Part 1 is a test of objective political knowledge. (How many senators does each state have? Name as many Supreme Court justices as possible. Etc.) Think of it as a "Political IQ" test.
Part 2 asks respondents about their policy preferences. (Should we rely more on the market or government? Should we invade Iran? Etc.)
The survey also collects standard information about respondents' income, gender, party i.d., race, etc.
Once you've got all this information, you're ready to discover the public's "Enlightened Preferences." In essence, you estimate policy preferences (from part 2) as a function of Political IQ (from part 1), plus a bunch of control variables that you think might influence political preferences holding knowledge constant. If you're finicky, you can even allow Political IQ to have a separate coefficient (and sign) for various subgroups of the population. (Perhaps knowledge makes the rich more pro-market, but makes the poor more pro-government).
The final step is to use these results to simulate what public opinion would look like if you raised Political IQ up to the stratosphere but kept all other characteristics the same. The resulting distribution of opinion is what we call the public's Enlightened Preferences. It's what people would want, if everyone knew a lot more.
Overall, I am a big fan of the Enlightened Preference literature, and I won't conceal the fact that Enlightened Preferences are generally more socially liberal and economically conservative (in short, more libertarian) than the actual distribution of opinion.
Still, this approach has some potentially awkward implications for me. You could just as easily use it for consumers or workers as you could for voters, right? Just estimate consumer demand as a function of people's score on a "Consumer IQ" test, plus a bunch of control variables you think might influence consumer preferences holding knowledge constant.
For example, I strongly suspect that this approach would reveal that if people knew more about financial markets, they would be far more likely to invest in index funds that they actually are. It wouldn't surprise me if we found parallel results for health care.
I have no principled objection to this, but if we're going to generalize the Enlightened Preference approach, we should proceed with caution for at least two reasons.
First, in politics, you're generally picking a policy that everyone's got to live with. As a result, you really only need to understand how greater knowledge would change the distribution of preferences. In contrast, in the market, purchases are individually customized. Knowing that the average person would change his consumer behavior if he knew more doesn't mean that many consumers wouldn't change no matter how much he knew (or change in the opposite direction). From a slightly different perspective, what statisticians call "the error term" might be better-described as "person-specific preferences."
Second, in the market, there is a much bigger role for reverse causation. People who know a lot about reptiles buy more reptiles, but it's probably not knowledge changing preferences. It's preferences changing knowledge. In contrast, people rarely learn a lot about international trade purely because they think that "trade is fun." The best counter-example I can think of is that people who know a lot about politics might be more supportive of things like PBS because PBS shows programs that political junkies enjoy.