Yes, in theory, a shoeshine boy from a poor provincial town in Peru can go to Stanford and do a PhD, as the former Peruvian President Alejandro Toledo has done, but for one Toledo we have millions of Peruvian children who did not even make it to high school. Of course, we could argue that all those millions of poor Peruvian children are lazy good-for-nothings, since Mr Toledo has proven that they too could have gone to Stanford if they had tried hard enough. But I think it is much more plausible to say that Mr Toledo is the exception. Without some equality of outcome (of parental income), poor people cannot take full advantage of equality of opportunity.