An Island Game

There are five barbarians on an island (chief, first servant, second servant, third servant, fourth servant) playing a game. Each of the four servants will first vote on whether the chief stays chief or is burnt alive. If the chief is burnt alive, first servant becomes chief, second servant becomes first servant, etc. In the case of a tie, the current chief remains chief. The game continues in this way until the chief remains chief. Who will be chief at the end of the game?

Hint: Though brutal, all the barbarians are smart: they value their own life first, their rank second. They also know how the other servants will vote.

To win, tell me who won, and also give an explanation. Riddles are no fun if it’s just a foggy lucky guess!