The unspoken corollary is that many if not most politicians, like attorneys conducting a voir dire, actually depend on their constituents having an unwarranted faith in their comprehension of complex topics, and use their rhetoric to manipulate voters accordingly. (This is, to anyone who actually watches the news, an obvious statement.)

Voters with a competent understanding of issues (which sometimes just means understanding that some topics are too complex for a layman to fully grasp) have a large number of inflection points that have to be considered when stumping for votes; voters in the thrall of superficial and ideologically-driven simplifications of issues are relatively easier to manipulate, because they have fewer levers for a politician to pull. (There's a reason party committees love running Three Minute Hates against the ideological enemy of the moment: the easiest lever of all is to whip up a frenzy against an Obama, Cruz, Pelosi, Palin, etc. No policy arguments needed!)

The open question is, how long can a republic last that depends on ignorant (not stupid!) voters electing competent politicians? The recent influx of (I would argue) actively incompetent politicians (or, worse yet, competent politicians who support policies they know to be incompetent), many drawn from fringe voter movements, suggests we may discover sooner rather than later how such a system ends.

^Plato's philosopher kings. Ignorant folks aren't qualified to decide policy and hence should have no impact on it. I agree to an extant - there needs to be some sort of minimal qualification for elected representatives. Not sure how that would work practically.