The Gallup poll that Arnold talks about seems to have a shocking result: even though American political discourse obsesses over liberal versus conservative, for every three people who fit these labels, there are two who do not. If you ask one question about whether government should "promote traditional values," and another question about whether "government is trying to do too many things that should be left to individuals and businesses," 24% gives the liberal answers (no; no), 27% gives the conservative answers (yes; yes), 21% gives the libertarian answers (no, yes), and 19% gives the populist answers (yes, no).
This is particularly puzzling because left-right ideology is a very strong predictor of both public opinion and voting. How are these results possible? The answer is that classifications based on TWO yes/no questions are bound to have a lot of measurement error.
To see this, suppose that, in reality, 50% of Americans are liberal and 50% are conservative. Libertarians and populists don't exist at all. Now suppose further that on any given question, people have a 25% chance of giving the wrong answer. Maybe they speak before they think, misunderstand the question, or just want to get off the phone as fast as possible without being rude. What would a pollster find under these assumptions?
56.25% (75% squared) of conservatives would test conservative
6.25% (25% squared) of conservatives would test liberal
18.75% (25%*75%) of conservatives would test libertarian
18.75 (75%*25%) of conservatives would test populist
Just flip the words "conservative" and "liberal" to get analogous results for liberals.
The overall finding, then, would be that Americans are: 31.5% conservative, 31.5% liberal, 18.75% libertarian, and 18.75% populist, even though, by assumption, the last two categories are empty.
It would be great if 21% of Americans were libertarian. But once you consider the power of measurement error to distort results, it is very likely that the Gallup results are overstated. I predict that if you tried to correct for measurement error by (a) sampling the same people repeatedly, (b) asking more questions, or (c) letting respondents give a range of answers ("strongly agree," "slightly agree," etc.) instead of demanding a yes or no, the percentage of libertarian and populist respondents would fall to about half of what Gallup finds. Some of them would turn out to be liberals or conservatives who misspoke; others would turn out to be moderates in disguise.
I wish I were wrong, but come on! If 40% of Americans didn't fit on the liberal-conservative spectrum, we wouldn't need Gallup to point it out.
P.S. Measurement error is probably smaller for more educated respondents. So the finding that Arnold highlights - education predicts libertarianism - is more reliable than the overall results.