Regarding cross admits between Stanford, Ivies, MIT and top LACS, there is a general pattern of admits across all of these institutions. For the smaller schools, you occasionally do see some candidates opting for the faculty to student interaction and ability to play college sports offered by the LACS. Also, due to the smaller class size at the LACS, as mentioned previously, the need of creating an interesting class results in some random rejections or deferrals from candidates that are accepted at the larger schools and vice versa.