On The Spatial Model Of Public Opinion, Part Two: Applying To Congressional Votes

Introduction:

In the last article in this series, I discussed a graphical approach I’ve been using to try to illustrate the underlying logic and structure of “spatial models” of public opinion, before applying algorithms like DW-Nominate/ideal. The example datasets I used were generated by simple simulations. The main result was:

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.

Ultimately I want to apply these ideas to public opinion data like the CES, where the spatial structure was unknown (at least to me). I might provide a good contrast to first apply them to a dataset widely considered to be a strong example of a multi-dimensional “spatial model” — US Congressional roll calls.

In particular, for a large period of American history, Southern Democrats voted party-line on many issues but broke off on civil rights, leading to perhaps the archetypal “second dimension”:

Data Source And Preprocessing:

I chose the 1957–1958 Congress, or 85th Congress, because I knew it would have votes on the 1957 Civil Rights Act (and as it happens, I wrote about that Congress many years ago, I think). The roll calls and associated metadata are available from VoteView, as is the above screenshot.

Note: With real data, unlike with a simulation, for each question, you need to decide which vote or which response is the “correct” or “incorrect” response, or the “left-wing” or the “right-wing” or whatever. This decision actually doesn’t change too much about the graphics I’ll make — it doesn’t change which questions “end up on the axes” and which questions “end up on the diagonal” — but the right choice might make those graphics a little easier to interpret.

I decided to make the “left-wing” vote the vote relatively preferred by Northern Democrats, which are, for these purposes, Democrats from outside of TX/OK/LA/AR/KY/TN/MS/AL/GA/FL/SC/NC/VA. “Relatively preferred” means that if there’s a roll call in which Northern Democrats voted 55–45 “Yea”, but everyone else voted 70–30 “Yea”, then “Nay” would be the “left-wing position”.

Exploring All The Roll Calls:

I made an interactive version of the hypothetical Matplotlib plots from the last article, using the roll calls from the 85th Congress, which you can find at https://xenocrypt.github.io/RC_graphic_85th.html:

The different visual patterns from one vote to another should be immediately apparent, with some votes being more “diagonal” than others.

There is also information in the visual patterns across all votes. For example, compare to the clearly more one-dimensional shapes of the current (117th Congress) House votes:

“First Dimensional” Votes:

Let’s zoom in on the first vote, on electing the Speaker. Here the “people with a left-wing position” are just, well, Democrats.

Remember that “votes along the same dimension end up on the same axis” (or close to it). Here the “dimension” is whatever divided Democrats from Republicans. Therefore, along the x-axis of the RC-1 chart, we see votes that primarily or entirely split the Democratic caucus, like Roll Call 160 on protections for government employees:

As expected from a (one-dimensional) “spatial model”, the Representatives who voted “left-wing”, or Nay, on the RC-160 bill, also voted heavily in favor of the “left-wing” position on many other roll calls. This can be seen by how many issues run along the y-axis of the RC-160 graphic:

The presence of multi-dimensional voting, meanwhile, is suggested by how a number of votes votes still remain more “on the diagonal” than “on the axes”, even among the small fraction of members left-wing enough to vote Nay on this vote.

Going back to the RC-1 chart, on the y-axis, we can see votes on issues that primarily or entirely split the Republican caucus, like RC-76 on a federal salary increase, or RC-111 on flood construction funds. And in the individual charts for both of those roll calls, a lot of other roll calls end up pretty close to the x-axis, again as expected in the “spatial model”. The people who voted right-wing on these issues voted right wing pretty often:

“Second-Dimensional Votes”

One of the roll calls which ended up relatively “on the diagonal” for RC-1, the Speaker vote, was RC-137, which was about Alaskan statehood:

Note that RC-160, the government protections vote mentioned above, is “on the axis” here as well, so it’s an extreme under both of these (relatively) orthogonal dimensions.

But other votes (RC-56 on school construction assistance, RC-42 or RC-96 on the Civil Rights bill, RC-178 on aid to depressed areas) can be seen “along the axes” as well. These are votes that divided Congress in similar ways as Alaska Statehood or the Civil Rights Act, both of which split off a lot of Southern Democrats and the most conservative Republicans against everyone else:

The Many Other “Dimensions”.

This is more or less the conventional narrative of Congressional voting in this period as I understand it: the first dimension separates Democrats from Republicans and covers economic issues, while the second dimension separates out Southern Democrats (and the most conservative Republicans) and covers issues more like civil rights.

However, looking back at the charts for each of the roll calls, quite a few have almost every other roll call “on the diagonal”. That is, quite a few votes are somewhat or entirely “orthogonal” to every or almost every other vote. This is actually impossible under a purely two-dimensional system, and is really only possible when the number of dimensions is much higher.

For a (slightly funny) illustration, there were two votes, RC-125 and RC-126, on “A BILL TO AMEND NAVY RATION ACT TO PERMIT NAVY TO SERVE MARGARINE” and an “AMENDMENT TO BAR NAVY FROM USING MARGARINE WHEN SURPLUS BUTTER IS AVAILABLE, EXCEPT FOR USE IN OVERSEAS AREAS” respectively.

Note that almost every other vote is relatively “on the diagonal”, while RC-125 and RC-126 are “on the axis” for each other.

It’s worth going into a bit of detail about how this worked.

It does not mean that everyone voted the same way on both. About 157 representatives were “strongly pro-margarine” voting yes on RC-125 and no on RC-126; they wanted the Navy to serve margarine without restriction.

Another 80 members were what you might call “margarine moderates”, who voted yes on RC-126 and RC-125 — fine with serving margarine, but only if there’s no surplus butter alternative.

Another 36 were “strongly anti-margarine” voting no on RC-125 and yes on RC-126; they didn’t want the Navy serving margarine at all.

(And only 2 members voted yes on RC-125 and yes on RC-126.)

In other words, these two votes define a pretty consistent “margarine dimension” that ranges from “strongly pro-margarine” to “margarine moderates” to “strongly anti-margarine”, and this dimension is again relatively independent from everything else. Indeed you can see on VoteView itself how Yeas and Nays on RC-125 are scattered across the whole plane in all directions:

There are quite a few of these votes that seem to follow “mini-dimensions” to varying extents. Again, you can see them on the original plot as the rollcalls that induce relatively diagonal lines. Some of them have a handful of votes on the “dimension”, like three votes about a minerals bill (RC-184, RC-187, RC-188):

Others really do just seem to be that single vote, like RC-119 on recommitting a national monument project to the interior and insular affairs committee:

One advantage of consulting graphics like these, along with simply applying an algorithm, is that these “mini-dimensions” should be immediately apparent.

Conclusion:

What can we say about the structure of the roll calls of 85th Congress, just from these charts?

I think we can confirm that there are at least two strong “dimensions”, a partisan dimension and a dimension separating out Southern Democrats and Republicans who were liberal on some issues. Again, that is the conventional description (to the extent there is such a thing).

However we also learned that these two “dimensions” do not completely describe the spatial structure of the 85th Congress, since many other votes are somewhat or largely orthogonal with both of them. I don’t think we should brush aside all those “mini-dimensions” and what they imply. They certainly imply that the actual roll calls require more than two dimensions to completely describe.

But more than that, the “mini-dimensions” almost certainly imply that even more dimensions would be required to describe the potential issue space. After all, if naval margarine or mineral rights or national monuments happened to cross-cut each other (or everything else), why stop there? Those are after all only the issues that came to a roll call vote; they don’t exhaust the set of possible issues.

Therefore I wouldn’t want to call this data inherently “two-dimensional”, rather, I might say that two dimensions describe a lot of the structure but by no means all of it.