Bryan Caplan is back with more thoughts on my book. He tries a “noise” defense of his position that public opinion is “one-dimensional,” complains that we tested his actual statement rather than something else, and ends up ignoring important facts. Here we go.

We quoted Caplan, who said on p. 153 of The Myth of the Rational Voter: “There are countless issues that people care about, from gun control and abortion to government spending and the environment. …  If you know a person’s position on one, you can predict his view on the rest to a surprising degree.  In formal statistical terms, political opinions look one-dimensional. They boil down to roughly one big opinion, plus random noise.” (Caplan titles his recent post “Plus Noise!” and, sure enough, when he quotes our quote of his quote, the word random is somehow left out. I’m not sure this matters, though, given that calling it noise implies random.)

So, Caplan says it right there: “If you know a person’s position on one, you can predict his view on the rest to a surprising degree.” In our book, we set out to give an example that undermines this kind of statement. We show that if you know a person’s position on either income redistribution or same-sex marriage, you in fact can’t predict very well their view on the other.

Apparently our efforts have paid off, to a point. Caplan now agrees with us that if you know a person’s position on certain issues, you really can’t predict his views on certain other issues. For example, Caplan now admits that the correlation between gun control and abortion in the General Social Survey is near zero. This directly contradicts his statement in his book, unless what he meant by “to a surprising degree” is in fact “sometimes not at all.”

Noise and “one-dimensional”

But Caplan’s not backing down. He agrees with our take on the data, but maintains his overall point about “one-dimension.” His main defense is about noise. Yes, he says, everyone knows these are noisy relationships. He says that individual issue positions are especially noisy.

But here’s the problem with that. The correlation between views on abortion and views on school prayer is pretty big (around .27 in the 2002-2012 General Social Survey sample). The correlation between views on income disparity and views on spending levels on the poor is pretty big (.31 in the GSS). But the correlations between abortion or school prayer, on the one hand, and income disparity or spending on the poor, on the other hand, are really small. Indeed, for example, the correlation between school prayer and spending on the poor is actually zero in the 2002-2012 GSS sample.

So it’s not that individual issue positions never correlate with each other, but that a given issue often correlates with some issues but not others. (We talked about this on pages 12 to 13 of our book, in the section Caplan’s current post discusses.) Caplan says: “When you correlate two noisy things with each other, you get a really tiny correlation.” OK, so why does school prayer have a big correlation with abortion but a near-zero correlation with income disparity?

What this means, then, is exactly the point at issue: public opinion is not one-dimensional. There are some issues that hang together pretty well with each other (e.g., religious and lifestyle issues), and other issues that hang together pretty well (e.g., issues relating to redistributive economic programs), and yet these two sets of issues don’t relate strongly to each other. That’s what things look like when public opinion has more than one dimension.

And it’s not that there are just two dimensions. Views on immigration, for example, don’t relate very strongly to either views on abortion or views on income disparity.

Caplan wants his comments about noisy data to buttress his claim about one-dimension. I certainly agree that the data are noisy. But that’s not enough to defeat the obvious fact that diverse political issues form more than one statistical clump. And it’s not enough to defeat the obvious fact, which Caplan now admits, contrary to his statement that we quoted from his book, that some important political issues have near-zero correlations with each other.

Changing the subject

Caplan then proceeds to change the subject: “If Weeden and Kurzban really wanted to dispute the one-dimensionality of political opinion, they should have been correlating specific issue views with ideology, not specific issue views with each other.” In other words: To dispute Caplan’s point about one-dimensionality, we shouldn’t have tested his own claims about one-dimensionality, where his go-to point was that individual issues predict each other to a surprising degree. Instead, we should have tested a different point. Right…

The thing is that it’s not enough to just correlate individual issues with ideological labels. It’s perfectly possible that if pro-choice people tend to call themselves “liberal,” and if pro-redistribution people tend to call themselves “liberal,” you can still get ideology-issue correlations without the issues having much to do with each other. As I said in my earlier response to Caplan, these ideological labels can be in large part effects in addition to causes of issue opinions.

In short, the correlations between issues and ideological self-placement can’t address the point about dimensionality. Dimensionality is about the old political science notion of “constraint,” about “what goes with what,” about knowing that a person who leans in a given direction on issue X also leans in a predictable direction on issue Y. Which takes us right back, of course, to Caplan’s own original statement and our test of that statement.