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Since Brown vs Board of Education established that racial segregation laws were unconstitutional, school assignment has been a contentious issue, shaped by shifting legal standards and political struggles over race, equity, and the state’s role in civic society. More than 100 American school districts now assign students to public schools through an open enrollment process that uses algorithmic matching systems based on individual preferences. In principle, algorithmic matching promises to democratize access to education by decoupling school assignment from residential location—giving all students the same chance to attend high-performing schools, rather than being bound to segregated and unequally resourced neighborhood schools. Yet in practice, these systems exacerbate economic and racial inequalities, and families view algorithmic systems as opaque, unpredictable, and unfair even though they remove human discretion from assignment decisions. We ask: How do families conceptualize fairness in algorithmic school assignment? How does the structure of the assignment system shape these understandings? How do ideologies like neoliberalism relate to the design and perceptions of this system? We answer these questions drawing on surveys and in-depth interviews of parents in the San Francisco Unified School District. We find that parents’ conceptions of the fairness of algorithmic school assignment vary not only quantitatively (how fair they perceive the process to be), but also qualitatively (what fairness means to them). In addition, their perceptions are shaped by race, class, and geography, and the structure of the school assignment system itself. Open enrollment’s focus on the process, including the family’s role in ranking schools, helps legitimate assignment outcomes through factors that increase procedural justice. Procedural justice, however, measures parents’ perceptions that the outcomes are fair, not whether assignments are objectively fair. Delegating decision-making authority to technology obscures how unequally resourced schools map onto residential segregation, creating structural inequality not addressed through preference satisfaction.