No but, in chapter 8: Gift for the Darkness, Jack did ask the rest of the boys to put their hands up if they didn't want Ralph to be chief anymore. None of the boys raised their hands.
No, in "Lord of the Flies," Jack did not directly tell Ralph to quit as chief. Instead, he used manipulation and rebellion to undermine Ralph's leadership and eventually take control himself.
As chief(leader).
Ralph is elected as the chief but Jack assumes the role of chief of the hunters.
The vote was between Jack and Ralph. When all the boys voted they chose Ralph as their leader. :)
In "Lord of the Flies," after the boys' assembly, only Jack and his choirboys vote for Jack to be chief. This means the majority of the boys, including Ralph, did not vote for Jack to be chief.
They were fighting to becoming better chief in the island
Ostensibly it is Ralph, although his position is challenged later in the story by Jack
Ralph is made chief in Chapter 1 of "Lord of the Flies" by William Golding.
He puts Jack in charge of the choir and asks Jack what he wishes them to be, to which Jack replies "Hunters."
Ralph
Jack and Ralph.
Ralph is elected as the chief but Jack, no longer content with just controling his hunters, later apoints himself as a rival chief.
When they are rescued in "Lord of the Flies," Ralph claims to be the chief as he is the protagonist who tried to maintain order and civilization on the island. However, he is challenged by Jack, who led the boys into savagery and rebellion against Ralph's leadership.