Well, when the boys decide that they should have a chief, Jack immediately chirps up and puts himself forth for the role:
'Shut up,' said Ralph absently. He lifted the conch. 'Seems to me we ought to have a chief to decide things.'
'A chief! A chief!'
'I ought to be chief,' said Jack with simple arrogance, 'because I'm chapter chorister and head boy. I can sing C sharp.'
'Well then,' said Jack, 'I-'
He hesitated. The dark boy, Roger, stirred at last and spoke up.
'Let's have a vote.' 'Yes!'
'Vote for a chief!' 'Let's vote-'
One rather suspects that, were the boys not to have opted for democracy, Jack would probably have ensured that he was in charge of the island just as he arrives in charge of the choir ("chapter chorister"). "Jack started to protest..." Golding tells us, but it was too late.
Ralph counted. 'I'm chief then.'
The circle of boys broke into applause. Even the choir applauded; and the freckles on Jack's face disappeared under a blush of mortification. He started up, then changed his mind and sat down again while the air rang. Ralph looked at him, eager to offer something.
'The choir belongs to you, of course.'
Jack is indeed annoyed, "mortified", by Ralph winning the election. And Ralph knows it: he offers him the choir to lead. This simple act of empathy from Ralph might well be considered the biggest mistake Ralph ever makes!