On The Spatial Model Of Public Opinion, Part Three: Applying To The CES

Introduction

In the first article in this series, I described a graphical approach to visualizing the spatial structure in survey responses or voting records:

Compared to the splitting question, questions in the same dimension end up on the axes, questions in orthogonal dimensions end up on the diagonal, questions in topics that are somewhere in between end up somewhere in between.

In the second and previous article, I applied that approach to US House of Representatives voting records from the 1957–1958 Congress.

In this article, I’m going to try to apply the approach to something more contemporary — current American public opinion, as measured by the 2020 CES.

Data Source And Preprocessing:

My data source here was the Cooperative Election Study Common Content 2020. I identified 70 questions that seemed to be binary public opinion questions (questions with only two answers) or that could be converted into binary public opinion questions (by merging “strongly disagree” and “somewhat agree” and the like). One of these questions was Presidential support in 2020, and here I actually merged several different questions across the two waves together.

To give each question a “left-wing answer” and a “right-wing answer”, I used whichever answer was relatively preferred by Biden supporters. For example, Biden supporters favored ending mandatory drug minimums 84–16, while Trump supporters also favored ending them, but only 54–46. By my definition, that makes ending mandatory drug minimums the “left-wing answer”, and keeping them the “right-wing answer”.

Data Notes: I decided against using weights on the respondents, since I wanted to compare this analysis to running “ideal” or “DW-Nominate” on the same dataset, and I do not know how exactly I would use weights with those algorithms. Notably this means the sample is 54% Biden supporters to only 37% Trump supporters. I don’t know if using weights would do more than give the appearance of accuracy for the sorts of subgroups and intersections that come up in this kind of analysis.

Another interesting source of bias is from the questions themselves. In almost all of the questions, the left-wing answer has at least 38% support, and for a few questions the left-wing answer tops 80% support. I didn’t see any questions where the right-wing answer had such heavy support. Presumably this will have consequences in analyzing the data, perhaps in the same way that a math test without any very hard questions would make it difficult to distinguish somewhat strong students from very strong students.

Whether this is because of the nature of the sample, because of the nature of American public opinion itself, or because of the choice of questions is an interesting topic itself. Personally, I think there are probably questions that would have had heavy right-wing answers if the researchers had thought to include them, maybe questions like “should private property exist” or “is America a force for good in the world”, and I would have liked to see such questions included.

Results:

I made an interactive version of the plots from the previous articles at https://xenocrypt.github.io/CES_graphic_2020.html: It has the (unweighted) splits by each question, and the crosstabs by every pair of questions.

Even before looking at individual issues, the range of different patterns given by the graphs of different questions should be clear enough. As with the roll call votes, some questions lead to very “diagonal-heavy” graphs; and these will probably correspond to dimensions that are unique or almost unique across the dataset. Other questions lead to very “axis-heavy” graphs; these will probably correspond to more common or prominent dimensions.

“First-Dimensional” Questions:

Perhaps unsurprisingly, the graph of the Presidential preference question is a good way to explore which questions come from the “first dimension” and which questions come from more orthogonal dimensions:

A lot of questions are more or less “on the axes” in the Biden graph. Again, this does not mean that Biden voters and Trump voters were monolithic on those questions. It just means that a lot of questions mostly either split Biden voters or Trump voters — which is what a one-dimensional model would predict.

For example, “More Border Patrols?” splits Biden voters 64/36, while Trump voters split more like 92/8:

And indeed, those people who gave the left-wing answer on “More Border Patrols?”, who should be quite left-wing in general under a one-dimensional model, did indeed answer quite heavily left-wing on a bunch of other questions:

Conversely, letting the EPA regulate CO2 does almost the exact reverse, splitting Biden voters 91/9 and Trump voters 60/40:

And those people who gave the right-wing answer on “Let EPA Regulate CO2?”, who should be quite right-wing in general under a one-dimensional model, did indeed answer pretty heavily right-wing on a bunch of other questions, although not as uniformly as in the previous case. If I split by “Let EPA Regulate CO2?”, I can see the other questions line up somewhat around the x-axis:

All of that is fairly consistent with a “one-dimensional” model, where questions end up on the axes, mostly splitting either left-wing voters or right-wing voters but not both.

Possible “Second Dimensional” Questions Vs. Purely Orthogonal Questions:

If questions with graphs that put a lot of other questions on the axes are probably “first dimensional”, what is the visual indication of a “second dimensional” question?

If I return to the “Biden 2020?” graph and look at the questions that end up relatively close to or on the diagonal, there are a few varieties of them. For example, the question I called “Ban Clinic Abortion Ban?” ended up basically right on the diagonal:

This seems to have just been because this was a confusing question — the full text is “Prohibit states from requiring that abortions be performed only at hospitals (not clinics)?” — that respondents answered more or less randomly:

Technically this would make “Ban Clinic Abortion Ban?” its own “dimension” in a spatial model. (Although it may not be a very meaningful one, as any question that respondents answered more or less randomly would also be its own “dimension”.)

Exploring the data this way, the most plausible candidate for a more useful “second dimension” I found related to a battery of questions on tariffs, which often split both Biden and Trump voters at least 75–25 or so:

Looking at the graphs of tariff questions themselves often show other tariff questions noticeably more “on the axes” relative to everything else ending up noticeably more “on the diagonal”.

In other words there is a decently-consistent “tariff dimension”, where the right-wing by this dimension supports all tariffs, the left-wing by this dimension opposes all tariffs, and moderates by this dimension are somewhere in between. And the “tariff dimension” is relatively orthogonal to the Biden/Trump dimension, at least relative to other issues that were asked about in the 2020 CES.

For this reason, the tariff battery definitely seemed to be one of the likeliest candidates for a “second dimension” when I was doing this sort of exploratory data analysis. I did also consider other issues as potentially giving rise to their own “dimensions” (abortion, guns, immigration, foreign policy…).

Conclusion:

I don’t know how accessible anyone else finds these graphs, or whether or not it’s a standard form of EDA. Personally I found them to be a useful way to explore the spatial structure of these datasets and find candidates for dimensions along with other nuances that I might have missed by simply applying an algorithm.

There are somewhat (still) more complex versions that might allow for closer looks at higher-dimensional spatial structure, however, I might write about that if and only if any of this makes any sense to anyone else.

David Broockman, I believe, has written about how voters have internally-consistent positions on various individual issues that don’t necessarily add up to any single larger “dimension”. I think this makes an approach that reveals and allows for the exploration of “mini-dimensions” particularly important.