I think that a couple of things favor Columbia in this decision:
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Both are great schools with excellent student:teacher ratios, but it’s 6:1 at Columbia with 80% of classes under 20 vs 9:1 and 60% at Notre Dame. A great situation at Notre Dame is even better at Columbia.
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My friend’s son told me that almost all of his classes at Columbia were small seminars with a lot of discussion. I think that for someone who is interested in academia and really getting into the subject matter, the small seminars and low teacher:faculty ratio favor Columbia for the kinds of experiences and faculty relationships that you’ll find valuable.
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Columbia sponsors a full year study abroad program at the London School of Economics. Both schools have strong study abroad opportunities, but for a potential Econ major, even a semester at the London School of Economics would seem to be an invaluable experience - especially where the goal is to go on for a doctorate.
With two Top 20 schools, both will offer wonderful opportunities, so the small differences may be the tie breaker. These 3 stood out to me. There may be others in the fine print.