"Listen carefully, Feyd," the Baron said. "Observe the plans within plans within plans." (2.73)
Plans within plans within plans—is there a better definition of politics than that? Probably, but it's still a pretty good definition.
"In politics, the tripod is the most unstable of all structures." (3.26)
Of course, the novel is being self-referential here. It's not like there are any real political systems based on a three-way split of checks and balances… oh, wait. Hey, what are you trying to say here, Dune?
"Grave this on your memory, lad: A world is supported by four things…" [The Reverend Mother] held up four big-knuckled fingers. "… the learning of the wise, the justice of the great, the prayers of the righteous and the valor of the brave. But all of these are as nothing…" She closed her fingers into a fist. "… without a ruler who knows the art of ruling. Make that the science of your tradition!" (4.40)
Notice how the four things the Reverend Mother lists are all romantic ideals that still need something practical—like a good politician—to support them. What do you think: does Paul later in the book take this advice to heart?
"This is like single combat, Son, only on a larger scale—a feint within a feint within a feint… seemingly without end." (6.32)
Politics compared to fighting? That's a little extreme, don't you think? Oh, guess not.
"Power and fear," [Leto] said. "The tools of statecraft.[…]" (14.42)
Hold on to this thought and head over to the next quote…
Let him sweat a little, the Baron thought. One must always keep the tools of statecraft sharp and ready. Power and fear—sharp and ready. (26.8)
Well, look at that. Baron Harkonnen and his foil, Duke Leto, agree on what makes a good politician, even as they disagree on what makes for good politics. Or, to say it another way, they seek different ends, even if they have the same means.
"[…] A leader, you see, is one of the things that distinguishes a mob from a people. He maintains the level of individuals. Too few individuals, and a people reverts to a mob." (32.62)
What do you think about Stilgar's message here? Are leaders necessary to keep a people from reverting into a mob? Do people only obtain individuality under a successful leader?
And the Baron thought: Let us see now how the Emperor's errand boy gets across whatever message he carries without ever being so crass as to speak it right out. (35.34)
In other words, Fenring uses doublespeak, the great political switch-a-roo. Dune gets a little of Orwell's 1984 for flavoring (source).
"Control the coinage and the courts—let the rabble have the rest." Thus the Padishah Emperor advised you. (41.Intro)
"For the love of money is the root of all evil" (1 Timothy 6:10). Actually having money? That's the root of all politics.
"I swear to you now," [Paul] whispered, "that you'll need no title. That woman over there will be my wife and you but a concubine because this is a political thing and we must weld peace out of this moment, enlist the Great Houses of the Landsraad. We must obey the forms. […]." (48.362)
Politics pushes its influence onto family in this quote. Both Paul and Irulan must marry for political peace. Even Paul, the great Muad'Dib and conqueror, must give up a piece of his happiness to "obey the forms."