MICHAEL WANG, a young Californian, came second in his class of 1,002 students; his ACT score was 36, the maximum possible; he sang at Barack Obama’s inauguration; he got third place in a national piano contest; he was in the top 150 of a national maths competition; he was in several national debating-competition finals. But when it came to his university application he faced a serious disappointment for the first time in his glittering career. He was rejected by six of the seven Ivy League colleges to which he applied. “I saw people less qualified than me get better offers,”...