Since the late 1950s, many political scientists, economists, and political psychologists have measured what Americans and others know about politics. The results are uniformly stark and depressing: Around the world, the majority of citizens are deeply ignorant about basic knowledge. In the US, the average citizen knows who the president is but not much else. That citizen doesn't know what bills have passed, what various indicators are of economic or social health, who their representatives in congress are, who controls congress, or most of the other stuff you'd think they'd need to know to vote well. They are also systematically misinformed about the basics in the social sciences.
When I cite such stats, some democrats dissent. They say that while the kinds of knowledge that Pew or the American National Election Studies test are indeed forms of political knowledge, they are not the only forms. Lots of things matter for politics: the local price of daycare, a bus ticket, or milk, the way police treat you in your neighborhood, and so on. We shouldn't privilege what political scientists call "basic political knowledge" because the actual knowledge needed to make good political decisions is far wider, and many so-called "ignorant" or "misinformed" citizens in fact have this kind of knowledge.
Two responses:
1. Even if so--and I agree that citizens have such local knowledge--that doesn't tell them how to vote. So you know the local price of milk and know that the jobs are drying up in your local town. (Actually, citizens almost never know their local unemployment rate.) Your local school system sucks. Should you vote for protectionist Trump, anti-immigration Bernie, or free-trade and pro-immigration candidate? Your local knowledge doesn't help you. Should you vote for someone who wants to raise or cut the minimum wage? Your local knowledge doesn't help. Should you vote for someone who wants to strengthen teachers unions or expand school choice? Your local knowledge might help a bit here, but then perhaps the national problem is distinct from your local problem, and you still need to understand the political economy of unions and the social science of school choice. So, yes, your knowledge matters, but it's not enough to ensure you can vote for your professed goals or interests. You need more than that. Knowing there is a problem does not mean you know how to solve the problem.
2. A deeper response is that I don't think the people who make these arguments actually take their own arguments seriously. What I mean is that they are onto something deep, but their arguments are actually arguments against expanding the scope of democracy precisely because democracy--and, indeed, all political systems--does a terrible job accommodating and using local knowledge.
As Hayek pointed out in 1945 (and others before him), decision-makers need to know not just general statistics, but various kinds of local and dispersed forms of knowledge in order to make good decisions which properly solve the economic (or social) problem. The problem decision-makers face is that much of the knowledge they need is dispersed among the many, is implicit or tacit, and is constantly changing. Even if you had a snapshot of all that is known right now, the economic and social situation constantly changes. Make a decision tomorrow based on information from today and it will be suboptimal at best, because things have changed.
Market prices turn out to be excellent (if imperfect) ways to communicate this knowledge because they are functions of supply and demand, and because supply and demand curves are functions of our individual actions in response to our disparate knowledge. Market prices are an emergent feature of the aggregation of individual decision-makers acting on their local knowledge, personal desires, and so on. Market prices communicate information to others in ways they can use. Even better, they do so without requiring the people using that knowledge even understand what the information means. If a fire closes the mine, the price of tin will increase, and people will substitute aluminum or plastic, even if they have no idea why the prices have changed.
Market prices are an excellent way to communicate disparate, local knowledge to all decision-makers. (In a market, everyone is a decision-maker and planner.) Voting is not. It is not even comparable. It is many orders of magnitude worse. Voting is infrequent. It is monopolistic. You vote on only a few things. The information signal is weak and unclear. It lacks the features that make market prices work.
It's precisely because of the importance of such local knowledge that we want, all things equal, to minimize the scope of politics and increase the scope of the market and civil society. The democrats who use "local knowledge" to justify voting actually don't take the very issue they invoke seriously. Their arguments actually undermine rather than support their conclusions. How does voting Democrat over Republican every four years help communicate my local knowledge of the price of a gallon of milk to the people in charge? Answer: It doesn't.