To be fair to Stanford, their yield itself is probably somewhat deceptive. Yale and Stanford accept a lot of the same people, and Yale's ridiculous yield must do nasty things to Stanford as a result of Stanford's small class size. While Harvard also factors into the equation (and also loses its fair share of cross-admits to Yale), its larger size works to make that less of a harm to their own yield.
That said, I still think Harvard probably beats out Stanford on cross admits, and probably somewhat clearly too. While the 20% yield difference is likely deceptive, it's still a 20% yield difference.
I agree with Inspector Javert on this. If you look at the hard numbers, approximately 270 people turn down Harvard every year and 230 people turn down Stanford. Considering that HYS are competing for pretty much the same students, the loss of Yale cross-admits (anywhere from 100-150 of those 200+ students) does a lot more to hurt Stanford's yield than it does to hurt Harvard's yield. The only real competition to HYS are the big scholarships at CCN and maybe the Darrow--and I don't think that many people take those over HYS.
Right, which leads to Stanford having fewer Black students and so on. What's interesting is that I don't think Yale practices any of this with regards to openly gay students, especially those with any background in activism. I suspect more than any discernable subcategory of applicants, this is where Harvard would trounce Yale in crossadmits. Yet Yale will go after students and play hardball to try to win them away, thinking that they can overcome any perceived advantage that Harvard has, including sheer size. I've seen it work (and fail). Stanford just seems a little fatalistic on this point. Their loss.
Purely anecdotal, but I got much more LGBT-related recruiting from Yale than Harvard. Yale sent me all their Outlaw information, put on a big gay party during admit weekend, invited LGBT'ers to the minority admits day, and even had one of my bf's friends (now a Yale 2L) try to convince me to attend. Harvard, on the other hand, never sent me any LGBT-related correspondence and didn't have very much diversity-specific programming during its ASW (sorry absy!).