The beginning of chapter eight of Lord of the Flies is primarily a power struggle between Ralph and Jack. Jack stages a kind of power takeover, but he is not successful. He accuses Ralph of being like Piggy--and he does not mean it as a compliment.
“He’s like Piggy. He says things like Piggy. He isn’t a proper chief.”
When Jack calls for a re-election but does not win, he leaves in tears, running off into the jungle.
Piggy immediately tries to scold Ralph, but Ralph is preoccupied and "Piggy gave up the attempt to rebuke Ralph." It is hard for Piggy to feel badly about Jack's departure, of course, and he says they are all better off now that Jack has vowed to stay on the mountain. Piggy does understand that Jack is more dangerous than ever to both him and Ralph, but he is relieved nevertheless.
Soon, however, Piggy gains some confidence. Knowing that no one who is left on the beach ("Ralph's lot") will mock him or tell him to shut up, Piggy begins to take charge.
Piggy was speaking now with more assurance and with what, if the circumstances had not been so serious, the others would have recognized as pleasure. “I said we could all do without a certain person. Now I say we got to decide on what can be done.”
Piggy suggests that they keep a fire going here on the beach (it had been moved up the mountain for a better chance of rescue), and the idea was well received.
The greatest ideas are the simplest. Now there was something to be done they worked with passion. Piggy was so full of delight and expanding liberty in Jack’s departure, so full of pride in his contribution to the good of society, that he helped to fetch wood.
After Jack leaves, Piggy changes dramatically, from an intimidated boy into a real leader. It is a timely transformation, since Ralph is struggling to collect himself after his confrontation with Jack.