(We can also add the Bismark corollary, which says that it doesn't really matter how we choose our leaders because G-d's going to take care of us anyway, but I assume that it's obvious why the less we talk about that, the better.)
- The people, corporately, make good decisions (which I'll call the "kindergarten thesis");
- Election to office lends legitimacy from the sovereign people to our temporary leaders (the "Jeffersonian theis"); or
- We need to get our leaders somewhere and voting beats accident of birth or force of arms (the "black box thesis").
There's some truth to all of this, but each thesis has different policy implications. If the kindergarten thesis is right -- given the chance, the American people will do the right thing -- then we care about information flow and informed voters. We want to think about things like poll taxes or literacy tests, and we want to force the candidates to make public their specific plans. We care about campaign promises the same way we care about product warranties and fitness for a particular purpose. Parliamentary systems tend to follow this model.
In the Jeffersonian thesis, we're more interested in the people running for office than in what they plan to do. We want exposure to the candidates personality so that we can judge what kind of people they are, rather than their specific plans for specific problems. This is a pretty good positive description of the current system in which we make the candidates spend two years working long hard hours debating, eating corn dogs, giving speeches, going on Letterman, writing (or putting their name to) articles in Foreign Affairs, etc.
In the black box model, all we need as a decision. We don't have to know or care how that decision was arrived at. Random works fine, so long as all the actors agree to be bound by the decision. the black box thesis doesn't have much to say about the campaign, but it loves the Electoral College in which even a random and ambiguous close vote is translated into a clear win.
I find, as I get older, that I become more attracted to the black box thesis. Given that we need to have a president, for example, and that he needs to be the clear winner, an election is as good a way to choose him as any and better than most. At that point, retrospective sense making and our psychological need to see ourselves in control of our fate will kick in and we'll all agree that he is the legitimate leader, chosen by the Jeffersonian electorate. (And, if push comes to shove, G-d won't let anything too bad happen to us.)