Ralph and Jack, who become the leaders of the group, lack this kind of legitimacy. Similarly, state governments have the authority, within their own boundaries, to set laws and expect them to be followed, but based on the principle of state sovereignty they lack the authority to tell other states what to do (even if they're more powerful economically and/or militarily). As a general rule, In order for one state to get another state to do what it wants it must use force.
This situation mirrors the position of Ralph and Jack who have some authority but little legitimacy, and in order for them to maintain their authority they rely on continual shows of force. Ralph does this primarily by blowing the conch and ordering an assembly where he's the dominant figure. Jack on the other hand derives his authority from the power to kill and get meat. As the boys sink into savagery becoming more and more desperate, Ralph's power, which is more ideological than material, proves inferior to Jack's more tangible power. In essence, Ralph has influence but he lacks true power in the Realist sense. On the other hand, Jack proves more capable of fulfilling a social contract with the boys on the island. He offers them meat and protection from "the beast" in return for their loyalty while Ralph can only appeal to their vague and immaterial hope of being rescued. When push comes to shove, the boys prove willing to sacrifice order, civilization, and long term goals in order to meet their basic needs and animal instincts in the short term. Proponents of Game-theory and scholars such as Rosseau argue that this idea holds true in the arena of international politics; states are willing to sacrifice peace and order in the international system for the sake of national interest. .
The distribution of power in "Lord of the Flies" is extremely bipolar. Golding wrote the novel during the Cold War, so he was probably alluding to the division of world power between NATO (the west) and the Warsaw Pact (the east).
