[nindalf]

A lottery appears to be a reasonable solution but it has a problem. The admissions system has two objectives - selecting students according to criteria that Harvard deems important and second, giving the public perception of selecting quality students. If it was publicly known that getting was a lottery, then the perception of quality takes a hit.

[taormina]

I mean, if we really have this many "perfect on paper and equivalent" students applying, toss out everyone who was less than perfect and then run the lottery on the cream of the crop.