But the current system doesn't give the Presidency to the person who gets the majority of popular votes. It goes to the guy selected by the electoral college, regardless of whether fifty million people voted to him or none, in theory. So clearly there's no requirement that the person who gets the majority of popular votes wins.

(What happens if guys in the electoral college say "Hey, I'm not voting for either one" and thus make it impossible for a majority to be achieved? Yes, it's never HAPPENED, but I see no reason to believe it's physically impossible)