Checkers, at least as played in tournaments and matches. Though this may not qualify as a "popular" game, since almost everybody plays checkers/draughts without any three-move ballot or other randomization.
First, Capablanca decides that the game is played out and proposes a new form of chess. Then, Bobby Fischer decides the same thing and proposes Fischer Random chess. Now Carlsen wants to change the rules; at least, he goes with Fischer's version rather than suggesting something brand new.