In chapter one Jack states, "I ought to be chief, becasue I'm chapter chorister and head boy. I can sing C sharp." In chapter eight Jack criticises Ralph's leadership by say "He's not a hunter. He'd neevr have got us meat." Which by implication means that as Jack is a hunter and has got them meat he should be leader.
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Ralph is elected as the chief but Jack assumes the role of chief of the hunters.
Ralph is elected chief during the very first meeting, which happens very early in the book.
When Ralph is elected to be chief he knows Jack is dissapointed (as Jack also wished to be chief) so he appoints Jack as leader of the choir and asks him what he wants them to be, to which Jack replies, "hunters."
During the first meeting, which was held in chapter 1: The Sound of the Shell, Ralph was elected as the chief. Later in the book Jack formed his own tribe and appointed himself as chief.
Chief Jack House died in 1971.