Across the United States, a growing number of school districts are turning to matching algorithms to assign students to public schools. These algorithms have theoretical properties that should guarantee fair and efficient assignments. However, school districts have encountered practical challenges in their deployment. For instance, schools in San Francisco have become even more segregated than the neighborhoods they are in since the district introduced an assignment algorithm. Using the assignment system in San Francisco Unified School District as a case study, we find that the theoretical promises of matching algorithms rely on modeling assumptions that fail to account for the complex sociopolitical dynamics that exist in the student assignment context. Drawing on Elinor Ostrom’s principles for effective governance, we argue that standard matching algorithms are an insufficient institution for controlling the distribution of public resources where issues of distributive justice are important in addition to individual preferences. We suggest four design improvements: provide accessible, relevant information; balance optimizing for individual preferences and community-level goals; define collective goals in collaboration with stakeholders; and support informed deliberation of trade-offs. These principles expand our understanding of fair and democratic participation beyond eliciting and efficiently satisfying individual preferences.