Hare today... Good idea
! 'Twas even better when Hendrik Hertzberg first proposed it. (Okay, if we really
want to play this game, maybe we have to go back to John Mill or something… whatever!) The only real obstacle, I think, is Article I of the U.S. Constitution, saying that every state "shall have at Least one Representative." To get around that pesky business, I think Hertzberg suggested having 435 regular Congressmen, and 50 "at large" congressmen. But for the at-large folks, the Hare method would be too messy for any more than about 50 candidates, so it's easier to just vote on a slate of candidates.
However, if you wanted to split up the Senate 50-50 (50 in-state candidates, 50 at-large candidates), then you could select the at-large Senators by the Hare system, since mathematically you would only need to list about 7 candidates at most. Too messy for Congress, though. Yup!