"In a room sit three great men, a king, a priest, and a rich man with his gold. Between them stands a sellsword, a little man of common birth and no great mind. Each of the great ones bids him slay the other two. 'Do it,' says the king, 'for I am your lawful ruler.' 'Do it,' says the priest, 'for I command you in the names of the gods.' 'Do it,' says the rich man, 'and all this gold shall be yours.' So tell me—who lives and who dies?" (4.Tyrion.147)
This riddle is the key to understanding how power works in A Clash of Kings. There are various political and social institutions vying for power, and they need to convince people of their power to gain power over other guys. Of course, it's more complicated than that, but we wouldn't want everything given away in the first four chapters, would we?
Tyrion cocked his head sideways. "Did you mean to answer your damned riddle, or only to make my head ache worse?"
Varys smiled. "Here, then. Power resides where men believe it resides. No more and no less."
"So power is a mummer's trick?" (9.Tyrion.101-103)
The irony is the average Joe with the sword has the power, but as Varys points out, he gives his power to the one he believes truly has the power. By the way, a mummer is an old-timey actor, meaning that in Varys's analogy, power is all pageantry.
A man like Petyr Baelish, who had a gift for rubbing two golden dragons together to breed a third, was invaluable to his Hand. Littlefinger's rise had been arrow-swift. (18.Tyrion.106)
One might be tempted to say that Littlefinger's power comes from money, but it's more than that. Instead, Littlefinger's power comes from his ability to manipulate the financial system to create more money. Since few people in the Seven Kingdoms seem to have this power, Littlefinger's gift becomes rarer and more powerful.
It pleased [Dany] to hear that the Usurper's dogs were fighting amongst themselves, though she was unsurprised. The same thing happened when her Drogo died, and his great khalasar tore itself to pieces. (28.Daenerys.58)
While loyalty is all well and good, it is the perception of power that really keeps the society in line. When the figurehead is gone, this creates a vacuum as others strive to claim the power for themselves. We saw this with Robert's death, too, and we'll see it time and again throughout the series.
A few voices raised a cry of "Joffrey! All hail, all hail!" as the young king rode by, but for every man who picked up the shout, a hundred kept their silence. (42.Tyrion.26)
In some ways, the smallfolk know they grant Joffrey the power to rule them, and they're good with it as long as they are kept safe and fed. But when those two things become less certain, well, let's just say it leads to a lot of questions being asked in hushed voices.
The council had extended [Tyrion's] curfew; it was death to be taken on the streets after the evenfall bells had sung. The measure had restored a degree of peace to King's Landing and quartered the number of corpses found in the alleys of a morning, yet Varys said the people cursed him for it. They should be thankful they have the breath to curse. (45.Tyrion.25)
Heavy is the head, right? One of the disadvantages of power is that things will go wrong. And when they do, everything wrong becomes your fault. Just ask any U.S. president ever.
[Arya] was alone with the dead men. They deserved to die, Arya told herself, remembering all those Ser Amory had killed at the holdfast by the lake. (48.Arya.168)
Arya's path to power is a little more direct than other types of social power we've been considering—hers comes from a law of kill-or-be-killed. And kill she will.
"To lead men you must know them, Jon Snow. I know more of you now than I did this morning."
"And if I had slain her?" asked Jon.
"She would be dead, and I would know you better than I had before. But enough talk. You ought be sleeping. We have leagues to go, and dangers to face. You will need your strength." (54.Jon.29-31)
Qhorin understands that Jon will be a leader among the Night's Watch one day, so he's teaching him how to wield that power properly. Here's hoping Jon is taking notes.
That shamed them well enough. A knight mounted, helmetless, and rode to join the others. A pair of sellswords followed. Then more. The King's Gate shuddered again. In a few moments the size of Tyrion's command had doubled. He had them trapped. If I fight, they must do the same, or they are less than dwarfs. (60.Tyrion.38)
Being a dwarf has led Tyrion to lack power in the arm wrestling or sword fighting departments. But his ability to read and understand people has given him a power to motivate others to act as he wants. In other words, in not possessing one type of power, Tyrion has developed another.
"When it comes to swords, a queen is only a woman after all." (61.Sansa.32)
The institution of royalty grants some people the power to rule over the Seven Kingdoms. Individual kings and queens, on the other hand, are just people—and as such, they have the same deadly allergy to being stabbed with a sword as anybody else.