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We embed the problem of public school choice design in a model of local provision of education. We define cardinal (student) segregation as that emerging when families with identical ordinal preferences submit different rankings of schools in a centralised school choice procedure. With the Boston Mechanism (BM), when higher types are less risk-averse, and there is sufficient vertical differentiation of schools, any equilibrium presents cardinal segregation. Transportation costs facilitate the emergence of cardinal segregation as does competition from private schools. Furthermore, the latter renders the best public schools more elitist. The Deferred Acceptance mechanism is resilient to cardinal segregation.