I get it, but it doesn't change my opinion that prestigious US universities are harder to get in to than British ones. That may be because 1) the US simply has a larger population (though you would think UK unis especially LSE would be an aspirational destination for students from throughout the entirety of the former empire), or 2) it may reflect the peculiarities of the application process, specifically in the sense of you can only apply to 5, to either Oxford OR Cambridge, etc.
However I find those two reasons not convincing enough to change my original opinion. Of US universities' applicant pools, probably 75% stand a solid chance of admission (a number plucked from out of the blue). Yet for almost all prestigious US universities, of which there are probably 40 or 50, admissions rates hover around 20% and, in the case of at least 30 of them, go below (sometimes wayyy below). Therefore, just as Oxbridge turns away a ton of qualified applicants, so do most US schools. This is important to refute the notion that a bunch of stupid people wing applications at Harvard because of the Common App and this distorts statistics; the vast majority of people who apply(ied) to Harvard, myself included, were well-qualified yet still got owned in the end. The admissions stats of the Ivy League, which would be most analogous to Oxbridge in terms of prestige, fall into the sub-10% range, while Cambridge's chill in the mid 20's.
Furthermore, what you have to remember is that the manifold special interests which exercise a disproportionate amount of influence in the American college admissions game - specifically athletics departments, affirmative action initiatives, and legacies - simply do not exist in Britain, or at least do so in much reduced form. In America, these special interests combine to positively influence the applications of probably 30% at least of the admitted students (10% URMs, 10% athletes to get the big donors to maintain their ties to the school by coming to games and thereby keep those donors' money flowing in, 10% Board of Trustees' sons/daughters). These special interests therefore get at least 30% of the spots in your average university class, yet they make up probably 5% or less of the applicant pool. That leaves the rest of the applicant pool, probably 95% (of whom probably 75% could conceivably stand a chance being admitted) to compete for the remaining 70% of leftover spots.
Let me quantify this to make this easier. Say we take a relatively prestigious (not Ivy, but "very good" lower 1st tier uni) that says it has an admissions rate of close to 20%. 500 spots. 2500 applicants. Yet the special interests get 165 (30%) of the spots. That leaves 2,335 applicants (of whom 75%, or 1750-odd, are probably eligible for admission) to compete for the remaining 335 places. Thus the stated admissions rate of 20% in reality is, for someone without special connections, 335/2335= 14%. That's theoretically Ivy territory; imagine the process at work in Ivy admissions, and 14% goes down to 7, or 7% goes down to, God knows what, 3%? So US college admissions rates are even lower than advertised; yet even using the advertised rates, the rates are still lower than in Britain.
Allz I'm saying is that it's harder to get into prestigious US universities than UK ones. Don't flame me yet. I never said the quality of the EDUCATION you receive at prestigious US schools is better than at equivalent British ones on account of the more-competitive student bodies they have. I haven't formed a general opinion on which system is superior to which once you've gotten in the door and actually arrived at university. All I've said is that I think US universities are harder to get into.