such as neighbourhood segregation, student interests not adequately reflected, and how the screening out of candidates is done) but decided that the algorithm had the largest influence.
The benefit of this cultural record is that it raises the role of particular advocacy groups, such as IntegrateNYC, a group of youth leaders 'who repair the harms of segregation and build authentic integration and equity' (NYCIntegrate 2022). In 2020, the group launched a campaign to end discriminatory admission screens which claim to be 'open choice' but 'the choices students have are dictated by factors like zip code, grades, number of suspensions and arrests, and if a student is able to attend an in-person interview' (NYCIntegrate 2022). Future additions to this counter-archiving category could be other records generated by activist, youth, and community groups advocating for school choice reform targeted not only at the matching algorithm, but also broader inequalities impacting 'choice', for example, the historic efforts and vital role of the National Association for the Advancement of Colored People (NAACP) to address educational inequality, including calls to limit charter school expansion and enhance governance oversight (Jones 2016).

Discussion
Applying our education counter-archiving tool to the NYC matching algorithm case highlights what Amoore (2021) notes as the multiplicity and history of algorithms.
Of key importance is how data infrastructures and inequalities in education emerge in relation to cultural records signifying interrelated societal and technological changes. For example, the central calculative realm of the NYC algorithm is that school choice is not seen as a problem to be removed, but rather refined and made more efficient. While this algorithmic logic attempts to capture, classify, categorise, and sort various data (school, student, spatial, socio-economic) to enhance school choice, this ignores the wider infrastructure in which such automated decision-making operates. For example, in the NYC algorithm counter-archive, we also described the introduction, development, and scale of the NYC Automate the Schools student information system. This record also demonstrates the essential and power role of infrastructure, classification, and its consequences (Bowker and Star 1999): (i) how knowledge is produced; (ii) the visible and invisible work involved; and (iii) who/what is marginalised, ignored, and silenced in the process.
Our NYC algorithm counter-archive also exposes the way in which school choice algorithms are 'uncertain archives' (Agostinho et al. 2019) due to a key tension: between the proclaimed 'knowns' of algorithmic logic and, what ultimately exceeds the archive, the 'unknowable'. For example, the quest to ascertain certainty, drive efficiencies, and expand 'school choice' is promulgated as a key driver for developing, funding, and iterating the school choice algorithm. Yet the ADM enabled via algorithms relies upon foundational dataset inputs and outputs of increasingly digitised and networked organisational archives which embed inequalities by way of the diversity they cannot contain, for example, claims that algorithmic innovations offer more choice to parents and students belies that, while agency has been distributed in new ways, this 'choice' remains trapped in the narrow confines of algorithmic and choice logic. The consequences of these narrow confines are evident. As a form of ADM, school choice algorithms are forms of computation that 'aid or replace government decisions, judgments, and/or policy implementation' (Richardson 2021: 13) which can impact opportunities, access, rights, and liberties. Furthermore, what exceeds, or cannot be contained, within the algorithmic 'aperture' (Amoore 2021) are the broader spatial and socio-economic forces which impact school choice. Our NYC algorithm counter-archive, for instance, showed how existing school choice mechanisms impact families from predominantly black and low-income neighbourhoods in multiple ways. In addition, the NYC income and racial makeup map highlighted the broader repercussions of socio-economic and housing status, in particular, that opportunities are eroded for families to access quality public schools in close proximity to their home (due to historical spatial divisions and limited quality schools nearby), thereby restricting their right to education as a public good, as well as conditions for livelihood and liberty. The limits of the school choice algorithm therefore subjects families to only a superficial veneer of 'choice' and ignores existing spatial and socio-economic inequalities which perpetuates vulnerabilities associated with income and housing status. These inequalities are potentially perpetuated further by particular modes of philanthropy and funding, such as the encroaching Portfolio district schools model, plus legislation and policy changes, as evident from the 2003 Charter School Initiative.
This leads us to another aspect which the NYC algorithm counter-archive helps identify: the school choice algorithm as a site of knowledge politics and production which produces multivalent errors and inequalities as part of algorithmic logics (Amoore 2021). Recognising archives as 'political sites of information distribution' rather than as 'objective statements of truth' (Agostinho et al. 2019: 433) helps to detect the 'errors' which are not simply a technical deviation from a purported categorical claim, but rather hegemonic errors which deviate from attempts to ameliorate broader societal inequalities. For example, the NYCIntegrate algorithm prototype showed how young people from a youth activist organisation sought to query existing school choice datasets, by including other algorithmic inputs that they thought should inform the decision-making process (such as census tract/neighbourhood data, access to free/reduced lunch, and English as a Second language information). What these students have achieved is to highlight the 'residual categories' (Star and Bowker 2007) of what is silenced, or left out, of existing school choice classifications.
As ADM systems become more endemic across everyday life, how to recognise the politics of knowledge production, and reinforce the perspective of diverse community members, is critical. This recognition of categorical and societal inequalities aligns with calls to support and connect efforts for school choice with the ongoing 'Black freedom struggle for equality in education and all aspects of American life' (Horsford 2019: 268). A politics of knowledge around algorithms is evident in the NYC case. In 2019, the AI Now Institute, a policy and research centre, proposed a set of recommendations to the NYC DoE about its automated decision-making system (AI Now Institute 2019). We suggest that our education counter-archive could enact and expand their recommendations in the following ways: (i) to recognise ADS technical errors/failures through identifying the broader inequalities 'baked' into the data infrastructures in education; (ii) to assess ADS bias and discrimination by highlighting both categorical and societal inequalities; (iii) to illustrate how the ADS of emerging tech (such as facial recognition technology) interrelate with diverse cultural records (data, algorithm, and AI-based technologies, innovation and industry, philanthropy and funding, policy and legislation, spatiality and 1 3 socio-economics, activism and communities); and (iv) to inform ongoing evaluations of ADS and 'community listening sessions' to show the 'bigger picture' of ADS and how inequalities are exacerbated or could be ameliorated.
As machine learning, which utilises probabilistic methods to predict optimal decisions, is an increasingly relevant type of ADM in education (Gulson, Sellar, and Webb 2022), our counter-archiving tool offers a novel way to build upon existing approaches to evaluating and archiving ADM systems. For example, the education counter-archiving approach could augment existing methods for archiving and documenting ADM systems, such as 'datasheets for datasets' (Gebru et al. 2021) and 'model cards for model reporting' (Mitchell et al. 2019). Informed by critical and cultural-theoretical perspectives of data and archives (Thylstrup 2022;Agostinho et al. 2019), our localised and contextual nature of education counter-archiving offers an explicit tool for accountability that aims to expose the range of cultural records which shape the parameters of ADM systems.

Conclusion
In this paper, we have explored how certain kinds of inequalities become 'baked' into the algorithms and automated decision-making of data infrastructures in education. Our paper had the following aims: one, to explore the interrelationship between school choice algorithms and data infrastructures in education, and two, to propose a novel, multidimensional method to investigate how inequalities become embedded within ADM systems. These aims underpinned the creation of the education counter-archiving tool. The tool seeks to emphasise that the choices regarding which inequalities are mitigated, or reinforced, across data infrastructures in education are inherently ethico-political choices. Furthermore, the decisions regarding ADM systems (such as school choice algorithms) would benefit from being explored against a range of cultural records signifying socio-technical changes over time and within specific contexts.
Due to the limits of this article, the cultural record examples chosen reflect only a small proportion of what could inform the NYC algorithm counter-archive. For example, future iterations could include additional cultural records uploaded to a digital archive. This digital counter-archive could be a knowledge-sharing resource which policymakers, researchers, and educators could practically utilise as a collective learning tool to explore the range of cultural records which shape the history and present of ADM systems, such as school choice algorithms. This form of counter-archival participation and insights could then be used to advocate for change which ameliorates, rather than exacerbates, inequalities in education.
The future possibilities of interrelated cultural records across education policy and governance have a long history, steeped in specific contexts and cultures, which must be critically and creatively addressed in the present. This is because novel forms of digital archives reflect the uncertainty of traditional archives (Agostinho et al. 2019) and are the 'latest instalment in a long negotiation between surveillance technology and its subjects (or objects), between control and uncertainty, order and chaos, and ultimately between power and knowledge' (423). Our education counter-archiving tool seeks to counter the glossy 'newness' and efficiency 'knowingness' of emerging technologies introduced across increasingly automated data infrastructures in education. We argue that to better understand the futures and consequences of ADM in education, we must better understand the histories and inequalities embedded in the present.