How much does an undergrad math education differ among top colleges?

I don’t know if Yale does or does not protect its yield. But if it does, it would usually not do so with a flat out reject since there is no compelling reason for Yale to assume a student strong enough for Princeton would not choose Yale. If Yale were protecting their yield they would use the wait list and see if the students asks to get off the wait list.

But Yes IxnayBob, the syndrome is real and has been demonstrated. see
http://onlinelibrary.wiley.com/doi/10.1002/ir.187/abstract and http://www.nber.org/papers/w10803 and http://www.nber.org/papers/w15772