"The shareholders elect the Board which has the responsibility to hire and fire the CEO. The Board has the right and the responsibility to fire the CEO if they believe it is in the best interests of the company. If the shareholders don’t like the decision, they can call a special meeting of the shareholders to fire the Board and appoint new Directors. The new Board may re-hire the recently fired CEO. So the majority shareholder CEO will ultimately prevail."
https://www.quora.com/Can-a-board-of-directors-fire-a-CEO-th...
It seems like a rock, paper, scissors kind of game if the CEO owns the majority of voting shares.