What is Jack's style of leadership?

Jack's style of leadership is dictatorial. And as with all dictatorships, Jack's rule is based on fear, repression, and the use of violence. Almost from the start, Jack makes it abundantly clear that he doesn't have much time for the kind of rules-based civilization that Ralph wants to establish. He looks upon rules as a source of limitation, a way of holding back the strong from taking what's rightfully theirs. As far as Jack's concerned, the only law that matters is the law of the jungle, where the strong thrive, and the weaker members of society go to the wall.
But Jack's not simply a brainless thug; he's also quite clever, and uses his cleverness and cunning to cement this power over the other boys. For instance, he encourages everyone to believe in the existence of the mysterious Beast, which he knows full well doesn't actually exist. However, he also knows that if the other boys continue to believe that the Beast is real, then they'll be more likely to look towards him as their protector. Jack understands that being a dictator involves more than just the application of brute force. (Though that's still very important, of course). You also have to be devious and manipulative to get what you want, to consolidate your power-base and maintain control.