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.

(Continued from Page 1)

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.

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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.