[Tywin]

One of the major themes that GRRM plays with is the nature of power, and I think that we're not giving Ned enough credit here because in the story his form of power did not work out. We say above that he was playing the game of thrones with checkers while everyone else was playing with chess pieces, but I would contend that he was playing with checkers for the sake of appearances while he held a shotgun in his lap. He was above the pettiness of "summer politics" because he knew the truth that when the power of violent men is unleashed it can wash everything away before it.

I think the TV show did a pretty good job of drawing out some of that theme where Ned would reply to comments about how important political subtleties are with questions like "Then how is Robert Baratheon King?", or when Littlefinger commented to Cersei that "Knowledge is power" and she demonstrated how the four guards around her could easily kill him at the snap of her fingers and replied "Power is power."

The backbiting "summer politics" of King's Landing may have bested Ned's brute power, but only because of his own hubris. Although we like to think about his successor Tyrion as a schemer, remember that he came to King's Landing with a sizeable force and established a base of physical security (and physical threat) prior to all his more devious scheming.