In a recent paper excerpted by Bryan Caplan, Brown philosopher Jason Brennan argues that the answer to this question is yes, and even suggests that poorly informed citizens have a moral obligation not to exercise the franchise:

Irresponsible individual voters ought to abstain rather than vote badly. This thesis may seem anti-democratic. Yet it is really a claim about voter responsibility and how voters can fail to meet this responsibility. On my view, voters are not obligated to vote, but if they do vote, they owe it to others and themselves to be adequately rational, unbiased, just, and informed about their political beliefs. Similarly, most of us think we are not obligated to become parents, but if we are to be parents, we ought to be responsible, good parents. We are not obligated to become surgeons, but if we do become surgeons, we ought to be responsible, good surgeons. We are not obligated to drive, but if we do drive, we ought to be responsible drivers. The same goes for voting.

Concluding that voters have a moral duty to be informed about politics doesn't require one to also believe that government should deny the franchise to the poorly informed. One can believe that all adult citizens should have a right to vote, while also holding that they have a duty to either become adequately informed or refrain from using that right. The latter obligation may not be enforceable by the government; but that doesn't mean that it doesn't exist. We have many moral duties that cannot or should not be enforced by law. Consider, for example, our moral obligations to our friends. If I betray a friend's trust, the government does not and should not punish me for it. But that doesn't mean that it's a morally acceptable thing to do.

If ignorant voters were choosing leaders and policies only for themselves, there might be no ethical problem with their being ill-informed. They would bear the full cost of their ignorance. Unfortunately, as John Stuart Mill pointed out, to vote is to wield "power over others." The politicians elected by ignorant voters will rule over all of us, knowledgeable and ignorant alike. The ethical voter therefore has a responsibility to his fellow citizens as well as to himself.

Unfortunately, the evidence suggests that the vast majority of citizens are both poorly informed about politics and often highly biased in their evaluation of the information they do know. If citizens do indeed have a duty to either become informed about politics or refrain from casting a ballot, most of them aren't living up to it. I have argued that this is perfectly rational and not a sign of voters' "stupidity." But rational conduct isn't always morally defensible conduct.

I'm not yet completely convinced that citizens have a moral duty to become informed about politics or not vote. Even if they do, it might be overriden by other moral imperatives in some cases (e.g. - if you can't become informed about this year's election because your time is taken up by other pressing moral duties, such as the need to care for a sick relative who requires round-the-clock attention). It's also difficult to determine exactly how much knowledge should be considered sufficient to meet the average voter's moral obligations to fellow citizens. However, I am sympathetic to the general outline of Brennan's argument as I understand it so far. I look forward to reading his paper in detail once I get my hands on the full version.