How we cite the quotes:
Citations follow this format: (Chapter.Paragraph)

“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.” (1.229-231)

Jack’s desire for power is no product of the island; this is a trait that he’s had from the start.

The suffusion drained away from Jack’s face. Ralph waved again for silence.
“Jack’s in charge of the choir. They can be – what do you want them be?”
“Hunters.”
Jack and Ralph smiled at each other with shy liking. The rest began to talk eagerly. (1.254-257)

Ralph and Jack are made similar by their desire for power, but differ in their treatment of that power. Ralph is happy to parcel it out, but Jack will later want it all for himself.

“You're no good on a job like this.”
“All the same –”
“We don’t want you,” said Jack, flatly. “Three’s enough.” (1.274-276)

While Ralph and Jack both assert authority over Piggy, Ralph at least tries to explain his reasoning (the mark of a good leader), whereas Jack brings personal insult to the matter (the mark of a bad leader).

“A fire! Make a fire!”
At once half the boys were on their feet. Jack clamored among them, the conch forgotten.
“Come on! Follow me!”
The space under the palm trees was full of noise and movement. Ralph was on his feet too, shouting for quiet, but no one heard him. All at once the crowd swayed toward the island and was gone – following Jack. (2.120-123)

Jack takes advantage of impulsive mob mentality to get his way, whereas Ralph appeals to reason.

Henry was a bit of a leader this afternoon, because the other two were Percival and Johnny, the smallest boys on the island […].
Roger and Maurice came out of the forest […]. Roger led the way straight through the [sand] castles, kicking them over, burying the flowers, scattering the chosen stones. Maurice followed, laughing, and added to the destruction. (4.7-8)

On this island, power is gained by tyrannical actions against others.

Ralph pushed Piggy to one side.
“I was chief, and you were going to do what I said.” (4.132-133)

Although Ralph asserts his power here, he does for the sake of the signal fire and the prospect of getting rescued. For Ralph, power is a means to an end, not the end itself.

“I painted my face – I stole up. Now you eat – all of you – and I –“ (4.191)

Jack tries to gain authority by giving the others meat. This is the only way he can derive power.

Jack’s face swam near him.
“And you shut up! Who are you, anyway? Sitting there telling people what to do. You can’t hunt, you can’t sing –”
“I’m chief. I was chosen.”
“Why should choosing make any difference? Just giving orders that don’t make any sense –” (5.238-241)

Democracy has no value for Jack. His ambition blinds him to the point where he sees no “sense” in Ralph’s grounded and reasonable orders.

Something deep in Ralph spoke for him.
“I’m chief. I’ll go. Don’t argue.” (6.155)

When Jack painted his face, we saw that “the mask compelled” the boys to obey. Here, too, it is not Ralph, but rather “something deep in” him that speaks. For better or worse, both boys are affected by their roles as leaders.

“Who thinks Ralph oughtn’t to be chief?”
He looked expectantly at the boys ranged around, who had frozen. Under the palms there was deadly silence.
“Hands up?” said Jack strongly, “whoever wants Ralph not to be chief?”
The silence continued, breathless and heavy and full of shame. Slowly the red drained from Jack’s cheeks, then came back with a painful rush. He licked his lips and turned his head at an angle, so that his gaze avoided the embarrassment of linking with another’s eye.
“How many think –”
His voice trailed off. The hands that held the conch shook. He cleared his throat, and spoke loudly.
“All right then.”
He laid the conch with great care in the grass at his feet. The humiliating tears were running from the corner of each eye.
“I’m not going to play any longer. Not with you.” (8.67-75)

This quote actually causes us (the reader) to feel sorry for Jack. Passages like this are important to remind us that the boys really are young children; they get embarrassed, they cry, and they throw temper tantrums. When we are hit in the face with the boys’ humanity, we are that much more disturbed by the horrors that follow.

“I’m warning you. I’m going to get angry. D’you see? You’re not wanted. Understand? We are going to have fun on this island. Understand? We are going to have fun on this island! So don’t try it on, my poor misguided boy, or else–”
Simon found he was looking into a vast mouth. There was blackness within, a blackness that spread.
“–Or else,” said the Lord of the Flies, “we shall do you, see? Roger and Maurice and Robert and Bill and Piggy and Ralph. Do you. See?” (8.345-349)

The Lord of the Flies derives power through intimidation.

Jack spoke.
“Give me a drink.”
Henry brought him a shell and he drank, watching Piggy and Ralph over the jagged rim. Power lay in the brown swell of his forearms: authority sat on his shoulder and chattered in his ear like an ape.
“All sit down.”
The boys ranged themselves in rows on the grass before him but Ralph and Piggy stayed a foot lower, standing on the soft sand. Jack ignored them for the moment, turned his mask down to the seated boys and pointed at them with his spear.
“Who is going to join my tribe?” (9.52-57)

Jack wears his chiefdom with all the pomp and circumstance that was notably absent from Ralph’s character.

Roger edged past the chief, only just avoiding pushing him with his shoulder. The yelling ceased, and Samneric lay looking up in quiet terror. Roger advanced upon them as one wielding a nameless authority. (11.231)

Here we see the tension between Roger and Jack, and also that, as bad as Jack is, Roger is the real one to look out for. Also, what is the “nameless authority?” Violence? Intimidation?

Her bows [were] hauled up and held by two ratings. In the stern sheets another rating held a sub-machine gun. (12.211)

The desire for power and the taking of power by violent means is not limited to the island.