Mapping Congress' growing polarization.

A mathematician's guide to the news.
Dec. 26 2001 10:57 AM

Growing Apart

The mathematical evidence for Congress' growing polarization.

The bipartisan era didn't last long. Three months after 9/11, the unity that Congress promised has evaporated. Should we be surprised? Political scientists Keith Poole and Howard Rosenthal are not. According to their research, there's no evidence that a national crisis—Pearl Harbor, World War I, the Kennedy assassination—can produce even a short spike in legislative fellow-feeling, let alone a lasting change in political culture. So it's to be expected that the shockwave of September, while big enough to upend a tyranny on another continent, will not create a ripple—statistically speaking—in the business of Washington.

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Poole and Rosenthal found that the House and Senate grew steadily less polarized from around 1900 to 1980. Then something happened; polarization has been sharply increasing ever since.

Can "polarization" really be quantified? Poole and Rosenthal argue convincingly that it can and that even more delicate information about the political universe can be coaxed out of raw statistics. In order to explain what I mean, I have to tell you why we make maps of New Jersey.

We make maps of New Jersey because doing so is a superlatively concise way of organizing the vast amount of geographical data that New Jersey embodies. Glancing at the map, one sees instantly that Trenton is about 10 miles from Princeton but 70 miles from Hackensack; that Hackensack in turn is just 6 miles from Passaic but 70 miles from Frenchtown. If you'd never heard of maps, you could certainly store in a spreadsheet the numerical data of the distances between every pair of cities in New Jersey. You'd have exactly the same information. But you wouldn't know what New Jersey looks like.

When it comes to visualizing American politics, Poole and Rosenthal believe, we're a lot like the person navigating New Jersey with the massive spreadsheet but no map. Anyone can tell you that Barbara Boxer is politically closer to Dianne Feinstein than she is to Zell Miller. One could even quantify this "closeness" by computing the proportion of roll-call votes on which Barbara Boxer and Dianne Feinstein agreed. But can we use all this numerical information to produce a "map" of the U.S. Senate? Put another way, if we know the distance between each pair of cities, can we reproduce the map of New Jersey?

Yes, and much more. Using a mathematical technique called multidimensional scaling (MDS), we can make a map of any set of points if we know how "close" each pair of points is supposed to be. Researchers have used MDS to make maps of family relationships (scroll down to Figure 5, "Example"), emotions, and even rock bands.

Poole and Rosenthal don't use MDS but a technique of their own and a computer program called DW-NOMINATE to produce a two-dimensional map of the House and the Senate.

A statistical method is fundamentally sound only if it tells you things you already know. The DW-NOMINATE maps tell us, first of all, that throughout the last 100 years both houses of Congress have split into two grand clusters, Democrats and Republicans. Within the Democrats, the Northern and Southern members form two clusters. Sometimes the Northern and Southern Democrats meld into each other without a gap, and other times (especially in the 1940s and '50s) the two clusters are so distant that they seem to constitute two different parties.

The other thing about Congress we already know is that politicians naturally fall on a left-right axis. And indeed, the legislators on the left-hand side of the DW-NOMINATE maps are precisely the ones we think of as "furthest left." In the 106th Senate, for instance, the senator furthest to the left is Barbara Boxer, followed by Paul Wellstone and Tom Harkin. The rightmost senator is Phil Gramm, followed by Oklahoma's James Inhofe and Colorado's Wayne Allard. The rightmost Democrat? Easily Zell Miller of Georgia. The leftmost Republican? Arlen Specter just beats out Jim Jeffords. To see the numbers for every senator and member of the House, look at the data pages.

We don't need mathematics to tell us that Wellstone and Inhofe are far apart. But the mathematics assigns quantities to these qualitative observations based on their roll-call votes, allowing us to answer more fine-grained questions. We can, for instance, assign a numerical value to the "polarization level" of the House and Senate and track the changes in this number over time. Poole and Rosenthal have taken this analysis still further. They show that legislatures become more polarized not when individual politicians adopt more extreme views, but when they are unseated by more extreme politicians. Polarization, as they put it, is an effect of replacement, not conversion.

Still more impressive than the numbers are the pictures. As you watch the animated GIF of the House and Senate from 1879 through the present, you can see the two great clusters circle each other, trying to capture the center. You can see that the two chambers of Congress move in tandem, belying the Senate's supposed immunity to the winds of fashion that bat the House around. And around 1985, something—nobody is exactly sure what—happened, with polarization sharply increasing ever since. On the animated GIF, you can see the Democrats and the Republicans jerk apart, leaving an empty space between them that persists, war or no war, to the present day.

But the most startling finding isn't visible in the pictures. Let's go beyond left and right for a moment and ask: What does the vertical axis on the DW-NOMINATE map mean? Senators at the top of the map include John Breaux and Mary Landrieu of Louisiana, Peter Fitzgerald of Illinois, and George Voinovich of Ohio. At the bottom we find Olympia Snowe and Susan Collins of Maine, Arlen Specter again, and Robert Byrd. Poole and Rosenthal theorize that the vertical dimension describes a legislator's stance on race, with Northeastern, pro-civil rights politicians near the bottom and Southerners near the top. That seems somewhat right—but then, Byrd is no one's image of a modern racial liberal. The reason the vertical axis doesn't seem to say that much, Poole and Rosenthal suggest, is that race is no longer the polarizing issue it was 30 years ago. Today's Congress is governed by the calculus of left and right—that and not much else.

To be more precise, let's go back to New Jersey. Suppose you had data for only three towns, called A, B, and C. Let's say the distance between towns A and B was 1 mile, between B and C was 1 mile, and between A and C was 2 miles. A minute's thought should convince you that towns A, B, and C must lie on a straight line. On the other hand, suppose there were four towns, A, B, C, and D, and suppose the distance between any pair of towns is exactly 1 mile. Try to draw four points on a map with this property—you'll find it's impossible. In fact, the only way to situate four points such that each is 1 mile from all the others is to place the four points in three-dimensional space, in a configuration called a regular tetrahedron.

In the first situation, the two dimensions of a map are superfluous. One dimension would suffice to describe the locations of the three towns along the line. In the second situation, the two dimensions are not enough. We need to introduce more dimensions to obtain the desired distances. In both cases, the data tells us the "true dimension" of the configuration of towns.

With this picture in mind, we can state Poole and Rosenthal's most remarkable finding: For the last 40 years, both houses have been one-dimensional. That is, you can pretend that Congress is a set of points on a straight line with Barbara Boxer at one end and Phil Gramm at the other, and you can pretend that each vote is a mark on that line. Everyone to the left of the mark will vote one way, and everyone to the right the other way. It turns out that this crude model—which knows nothing about geography, gender, race, lobbies, exigencies, ideas, or history—correctly predicts more than 80 percent of votes cast. In the last 15 years, as Democrats and Republicans have drifted further apart, the one-dimensionality of Congress has increased apace. At the moment, the one-dimensional model gets over 85 percent of roll-call votes right. "People were surprised," Rosenthal says, "that such a simple model can explain so much of the data."

Surprised, and maybe disappointed, too. You might want to think your representative is, at every moment, incorporating your interests into a delicate and ever-shifting computation—something more nuanced than "As a 70 percent liberal, 30 percent conservative senator, my position is clear." You might get depressed if you think that American politics has degenerated into a straight-up dialectic between two weird agglomerates: affirmative action, teachers unions, and Social Security over here, the defense budget, tax cuts, and cheerleading for heterosexuality over there.

But Poole and Rosenthal's work, which now extends to many different countries and many different times, shows that one-dimensional legislatures are not degenerations of normal politics. They are normal politics. There have been two periods in American history when the legislature wasn't one-dimensional. One was the 1950s, when the Democrats split over civil rights. The other was the period after the Compromise of 1850 fell apart. One-dimensional voting breaks down, it seems, with the arrival of a new issue so divisive as to stretch the political world along its own axis and so fundamental as to strain the bonds of convention that keep the government running smoothly. Maybe we don't want the war on terrorism to be an issue like that. Maybe we should be thankful that, for the moment, Paul Wellstone is staying Paul Wellstone and James Inhofe, James Inhofe. In times like ours, partisanship could be an underrated virtue

What About Barry Bonds? Many people have written me about my assertion in July that "Barry Bonds isn't going to hit 72 home runs," and asked what went wrong with my analysis. Answer: Nothing. In July, it was extremely unlikely that Bonds would break the home run record. One great thing about baseball is that players sometimes accomplish the unlikely. (Ask Tony Womack.) If you bet a hundred bucks at the All-Star Break that Bonds would hit 73 home runs, you made a dumb bet. Now you've got a hundred bucks; it was still a dumb bet.

Jordan Ellenberg is a professor of mathematics at the University of Wisconsin and the author of How Not to Be Wrong. He blogs at Quomodocumque.

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