I think this matters--it partly explains why democracies choose bad policies. Every major democracy routinely does stupid and evil things; all of them fall very far short of justice, though they usually outperform dictatorships.
When I give talks on this, students and even some professors argue that it doesn't matter if most voters are ignorant and irrational. We make it up on volume. The mechanisms of representative democracy sufficiently check voter irrationality. Representatives and the technocratic bureaucracies they've empowered produce good policy, while voters put just enough of a check on leaders to force them to serve the public interest, more or less.
They're not entirely wrong. It may well be that democracies work so well in part because they are not that democratic; elites don't always cater to the evil, rotten ideas of the masses.
However, even if you think that's part of the story, we can test to see just how strongly you believe that.
1. Imagine I have a magic wand. When I wave it, it will make nearly all voters even more ignorant, irrational, and tribalistic. Would it be a bad thing to wave it? Would it hurt democratic performance? Would it lead to more injustice and worse outcomes? When I ask critics these questions, basically all of them say yes.
2. Imagine I have a second magic wand. When I wave it, it will significantly reduce voters' ignorance and irrationality; it will make them much better informed about both basic political facts and whatever theories are needed to understand those facts, about how to predict what policies will do, and so on. It will reduce their cognitive biases by a significant degree. Would it be a good thing to wave it? Would it help democratic performance? Would it lead to more justice and better outcomes? When I ask critics these questions, basically all of them say yes.
3. Imagine a world like ours, with the same kinds of institutions, but in which voters were completely rational and perfectly well-informed. (I think this is incoherent, because they would then all be cooperative anarchists. But let's put that aside.) Now imagine I show up with a third magic wand. When I wave it, I make all the citizens as ignorant and irrational as the actual living citizens of the US or France today. Would it be horrible to wave that wand? Would it hurt democratic performance, and lead to more injustice and worse outcomes? When I ask critics these questions, basically all say yes.
It's a good question just how much voter ignorance and irrationality matter. Achen and Bartels, Mason, Kinder and Kalmoe, Gilens, and a few others have convinced me it matters less than I thought it did as of, say, 2011 when The Ethics of Voting came out. (That doesn't affect my argument in that book, though, or in Against Democracy.) But it sure seems like matters, and it seems like everyone admits it matters when presented with thought experiments like these.