musical chairs

a child's game in which players march to music around a group of chairs that contains one chair less than the number of players; when the music abruptly stops the players scramble to sit and the player who does not find a chair is eliminated; then a chair is removed and the march resumes until only the winner is seated

a rearrangement that has no practical effect or significance

“the company is looking for stability after years of musical chairs with directors”