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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.