Well, Draug, actually a run-off election system can be shown to do just as bad a job as a majority-winner system at representing the people's will.
Say that there are three candidates, A, B, and C. 40% of people like A, followed by B, then C. 31% of people like C, followed by B, then A. 29% of people like B, followed by A, then C. They vote. A gets 40%, C gets 31%, B gets 29%. So there's a runoff between A and C. A wins with 69% of the vote.
But guess what? 60% of the populace would have preferred B.