Lack of diversity in higher education is partly driven by long-run belief distortions about admission chances at elite colleges. We depart from the rational expectation framework and propose a simple model of expectation formation in which students estimate their admission chances by sampling a pool of given size τ of peers who previously applied to elite colleges. Assuming students consider peers with abil-ity as close as possible to their own, two types of inefficiencies arise in steady state: high-achieving disadvantaged students self-select out of elite colleges, and average students from advantaged families apply to elite colleges even though their true admission chances are null. We then explore the working of the model when students from several possibly dissimilar neighborhoods compete for the same positions, thereby highlighting externalities related to the comparative neighborhood com-positions. Several policy instruments such as quotas or the mixing of neighborhoods are considered.