PurpleTitan, I think the numbers actually support the notion that in most cases, elite private universities prefer ED over EA overwhelmingly.
HYPSM know that their brand is powerful enough not to need ED. Those schools have yield rates in the 60%-80% range, even without ED. Caltech is a niche school. Their only true competitor is MIT.
Beyond those 6 schools, the vast majority of elite private universities offer ED, not EA. Chicago and Georgetown are the notable exceptions, which I admittedly do not understand…especially Chicago. Just look at the numbers among top LACs and Universities. The picture is pretty clear:
ED:
Amherst College
Bowdoin College
Brown University
Bryn Mawr College
Carleton College
Carnegie Mellon University
Claremont McKenna College
Colgate University
Columbia University
Cornell University
Dartmouth College
Davidson College
Duke University
Emory University
Harvey Mudd College
Haverford College
Johns Hopkins University
Middlebury College
Northwestern University
Pomona College
Rice University
Swarthmore College
Tufts University
University of Pennsylvania
University of Notre Dame
Vanderbilt University
Vassar College
Washington University
Wellesley College
Wesleyan University
Williams College
EA:
Georgetown University
University of Chicago