I am a Stanford undergraduate, and I recently looked at the comments that my admission officers made on my file. These comments as well as the comments that many of my friends received on their reader cards suggest that Stanford does, indeed, consider choice of major when evaluating applicants, despite their assertions to the contrary. It seems like they compare you to others who are applying for the same major. For example, one of my friends applied as an X major (not disclosing so as to protect his privacy), and his admission officers wrote something to this effect on his file: “Strong applicant, but we have stronger people who want to major in X.” Some of my friends who selected less popular majors (i.e., philosophy) had comments on their files to the effect of, “We should take this person since he/she is really strong AND wants to major in this underrepresented field.”
So it appears that your choice of major could potentially have SOME affect on your admission decision. It is true, though, that once you get to Stanford, you can choose whatever you want. I’ve known people who’ve entered wanting to do Music, Philosophy, History, Math, etc. and have ended up doing CS instead.
Since Stanford’s CS numbers are quite bloated, I can’t help but think that admissions is actively trying to keep the number of undergrads interested in CS under control. The Dean of Admission gets at least some of the blame from the Faculty Senate when they become discontent about so many students flocking to CS. Therefore, if I were choosing between ranking CS first and ranking Math first, then I would probably choose Math.
Please note that admissions has a pretty good ability to tell if people are misrepresenting their interests so as to gain an advantage. For example, if all of an applicant’s EC’s in high school involved programming/robotics and this person applied as a History major interested in pre-law, then admissions would likely be able to tell that this applicant is gaming the system. Such applicants are instant turn-offs and are usually rejected. So the “I want to major in something underrepresented” hook only works if you have demonstrated interest and talent in a field that is underrepresented at Stanford (i.e., anything involving the humanities). I don’t think that wanting to major in Math will help too much, as Math is still a STEM field, and Stanford is trying hardest to recruit humanities and social science kids.
You should also know that intended major is only one of many factors that are considered during the admissions process, and in some cases, applying for a very popular major like CS could be advantageous. I would be willing to say that a female minority with demonstrated interest in CS would be a very strong applicant, but that’s just speculative.