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Cosponsorship Networks in the U.S. Senate as of March 1, 2009

Cosponsorship, the act of registering one’s name as an official supporter of a bill, is a common activity in the United States Senate. Although the 111th Congress is less than two months old, 1753 cosponsorships for 495 Senate Bills and 11 Senate Joint Resolutions have been officially registered. That’s an average of 3 cosponsorships per bill, which may not sound like much for a body with 99 members, but there’s actually a fair amount of variation from that mean, with 180 bills having no cosponsors and one bill (the successfully passed Lilly Ledbetter Fair Pay Act) gaining 54 cosponsors.

Cosponsorship is an important behavior not only because it is associated with the likelihood of a bill’s passage out of committee and on to floor consideration (see Wilson and Young 1997: Legislative Studies Quarterly 12:25-43), but also because it can give us a glimpse into patterns of support for a wide variety of bills. If we only reference roll call votes to characterize patterns of legislative support, then we’re getting a biased picture, missing a majority of the activity that goes on in the Senate. Most bills never get a roll call vote; by studying cosponsorship we can get detailed information regarding patterns of cooperation on issues small and large, popular and unpopular.

At That’s My Congress we’ve been looking at which members of Congress have been more or less active in cosponsorship on an individual basis, but cosponsorship is more than an individual act. It is at least potentially part of a social bandwagon effort to build congressional coalitions for a bill. Advocacy groups certainly speak of cosponsorship this way in their legislative activism. But even if cosponsorship were to be a solitary act based on independent rational calculus, it would be relational in the sense that the similarity of patterns of cosponsorship between two members of Congress indicates the similarity of their policy priorities. Cosponsorship networks — whether they model social ties, policy similarity, or both — are an important object of study.

Perhaps the most intuitive way to measure ties between two Senators in a cosponsorship network is as the number of bills which both Senators have measured. Below is a matrix showing the cosponsorship network of Alaska Senator Mark Begich, California Senator Barbara Boxer, Delaware Senator Ted Kaufman and Arizona Senator Jon Kyl. Data is valid for all Senate bills with a prefix of S. or S.J. Res. (leaving out the procedural Senate Resolutions and Concurrent Resolutions) through March 1, 2009:

# bills both cosponsor Begich Boxer Kaufman Kyl
Begich 26 16 1 0
Boxer 16 42 1 1
Kaufman 1 1 5 0
Kyl 0 1 0 15

Across any row, the number of shared cosponsorships is a good indicator of the behavioral similarity of various pairs of Senators. The maximum value for any row is on the “diagonal,” the cell in which a Senator is compared to himself or herself. In the language of the specified relation, we could awkwardly say that Senator Mark Begich has cosponsored 26 bills that Senator Mark Begich has also cosponsored — or we could say in plain English that Senator Mark Begich has cosponsored 26 bills. In this set, Senator Begich’s behavior is most similar to Senator Boxer’s, with the two cosponsoring 16 of the same bills. Senators Begich and Kaufman have only cosponsored one bill together, while Senators Begich and Kyl have nothing in common.

But what happens if we want to make a comparisons between rows? We know, for instance, that the Senators Begich and Kaufman have cosponsored just one bill in common, and that Senators Boxer and Kyl have cosponsored just one bill in common as well. But looking down the diagonal we know that the overall levels of cosponsorship varies from Senator to Senator: 26 for Begich, 42 for Boxer, 5 bills for Kaufman and 15 bills for Kyl. You could argue that the shared cosponsorship of 1 bill between Begich and Kaufman is more meaningful for Kaufman than it the shared cosponsorship of 1 bill between Boxer and Kyl. For Barbara Boxer, that’s just one bill out of 42, but for Ted Kaufman it’s one bill out of five. Oddly enough, the very same number of shared bills between Senators Boxer and Begich — 16 — means something different from each Senator’s perspective. 62% of the bills Mark Begich has cosponsored (16/26) are also Boxer bills, while 38% of the bills Barbara Boxer has cosponsored are also Begich bills. The share of Boxer-type bills in Begich’s cosponsorship profile is lower than the share of Begich-type bills in Boxer’s cosponsorship profile… but the raw numbers don’t tell you that.

To create a standard measure that has the same meaning across all pairs of senators, we can use Pearson’s product moment correlation for each pair of Senators instead. To find Pearson’s correlation between two Senators X and Y here’s what we’ll do:

1. For every one of the 506 Senate bills introduced as of today i, ask the dichotomous questions, “Has Senator X cosponsored bill i?” and “Has Senator Y cosponsored bill i?” We’ll call the answer to the first question Xi and the answer to the second question Yi, and give each a value of 1 if the answer is “yes” and a value of 0 if the answer is “no.”

2. Why a 0-1 variable? One reason is that the mean of Xi for all 506 i Senate bills is equal to the proportion (or, when multiplied by 100, the percentage) of all of the bills that Senator X has cosponsored.

3. Now for each bill i, we’ll subtract the mean of Xi (for all bills) from Xi (this particular bill). That’s called the “deviation” from the mean, and the result is positive if cosponsorship happens and negative if cosponsorship doesn’t happen. We’ll do the same thing for Yi and the mean of Yi to obtain the deviation for Senator Y.

4. Then we’ll multiply the deviation for Senator X on bill i times the deviation for Senator Y on bill i. Why? Well, remember that a positive deviation occurs when cosponsorship of bill i has happened, and that a negative deviation means cosponsorship of bill i hasn’t happened. A positive deviation for X, multiplied by a positive deviation for Y, gives us a positive result. So when both Senator X and Senator Y cosponsor, we get a positive number. How about when both don’t cosponsor? Well, then we get a positive number too. But when Senator X cosponsors and Senator Y doesn’t (or when Senator Y cosponsors and Senator X doesn’t), we’ll multiply a positive number and a negative number, which always gives us a negative number. The end result of all this is a positive number if Senators X and Y do the same thing regarding bill i, and a negative number if they do different things regarding bill i.

5. We’ll do that same calculation over and over again, once for every one of the 506 Senate bills existing as of today. The result is that we’ll have 506 numbers for the 506 bills. Some of the bills will be positive (when Senators X and Y do the same thing), and some of them will be negative (when Senators X and Y do different things).

6. Now add all of those numbers up. If Senators X and Y tend to do the same thing regarding cosponsorship of bills more often than they differ, the sum of all those numbers will be positive. If Senators X and Y tend to diverge in their cosponsorship choice more often, the sum will be negative. If the sum is zero, then that tells you Senators X and Y differ as often as they do the same thing.

7. Here’s where I wave my hands a bit: dividing this result by the product of {the number of bills, the standard deviation of all Xi and the standard deviation of all Yi} standardizes the result so that the biggest possible positive value is 1 and the biggest possible negative value is -1. That’s so the value of the result can be interpreted the same way, no matter how many bills Senator X or Senator Y cosponsored overall.

8. Do this for all possible pairs of Senators, and you’ll have a number for every pair of Senators telling you whether the pair acts the same way regarding a bill more often than the pair acts divergently (a positive correlation) or whether the pair acts divergently more often than it acts the same way (a negative correlation).

So I did that. Rather, I had my computer do that, using a PHP program to access current reports on congressional bills via the online Thomas system and the awesome network analysis program called UCINET to run calculations.

Want to see the results? I could put them in a matrix, just as I did above, but then I’d have 99 rows and 99 columns for the 99 Senators currently seated, with 9,801 number-filled cells. How’d you like to interpret that? Blech. I sure wouldn’t, and besides, the table wouldn’t fit on your screen. Our eyes are simply better at perceiving patterns when they’re presented in the form of a picture, and our technologies are designed better to show such pictures. Pictures of relational data are called sociograms, and they work like this:

1. Every Senator is a dot.
2. Every relationship between two Senators (that meets some standard) is a line between the dots.
3. That’s it.
4. No, really, that’s it.

Let’s look at sociograms of those cosponsorship correlations between United States Senators for the 111th Congress so far. The ones you see below are generated using Netdraw.

There are two ways we can go with a sociogram. One is to look at a particular member of the Senate and to use the space of the sociogram to describe every other Senator’s relationship to that focal senator. Here’s just such a sociogram featuring Senator Mark Begich:

Who cosponsors bills with Senator Mark Begich of Alaska?  A sociogram with Begich as the sociometric star.

This form, the sociometric star, features shorter ties for higher correlations between Senators, since those indicate closer behavioral agreement. I’ve pulled aside the Senators who share absolutely no common cosponsorships with Begich. You’ll see they’re coded in blue and feature no line connecting them to Begich since they are wholly unconnected with Begich when it comes to supporting legislation in the Senate. Such unconnected individuals are called “isolates.”

The other sort of sociogram we can use draws a tie between two Senators when the strength of connection between them meets a certain threshold. In order to show relationships of strong correspondence between senators, correlations of positive 0.33 or greater merit a tie in the sociogram below:

Cosponsorship Networks in the U.S. Senate as of March 1, 2009 featuring cosponsorship correlation coefficients of 0.33 or greater.

One of the nice things about sociograms is that you can use graphic elements to display additional information. Here, I’ve given Republican senators the color red, Democratic senators the color blue, and Independent senators the color green. And finally, here at the end of our investigation, we can begin to address the assumptions behind those classic political colors. Most news reports on the Congress don’t go beyond such ideas of partisanship in describing the political coalitions in the Senate. Reporters will make blanket statements like “Republicans in the Senate are close to having no voice whatsoever” and references to “the growing strength of Democrats in the Senate”, but we don’t have to assume that the Senate is organized on a strictly partisan basis. Instead, without making any judgment about partisanship, we can look at the actual pattern of cooperation in cosponsorship and see what patterns naturally emerge.

In this sociogram, members of the Senate are made to appear close to one another not because they are members of the same political party, but because of strong cosponsorship bonds they share. Cliques of three, four, six, even ten senators are visible as well, groups within which all senators have a strong record of supporting the same sort of bills. These cliques do not encompass all members of a political party, but rather occur inside them. Senators Kay Hagan, Mark Warner, Ted Kaufman and James Webb form a strong Chesapeake-Carolina coalition of junior senators, but none of them have a strong tendency toward supporting the bills favored by a bigger clique of more senior Democratic senators including Barbara Boxer, John Kerry, Dick Durbin, Barbara Mikulski and Chuck Schumer (among many others). Conservative Senators Lindsey Graham, Johnny Isakson and Robert Bennett have a strong record of cooperation in their support of bills, but do not appear to be coordinating strongly with other conservatives like Sam Brownback or John Ensign.

That said, there’s a split in this cosponsorship network that is undeniable. All of the Republicans who have any strong correlations with other senators have those strong correlations only to other Republicans. All of the Democrats having any strong correlations in cosponsorship with other senators have those strong correlations only to other Democrats. That doesn’t look bipartisan, does it?

Well, looks may be deceiving. Yes, there are large groups of Senators whose support for bills isn’t strongly bipartisan. But remember that ties are reported only above a certain threshold of co-operation. There may be weak bipartisanship among many of these senators happening on an occasional basis. And look again at the sociogram. There are 24 senators who appear as “isolates” because they do not have a strong correlation in their pattern of bill cosponsorship with any other senator. Some of these senators, like Richard Shelby and Michael Bennet, appear as isolates because, frankly, they’re not doing much of anything but marking time and enjoying the Capitol Hill cafeteria.

But other “isolates” have earned low correlations with other senators not for their inactivity but for their high level of independent, eclectic activity. Senator John McCain, for instance, has not only introduced a number of his own bills but has cosponsored a number of bills written by and supported largely by Senate Democrats, Democrats as fiercely liberal as Russell Feingold. These cosponsorships have the effect of canceling out cosponsorships shared with fiercely conservative senators like Jim DeMint, giving John McCain a strong correlation with the cosponsorship record of no one else. That makes McCain, yes, a Maverick. It gives him weak behavioral ties to others. But these are, putting substantive judgment aside, bridging ties, ties connecting parts of the Senate in ways that the more insular ties of strictly liberal or conservative senators don’t.

There’s a lot to uncover in these cosponsorship networks, and a lot to explain as well. Look for more updates, information and analysis of congressional cosponsorship from Irregular Times and That’s My Congress.

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