Notwithstanding an ongoing concern about the low representation of certain groups in higher education, there is reluctance on the part of politicians and policy makers to adopt positive discrimination as an appropriate means of widening participation. This article offers an account of the different objections to positive discrimination and, thereafter, clarifies and criticises the view that universities ought to select those applicants who are expected to be most successful as students. It distinguishes arguments from meritocracy, desert, respect, and productivity and shows how these arguments are compatible with the use of positive discrimination in higher education. (Contains 20 notes.)