> Ranking would be necessary, because it could be that three people in school B want to attend school A, while only two people in school A want to attend school

> Ranking would be necessary, because it could be that three people in school B want to attend school A, while only two people in school A want to attend school B. That is exactly what I wrote, "That is some sort of perversion of personal greed into a form that instead limits what others may have." Do you honestly not see the injustice with choosing to disadvantage all five instead of only one in your example?