Understanding how people perceive algorithmic decision-making is remains critical, as these systems are increasingly integrated into areas such as education, healthcare, and criminal justice. These perceptions can shape trust in, compliance with, and the perceived legitimacy of automated systems. Focusing on San Francisco's decade-long policy of algorithmic school assignments, we draw on procedural and distributive justice theory to investigate parents' fairness perceptions of San Francisco's school assignment system. We find that key differences in parents' definitions of fairness shape their preferences for what constitutes a fair school assignment system, while also controlling for parents' school assignment outcomes. Moreover, parents' definitions and perceptions of fairness differ across socioeconomic and racial groups. For instance, among white respondents, the most used definition of fairness was "proximity'' to their assigned school, whereas, among Hispanic or Latino parents, the most popular definition of fairness was that the "same rules'' are applied to everyone. It is crucial for computational system designers and policymakers to consider these differences when deciding on the goals and values embedded in decision-making systems and who those goals and values reflect.

Emerging methods for participatory algorithm design have proposed collecting and aggregating individual stakeholders’ preferences to create algorithmic systems that account for those stakeholders’ values. Drawing on two years of research across two public school districts in the United States, we study how families and school districts use students’ preferences for schools to meet their goals in the context of algorithmic student assignment systems. We find that the design of the preference language, i.e. the structure in which participants must express their needs and goals to the decision-maker, shapes the opportunities for meaningful participation. We define three properties of preference languages – expressiveness, cost, and collectivism – and discuss how these factors shape who is able to participate, and the extent to which they are able to effectively communicate their needs to the decision-maker. Reflecting on these findings, we offer implications and paths forward for researchers and practitioners who are considering applying a preference-based model for participation in algorithmic decision making.