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”

“shareholders don't want the company playing musical chairs with their investment”