Thanks, Scott. This view has been extensively discussed by Bryan Caplan in The Myth of the Rational Voter. But we need to recognize that despite this cogent argument, people *do* vote. They may not spend days weighing up all the options, but they do make an effort, often a not inconsiderable one, to cast their vote.
That is the basis of our support for a democratic system. Just imagine how much legitimacy the system would have if, say, only 5% or even 20% of the electorate, rather than the 50%-ish (give or take) that now casts their ballot.
My point is that this legitimacy is not quite what it seems, because the motivation of the actual vote is impulsive.