Measuring voters and legislatures on the same scale

Joe Bafumi and Michael Herron write,

We consider a fundamental question about the elected American political institutions: do they work? . . . Any given set of democratic institutions may aggregate preferences fairly—i.e., the associated aggregation process yields an outcome that reflects an appropriately designated representative constituent—or it may fail to do so—i.e., the aggregation process leads to distortion between its outcome and a representative constituent. Thus, to discern whether the elected American political institutions fairly aggregate preferences, we must address the question, who precisely is represented by these institutions and, importantly, is this individual representative of Americans writ large?

Here’s what they find:


The scale has liberals on the left (the negative numbers) and conservatives on the right (the positive numbers). As is well known, voters tend to be more moderate than representatives, but the median of the voters is not far from the median of the current House and Senate. (Joe and Michael unfortunately ignored my advice and labeled the congresses by number rather than year.)

Joe and Michael made the graph by taking a large national survey and putting in questions asking about attitudes on a bunch of issues that were also voted on by the House and Senate. They then used an ideal-point model (see, for example, chapter 14) to line up voters and congressmembers on a common scale. They also did some adjustment to match the sample to the general population. Good stuff.

Questions about the distribution of voters

Getting distributions of congressmembers is standard now (Poole and Rosenthal, etc), but getting voters on the same scale is new. I just have two questions about those cool distributions of voters.

First, I wonder about the bimodality. There seem to be two things going on. On issue attitudes, voters are basically unimodal, with more people in the center and some in the extremes. On party identification, voters are bimodal, with many strong Democrats and strong Republicans. Bafumi and Herron put this all together and end up with a bimodal distribution, but I wonder how sensitive this is to their particular methods.

Second, I wanted to point out the asymmetry in their graph. According to the analysis, something like 20% of the people are more liberal than the median Democratic congressmember, but only about 5% are more conservative than the median Republican congressmember. An some basic level, this is hard for me do believe, but I suspect it has to do with the issues that congress votes on. It would be interesting to see this broken down, issue by issue.

The seats-votes curve

Regarding the point in the paper about 2006, it’s worth noting that, for various reasons (including incumbency, gerrymandering, and simple geography), congressional elections have shown a big partisan bias in the seats-votes curve in favor of the Republicians. (Before then there was a bias in favor of the Democrats).

So this explains part of what they found, I think.

See Figure 1 in this paper (to appear next year in PS): From 1996 through 2004, the Dems were getting 50% or more of the vote just about every year but getting clearly less than 50% of the seats.

See Figure 2 of that paper for estimated seats votes curves since 1958.

Even in 2006, the Dems didn’t get their fair share of the seats (compared to what the Reps would’ve gotten with that vote share).

The Bafumi and Herron paper is great but I think it would be strengthened by including the role of the seats-votes curve.

OK, OK, I had to say it . . .

Some minor comments:

Figures 5,6: Please, please, please don’t order these states alphabetically!!! It would be much more informative to order them from most conservative to most liberal. Also, I’d suggest putting the two graphs side by side on the same page. Similarly with Figures 7,8.

Similarly, Fig 9 should not be alphabetical either!!!!!!!!!!!!!!!!!!!!!!!!!! Other than that, though, the pictures are really pretty.

And don’t get me started on the tables.

1 thought on “Measuring voters and legislatures on the same scale

  1. I seem to recall that the original vote view work took note that the shift of the Republican party's legislators to the right was not matched by a shift in the voter numbers as measured by the Michigan surveys. That the Republicans legislators moved but neither the Democrats or the rest of the population did is was one of the thing I learned from that work.

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