Admissions rules play an important role in many aspects of life. Among others, they regulate the allocation of students to schools. Today digitalisation enables decision makers to use computer-based matching algorithms, which control how thousands of applicants are matched to schools in the blink of an eye. Admissions rules and criteria are decided in democratic processes, though, due to their controversial nature, they are often the subject of intensive debate. This is because intended outcomes may have adverse side effects. In late 2017, controversies surrounding criteria for admissions to university and kindergarten even made their way to the German federal constitutional and administrative court. The novel perspective of this research project is to conceptually and empirically analyse the design and outcomes of admission rules under alternative assumptions on the goals of policy makers. On the one hand, complementarities during teaching, arising from peer effects, among other factors, are one reason for fostering ethnic, socio-economic and gender diversity to improve equality of opportunity. On the other hand, politicians motivated by re-election concerns may instead design rules that favour certain social groups, and reinforce social segregation.