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.
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.
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.
Jordan Ellenberg is a professor of mathematics at the University of Wisconsin. His book How Not To Be Wrong is forthcoming. He blogs at Quomodocumque.