When I was at the APSA meetings, the famed Arthur Lupia gave yet another speech in defense of voter competence. He offered a long list of arguments. But his most important mistake, in my view, was his claim that voters have a simple problem: They merely need to decide which of the two major candidates they like more. As long as voters are able to identify the Better of Two Goods, they are, for all practical purposes, competent.

I call Lupia’s argument the Binary Fallacy. Here’s why it’s wrong.

Consider a simple median voter model where all voters are dogmatic protectionists. What happens? Both candidates converge to protectionist platforms. Even if everyone votes competently in Lupia’s sense, the result is that protectionism triumphs. In fact, if the median voter model works perfectly, the politicians offer identical platforms, so it’s impossible for voters to mistakenly choose the inferior candidate!

The lesson is that there is a lot more to voter competence than just making the better of two choices. Democratic competition drives politicians to offer popular policies. If voter competence has an effect on which policies are popular, it distorts policy – even if in equilibrium the voters skillfully compare Tweedledee to Tweedledum.

One common version of the Binary Fallacy: “Voter knowledge doesn’t matter because well-informed voters are about equally likely to vote for either party.” The problem with this argument is that if voters knew more, both parties would change to win their favor. Better voters would have little effect on the division of power between Democrats and Republicans; but better voters would give us better Democrats and Republicans.