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Test X predicts achievement Y in school A. Peter scores x on that test, and is therefore denied access to A. How unfair can that be? (Hint: predictive validity is a characteristic of test x population x situation; the test score is one of a particular human being)
The case of admission to the Civil Service: Francis Y. Edgeworth (1888). The statistics of examinations. ‘Journal of the Royal Statistical Society, 51’ 599-635. jstor.org/stable/2339898 The exam is a lottery offering better chances to the better prepared, which is not unfair. 
On lotteries in education, see benwilbrink.nl/projecten/lott… In the Netherlands admission to studies with a restricted number of slots was regulated by weighted lottery from 1975-2017 (since then selection is by whatever instruments are deemed opportune, lotteries being outlawed!)
