I know this will sound stupid, but I recently spoke with some friends who said that it's better to apply to just one school EA because it shows them that they really are your first choice. I want to apply to both MIT and Caltech EA, but I don't really have a FIRST choice school. Both schools are great, have unique nerd cultures, etc.
Do schools crosscheck students to see where they applied? Will applying to both Caltech and MIT hurt me?