I foresee this study being complicated by the problem of "ignorance-doubling." I'll offer two examples of what I mean by ignorance-doubling.

First, take the troubling phenomenon of people on the right of politics advocating free-trade. Why do they do that? One can talk about conspiracies and false consciousness, there is much to be said and one finds oneself ignorant of much of it.

There is a problem. The previous paragraph assumes an ignorance of Ricardo's Law of Comparative Advantage. More accurately it assumes that our hero has come across it, perhaps in some garbled account in a newspaper, and has not understood it. He fails to understand this basic law of economics but does not realise that it is important and does not realise that it is important, both for what it tells us about trade, and because it explains why people on the right of politics advocate.

One piece of ignorance, about Ricardo's Law of Comparative Advantage, leads on to more ignorance. Without the true explanation of advocacy there is forests of sociological explanations. Our hero cannot keep up with them as they are patched and mended to try to make them work, he suffers from lots of secondary ignorance.

If he could only go back and study Ricardo's Law, not only would that solve the primary ignorance, but all the secondary ignorance would evaporate.

My second example is Simpson's paradox. It is not as well known as Ricardo's Law of Comparative Advantage and I've written a short essay to bring out why it matters.

Think about the way that the newspapers are full of health stories. Tomatoes cause cancer. Tomatoes protect against cancer. Whatever. The stream of stories is endless and we all find ourselves ignorant of the latest health story.

Notice though that this is all secondary ignorance, caused by not grasping Simpson's paradox. All this non-experimental work is worthless. If we could but rid ourselves of the primary ignorance of not grasping Simpson's paradox all our secondary ignorance would go away.

Well, that was my comment. It might reassure you because it suggests that there are key simplifying ideas that make being a well-informed citizen more viable than it at first appears. Much ignorance is ignorance of bogus knowledge and goes away when the quest for bogus knowledge is abandoned. On the other hand the key simplifying ideas seem to be intellectually hard, the kind of ideas that only a mathematician would love, so perhaps we really are doomed. :-(

nebbish has a good point though. It's not just an isolated incident of one copper losing it.

You can't inspire people with facts
- Small Gods

As for capitalism going the wrong way to empirically validate Marx's theories, I think your conflating the goals, aims, and theories of early non-Marxist socialists with Marx. Marx's economic theory had nothing to do with exploitive factory conditions. He uses exploitation in a somewhat equivocal sense. It is the destruction of the Lockean view that property follows labor that that Marx finds exploitative in capitalism. The exploitation of the workers lies in the fact that they are alienated from the product of their labor in the same way that natural resources are exploited by removing them from where they are found in a state of nature. (Nationalized productive facilities do this no less than privatized ones.) That during Marx's day there was also a good deal of other types of exploitation is incidental to his chief complaint about capitalism.

Now, it may be true that Marx also complained about these other senses of exploitation: child labor, oppressive working conditions, etc. But those issues were really the pet issues of the non-Marxist socialist groups that were contemporary with Marx.  His analysis of capitalism had little to do with those factors and more to do with whether capitalism would ever reach a point where it was no longer viable. Things like minimum wages and working conditions are more or less incidental to that.