Who's So Vain?

70s singer/songwriter (and wife of James Taylor, 1972-83) Carly Simon turns 65 today.  Which reminded me of her 1972 hit single, "You're So Vain."  I don't recall if she ever admitted to the real subject of that song, but I do know there's been speculation for decades now about just who was the man in question.  Mick Jagger (who sangback-up on the song)?  Warren Beatty?  (If you know, tell us.  This isn't a quiz.  I'm curious).