Admission systems play a critical role in shaping educational opportunities by determining what choices are available to whom. Policy makers and institutions must balance multiple, often conflicting, goals which requires trade-offs between competing values. In this paper, we present core values for admission to higher education alongside a novel framework for centralized admission systems, addressing two central questions: (1) Who is eligible to apply? and (2) Who gains entry when there are more eligible applicants than seats available? Using the framework in combination with examples and ongoing policy discussions, we offer key insights into the complexities of admission systems.