Book: The Tyranny of Merit
Each year, more than 40,000 students apply for the roughly 2,000 places that Harvard and Stanford have to offer. The author's proposal is, of the over 40,000 applicants, we first filtered out those who may not be qualified to perform well. This would winnow out perhaps 10,000 to 20,000 students.
Next, rather than try hard to predict who is the most talented and most likely to be successful, we choose the entering class by lottery.
This proposal doesn't ignore merit, but it treats merit as a threshold qualification, not an ideal to be maximized. This is sensible since, firstly, even the wisest admissions officers can't assess precisely which student will wind up being successful.
And the most compelling reason for this proposal is that it combats the tyranny of merit. As in the author's words: "Setting a threshold of qualification and letting chance decide the rest would restore some sanity to the high school years, and relieve, at least to some extent, the soul-killing, résumé-stuffing, perfection-seeking experience they have become. It would also deflate meritocratic hubris, by making clear what is true in any case, that those who land on top do not make it on their own but owe their good fortune to family circumstances and native gifts that are morally akin to the luck of the draw." 
 "In an unequal society, those who land on top want to believe their success is morally justified. In a meritocratic society, this means the winners must believe they have earned their success through their own talent and hard work. Paradoxically, this is the gift the cheating parents wanted to give their kids. If all they really cared about was enabling their children to live in affluence, they could have given them trust funds. But they wanted something else—the meritocratic cachet that admission to elite colleges confers." - Sandel, Michael J. The Tyranny of Merit (p. 13)