Last year, I stumbled across a project by an Italian artist named Gianluca Gimini in which he asked people to draw what they think a bike looks like and then digitally rendered the result. It's really neat and worth taking a look at; as a cyclist, several things jumped out at me immediately. The first was that most people don't really seem to have any good conception of what a bike frame looks like, and the second is that they don't actually know how bikes work. A lot of these drawings have the chain either attached in the entirely wrong place or depicted in a configuration that would almost certainly fail to work correctly.
People of course make this mistake not because they're stupid but because they are unfamiliar with the details of bicycle mechanics. I suspect most people don't ever think too much about how bicycles actually move, but hopefully if they do, they quickly realize that in order for the bike to actually move, the rotation of the pedals has to be coupled to the rotation of the wheels via the chain. The chain is really a key component, but many people left it off entirely or misunderstood its purpose.
Which is all to say: thinking mechanically is hard. Even for a simple system like a bike, it's actually quite difficult, if only because it requires people to traverse a particular chain of potentially unfamiliar thought. It requires one to think carefully about what each component in the system is for: what function it fulfills and how it relates to the other components of the system. Most people are not used to working through a complex sequence of causal mechanisms in this way, but when the mechanisms in question power a bike, you get by more or less on instinct. It's when the mechanisms become more complicated that the troubles begin.
Ask an ordinary person, even a reasonably educated one, to draw you even an approximate diagrammatic representation of how the federal government (or state, or local, doesn't matter; I'm rolling with the federal example for now), and probably the modal reaction will be great confusion. Likely most people can figure out that the president is somewhere on top. There will also be a circle that represents the legislature (two circles for the two chambers if the respondent really paid attention in civics class) and those with some degree of political awareness will also include the Supreme Court, although the mechanism of its interaction with the other two branches will evade most. The vast federal bureaucracy that exists under the auspices of the executive branch will not be present; if any executive agency even appears, it won't have any relation to any other part of the government. I can't imagine any significant fraction of people would know anything about such minutia as House or Senate committees or the operations of the lower courts. Describing the interactions of these various actors with each other is also likely to be beyond almost all of them.
Again, this is not because people are stupid: it's because the details of how the government operates are extremely boring and also vastly complicated. This is sometimes lost when one's social network consists of politically informed people who genuinely find politics interesting. To most people, even people with advanced educations, policy discussions sound like that "wah wah" noise the adults in the Peanuts comics make.
Maybe none of this would matter so much if what was at stake was something as simple as voting. I'm of the opinion that parties are useful as information aggregators that abet the functioning of cognitive heuristics, so it's not as though ignorance of the mechanics of government would render people unable to make voting decisions. But this ignorance does have serious consequences for political rhetoric and thought. Faced with a problem of overwhelming complexity, people do not take the time to think mechanically through disparate pieces of evidence and arrange them into a coherent whole. Rather, people lean on various cognitive heuristics and biases to arrive, via motivated reasoning, at conclusions in agreement with whatever positions they already hold. This phenomenon presents itself across the political spectrum; perhaps the most recent and salient example on the left was the insistence by many Sanders supporters that his candidacy had the potential to usher in a fundamental political revolution. As someone who supported Sanders and voted for him, and who is generally quite closely aligned with him on most issues, I found these declarations to be downright delusional. They could only have been made by people who had but the vaguest ideas of how an administrative behemoth like the United States federal government actually functioned. What was missing in these declarations was any causal process that would lead to the promised transformation, and the missing spaces were filled in with magical thinking.
If the left was delusional about the promises of a Sanders presidency, then the right is delusional about... everything else. The conspiracist swamp in which the American right baptizes itself daily is home to a menagerie of monsters, from Agenda 21 to the ZOG. Routine operations of government are seen not for what they are (mostly boring administrative paper-pushing with occasional attempts to accomplish something), but rather as sinister operations to undermine the country. The most anodyne processes are endowed with occult implications; that bike lane is just a precursor for the invasion of the UN blue helmets, and don't let any egghead intellectual tell you different. The left's fault may be excessive wishful thinking, but the right has entirely abandoned even the pretense of commitment to existence in a shared reality. You might be able to convince someone who holds a different view from you, but you can't convince someone who denies the fundamental premises of (even approximately) verifiable truth and causal connection between events.
Richard Feynman once characterized science as "a way of trying not to fool yourself," while acknowledging that "you are the easiest person to fool." But fooling themselves is what a lot of people do when it comes to politics, over and over again. The mechanisms at play are incredibly complex and tracing their operations requires a great deal of cognitive effort, so by and large we don't even attempt it. And when it comes to teaching people how to think their way through these sorts of problems, we don't do that either. Much is made of the importance of "critical thinking" in education, but all too often those words are just that, unmoored from any actual critical approach to problems. We mostly throw a bunch of facts at people without explaining how those facts can be synthesized into a meaningful whole and move on. Of course the end result is, even among highly educated people, an inability to follow a chain of reasoning from end to end or understand how disparate aspects of a complex system connect to each other. And now here we are in the 21st century, with a world's wealth of information (much of it accurate!) available to us on demand and no handle on how any of it hangs together. We starve in the midst of plenty because we don't know how to digest the food.