ۑ ٺۦۋۑېۋڻۦڻۦٷڻٷۦ۩۞ڻڻۀ

ẰếỂẺẽẶ ẮẴẰẹẮẰ ۦ ۦ ٷۅ

ۦ ٺۆ ۀۦٷ ٷۇۦ ٺۆ ۀۦ۩ۑۦ ٺۆ ۀۦۦ ٷۦۆے ۦ ٺۆ ۀ ۩  ۦ

ٷۻۦٷێ ۺۦٷێ ٷێ  ٷۦۦێ

ۅۈۆۓۋ ڻۉ ېۇےۇێ ٷ ېۆۍۍۋ ۑۇۋۅۉ

ڽھڽ ­ Ұڽڽ  ںڿڽڼھ ۦۅ ڻ ڽڼ ۩ۉ ڻ ڽ ۩Џ ڻ ۑ ٺۦۋڿڽڼھ ۦۅ Ңڽ ۀ ۩ێ ںڿڻھڽڼھڻڻҮڽڼڽڻڼڽ ۀۉۍۆ

ڿڿڼڼڼڼھڽھۀھڽڼҢڼھۑۓٷۦٷڻۦڻۦٷڻٷۦ۩۞ڻڻۀ ۀۦٷ   ٺک

ۀۦٷ    ۈ ٺۦۋ ڻٷۻۦٷێ ۺۦٷێ ٷێ  ٷۦۦێ ڻ۶ڿڽڼھڿ ۅۈۆۓۋ ڻۉ ېۇےۇێ ٷ ېۆۍۍۋ ۑۇۋۅۉڿڻھڽڼھڻڻҮڽڼڽڻڼڽۀ ڽھڽ­Ұڽڽ  ںڽ ںۑ

ۦ ٺۆ ۀ ۦێ ۩ۥې

ڿڽڼھ ۩ۉ ڼڿ  ھۀھڻҮңڽڻھڻھҢڽ ۀۦٷ ێۉ ںۑېۋڻۦڻۦٷڻٷۦ۩۞ڻڻۀ ۦ ٷۆ

Network Science 1 (1): 119–121, 2013. c© Cambridge University Press 2013

doi:10.1017/nws.2012.3

119

END NOTE

Portrait of Political Party Polarization1

JAMES MOODY

Department of Sociology, Duke University, Durham, NC 27710, USA

(e-mail:)jmoody77@soc.duke.edu)

PETER J. MUCHA

Department of Mathematics, University of North Carolina, Chapel Hill, NC 27599, USA

How typical is the partisanship of current American politics and how do political

actors navigate divided networks?

To find out, we measure co-voting similarity networks in the US Senate and

trace individual careers over time. Standard network visualization tools fail on

dense highly clustered networks, so we used two aggregation strategies to clarify

positional mobility over time. First, clusters of Senators who often vote the same

way capture coalitions, and allow us to measure polarization quantitatively through

modularity (Newman, 2006; Waugh et al., 2009; Poole, 2012). Second, we use role-

based blockmodels (White et al., 1976) to identify role positions, identifying sets

of Senators with highly similar tie patterns. Our partitioning threshold for roles

is stringent, generating many roles occupied by single Senators. This combination

allows us to identify movement between positions over time (specifically, we used the

Kernighan–Lin improvement of a Louvain method greedy partitioning algorithm

for modularity [Blondel et al., 2008], and CONCOR with an internal similarity

threshold for roles; see Supplementary materials for details).

The figure maps this dynamic coalition network, one two-year Congress at a time.

Nodes indicate structurally equivalent positions, scaled by number of Senators and

shaded by their voter agreement level. In each period there are two “party loyalist”

positions, anchored on the y-axis proportional to the modularity score. The y-

position of other nodes—usually individuals—is based on the balance of their votes

relative to these anchors. Positions are linked over time by identity arcs connecting

each person to themselves over time, labeled to trace individual careers (the widths

of arcs between aggregate positions indicate the number of people moving between

them over time).

Substantively, we have not seen the current level of partisanship (by this measure)

since the early 1900s, begging the question whether this represents a qualitative phase

shift in the structure of Senate politics. For a long period (at least from 1932 to 1992),

it appears that Senators could occupy mixed-party roles in multiple terms, perhaps

because of an interplay between local and party politics leading to more cross party

1 Thanks to Joshua Medelsohn and participants of the Political Networks Conference (June 2010, Duke)for comments.

120

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End note 121

votes. It would seem that this started changing in Clinton’s first term (1993–1994),

and solidified in the 104th Congress (1995–1996), with polarization returning to

hyper levels not seen in nearly 100 years. At this transition, middle-role Democrats

joined majority-party coalitions and then similarly positioned Republicans followed

when they took over the majority in 1995, leaving the middle ground deserted. In

the current era, middle positions seem fragile and even longtime middle residents

follow party lines (Jeffords) or lose their seats (L. Chafee). Structurally, middle-

level positions also appear dominated by representatives of single parties, suggesting

something other than bipartisan cooperation. Unfortunately, this level of polarization

could be self-reinforcing, since success in middle positions requires coalitions and

trust that are unlikely given so many party loyalists.

Supplementary materials

For supplementary material for this article, please visit http://dx.doi.org/10.1017/

nws.2012.3.

References

Blondel, V. D., Guillaume, J. L., Lambiotte, R. E., & Lefebvre, E. (2008). Fast unfolding ofcommunities in large networks. Journal of Statistical Mechanics: Theory and Experiment,10, 10008.

Newman, M. E. J. (2006). Finding community structure in networks using the eigenvectors ofmatrices. Physical Review E, 74(3), 036104–036119.

Poole, K. T. (2012). “Voteview.” Retrieved from http://voteview.com.

Waugh, A. S., Pei, L., Fowler, J. H., Mucha, P. J., & Porter, M. A. (2009). Party polarization inCongress: A Network Science Approach SSRN. Retrieved from http://ssrn.com/abstract=1437055.

White, H. C., Boorman, S. A., & Breiger, R. L. (1976). Social structure from multiple NetworksI. American Journal of Sociology, 81, 730–780.

Online Appendix 1

Portrait of Political Party Polarization

JAMES MOODY and PETER J. MUCHA

Network Science / Volume 1 / Issue 01 / April 2013, pp 119 – 121

DOI: http://dx.doi.org.libproxy.lib.unc.edu/10.1017/nws.2012.3

Supplementary On-Line Material.

Purpose

Why write a 1-page research note and what do you expect readers to do with it?

Disciplinarily, we have two motivations. First, social science articles are getting longer,

and many papers are often buried with technical detail and dense literature reviews. Such

papers seek to wrap up problems, rather than open them. A short, empirical note or, since

the real substance of this project is a figure, a “portrait” is designed to open problems for

investigation. The advantage of a new journal and new format such as that afforded by

Network Science is to reshape the basic form of an empirical finding: the goal here is to

present a simple data-based puzzle for the scientific community to ponder. Here the

massive shift in polarization, and the ways in which this intersects with political party

politics, majority membership, presidential party and individual careers provides a deeply

complex puzzle to think about. This sort of puzzle, we think, is just the sort of problem

that Network Science is poised to work on.

Second, data visualization is a hallmark for network science, but exemplary data-deep

models are rare. Often network visualizations are wedded to program defaults and

generate images that provide very little substantive information. But visual approaches to

data can allow viewers to make connections between parts – to literally see a micro-

macro relation (Tufte, 2001) – which we seek to take advantage of here. As such, we

have built an image that informs immediately (the increasing trend in political

polarization), but also rewards detailed scrutiny (the coalition patterns within Senate

sessions, or the career trajectories of particular Senators over time, or the intersection of

executive and legislative control, to name just a few). In this, we are similar to work on

the visualization of agreement groups in the Senate (Friggeri, 2012), which also readily

demonstrates the political trajectories of individual Senators through time in a compact

visualization.

Substantively, the goal of this piece is to document an interesting political phenomenon in

a way that might lead to new insights. The U.S. Senate is experiencing a level of

polarization, as measured by the structural pattern of co-voting ties, unseen for over a

century. The potential causes of this pattern may be many, but it seems plausible that

endogenous coalition behavior captured through networks might contribute, and this

figure is designed to help us explore such possibilities. Current work in political

sociology suggests that such extreme professional polarization is at odds with American

popular opinion. This suggests that a simple voter-representation explanation cannot

hold, and that internal dynamics could be driving the divisions (Baldassari & Bearman,

2007; Baldassari & Diani, 2007).

Online Appendix 2

Methodologically, this image reflects advances in both network analysis and

visualization. First, network studies still have a strong cross-sectional bias and much

work tends to emphasize connectivity features (centrality, cliques) rather than positional

features (roles & systems patterns; see Burt, 1987). We seek here to expand on both of

these dimensions. First, we fold time into the network as a type of structure with identity

arcs (see Moody, 2010 for visualization and diffusion implications, Mucha et. al. (2010)

for community detection tools on such graphs). This allows one to capture network

dynamics in a straightforward way and ask how types of positions emerge over time.

Second, we add role information to the connectionist subgroups by combining new

community-detection tools (Blondel et al., 2008; Newman, 2006) with structurally-

equivalent blockmodels (White et al., 1976). The connectionist point of view captures

the extent of political polarization, while role positions help us understand how such

polarization evolves.

The most direct methodological advance of this piece is in the form of a careful new

visualization template. Visualizations of these sorts of data – the one-mode projections

of two-mode networks (also known as “persons-through-groups” data – Breiger, 1976) --

typically suffer from high density, since there is a weighted line between every pair in

the network, and standard space-based layouts typically result in large, uninformative

clusters. One solution is to plot only the strongest ties, but this can still leave a large

cluster of nodes in a fully-connected clique. This problem is amplified in co-voting

networks, where (nearly) every member votes on every item. Here, we simplify the

network by aggregating over the structurally equivalent positions. Since every Senate

session includes at least two positions consisting (almost) entirely of party-line voters, we

chose to anchor the layout with these “party loyalist” positions.

Data

The data are roll-call votes in each completed Congressional session as constructed by

Poole (2009; Poole & Rosenthal, 1997). We cleaned the data for name consistency (in the

raw data, party-changing Senators are sometimes assigned different ID numbers; we

instead continue to identify them by individual). For the purposes of investigating

differences in voting, we include only non-unanimous votes (less than 97% agreement; as

in Waugh et al., 2009). Data on the 112th

congress runs through June 7th

, 2012 and was

taken from: http://adric.sscnet.ucla.edu/rollcall/. To construct identity arcs in this figure,

all data were resolved to “name.state” level, with corrections for any instances with two

people having the same name (such as Jr. or when spouses are appointed for a deceased

member). In rare instances where the same senator had different ids within the same year,

we treated the data as given.

Methods

For each two-year Senate, we construct a network with Senators as nodes and their

agreement on votes cast as edges. The value of the edge is the proportion of all votes

made by the two Senators where they agreed on the vote (positive or negative). These

network “slices” are then joined over time by identity arcs to generate a fully time-

connected network. An identity arc captures the number of Senators who move from

position i at time t to position j at time t+1. If the positions are individuals, then the arc

Online Appendix 3

simply links a person from their past to future selves. If the positions are aggregates, then

the value of the arc shows the number of people moving between such positions over

time.

Measuring polarization

We operationalize polarization as the tendency for votes to fall within clearly defined

groups (called variously “clusters” or “communities” or “cohesive groups” in the

literature; we stick with “communities” here for simplicity). Communities were

identified endogenously using an algorithm that partitions the network into mutually

exclusive and exhaustive sets such that the weighted volume of ties within groups is

maximized relative to a null model (see Waugh et. al,. 2009).1 The code for this program

can be found at http://netwiki.amath.unc.edu/GenLouvain (Jutla, Jeub, & Mucha 2011-

2012). Specifically, communities were identified here using the Kernighan-Lin (see

Newman, 2006) iterative improvement of a Louvain method greedy partitioning

algorithm (Blondel, et al. 2008) for maximizing modularity. Modularity measures the

relative weight of ties within versus between communities, calculated as eq. 1 below.

(1)

Where:

s indexes communities in the network

ls is the total weight of lines in community s

ds is the sum of the weighted degrees of s

L is the total weight of lines in the network

With the exception of the 103rd

Senate (1993-’94) which included a small 3rd

group, all

networks plotted in figure 1 were maximized with a 2-cluster solution corresponding

(largely) to political party. The resulting modularity score is plotted as the y-axis in the

figure and the inset, and traces the extent of polarization over time (Waugh et al., 2010).

Since the division is typically split between two groups, we visually divide the distance

from pure integration (modularity=0) evenly between the two parties resulting in a

symmetric trend around the zero line (though the contribution to modularity made

individually by the two clusters are not equal).

Identifying Roles

To identify role positions, we modified the standard CONCOR strategy for identifying

structurally equivalent positions (White et al., 1976). The identification of positions is

done independently of the cohesive group detection algorithm, and the code for the

CONCOR split, construction of edge-identity links and initial graph output can be found

at http://www.soc.duke.edu/~jmoody77/congress/simpleread3_redone_wc111_c112.sas.

CONCOR is a divisive clustering algorithm that splits a whole into two parts, and then

continues to split each resulting group in two again until a user-defined threshold is met.

1 Why cluster instead of simply using the party affiliation labels? Because some nominal party members

frequently vote with the other party. For example, western Senators from states split between liberal

urbanites and conservative rural constituencies, (Oregon, Montana, or Maine, for example) or socially

conservative Southern Democrats are commonly in such positions.

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Online Appendix 4

This split is defined by the “convergence of iterated correlations;” where an initial

correlation between pairs based on the pattern of ties to all others is repeatedly correlated

until all cells converge on +1 or -1. A critique of CONCOR is that the bifurcation

strategy strongly constrains the resulting partition (Wasserman & Faust, 1994). To solve

this, instead of specifying a global number of splits, we specify a minimum correlation

threshold within each group, and only split along that branch if the internal similarity of

the group is below our correlation threshold (initially 0.85), ensuring a consistent level of

similarity amongst positions. Individuals will occupy unique positions if the internal

correlation of the branch they are part of never reaches the threshold.

Finally, the extent of polarization in later periods is so great, that a single

threshold over the entire time period set high enough to distinguish unique positions in

later periods resulted in little aggregation in the earlier period (often returning 50-60

positions). Thus, we adjusted the threshold correlation dynamically to ensure between 5

and 20 positions; if the process yielded more (less) than 20 (5) positions at a threshold of

0.85, we lowered (raised) it by 0.005 until the size bound was met. Substantively this

means simply that the global pattern (voting diversity early, polarized party-line later)

would be magnified by any constant threshold. Seen another way, cross-party vote

becomes more salient when most votes fall within party, and thus looking distinctively

“middle ground” requires fewer cross-party votes.

Visualization layout & display

The layout is achieved in four steps that combine fixed and space-based layout

strategies. The community detection was done in MATLAB and CONCOR was

conducted in SAS. Visualization was done using the PAJEK network analysis software

for the base layout and adjusting color and label details in Adobe Illustrator. First, for

party loyalist positions, the y-axis is set by the polarization measure and party

(-1*modularity for Republicans, + modularity for Democrats) and the x-axis is set by

date. Second, for non-loyalist positions, we apply a Kamada-Kawai spring-embedder

algorithm that adjusts the position of non-loyalists between the loyalist anchors. For this

stage of the layout process (only), we remove all ties except those linking the party-block

anchors to middle-level positions. Since each non-loyalist position is effectively

“suspended” between the anchors with a weighted link to each, the resulting y-position of

non-loyalists reflects their balance of agreement with the anchors. For presentation

clarity, we display the co-voting similarity edge if agreement is > 0.60 (green edge in the

display). The x-position is adjusted manually within the date-range to minimize line

crossings. Third, we size edges and nodes proportional to volume, generate labels and

export to Illustrator. Fourth, after the images are exported to Illustrator, we place labels

and keys and adjust shades and colors. Individual Senators are labeled so that one can

trace the careers of all Senators who appear more than once in non-loyalist positions

(though you may have to zoom in some to do it!). Aggregate positions are then shaded

relative to the average vote agreement (resulting in light to dark red/blue). For example,

the lowest “democratic loyalist” agreement level was in the 96th

Congress, with members

agreeing 72% of the time, which increases to 89% of the time in 108th

Congress.

Presidential term and Senate party balance is given in the timeline at the bottom

of the figure. We use a purple shade reflecting the Red-Blue balance of the senate,

interpolating the proportion Red/Blue in the RGB color balance to set purple as a 50/50

Online Appendix 5

split. For convenience, we label the dates of each Congress ignoring any final few

January dates of that Congress (e.g., we label the 110th

Congress as ’07-’08 even though

it was officially in session from January 4, 2007 to January 3, 2009).

References

Baldassarri, D. & Bearman, P. S. (2007). Dynamics of Political Polarization, American

Sociological Review, 72, 784-811.

Baldassarri, D. & Diani, M.. (2007). The Integrative Power of Civic Networks. American

Journal of Sociology, 113, 3, 735-780

Blondel, V. D., Guillaume, J. L., Lambiotte, R. & Lefebvre, R. (2008). Fast unfolding of

communities in large networks. Journal of Statistical Mechanics: Theory and

Experiment, 10, P10008.

Breiger, R. L. (1974). The Duality of Persons and Groups. Social Forces, 53, 181-90.

Burt, R. S. (1978). Cohesion Versus Structural Equivalence As a Basis for Network Sub-

Groups. Sociological Methods and Research, 7, 189-212.

Friggeri, A. (2012). Agreement Groups in the United States Senate. Retrieved from:

http://friggeri.net/research/senate/ (retrieved 2012).

Jutla, I. S., Jeub, L. G. S., & Mucha, P.J. A generalized Louvain method for community

detection implemented in MATLAB, http://netwiki.amath.unc.edu/GenLouvain

(2011-2012).!

Moody, J. (2010). Static Representations of Dynamic Networks Manuscript (R&R at

Social Networks)

Mucha, P. J., Richardson, T., Macon, K., Porter M. A., & Onnela. J.-P. (2010).

Community Structure in Time-Dependent, Multiscale, and Multiplex Networks.

Science, 328, 876-878.

Newman, M. E. J. (2006). Finding community structure in networks using the

eigenvectors of matrices. Physical Review E, 74, 3, 036104-19.

Poole, K. T. & Rosenthal, H. (1997). Congress: A Political-Economic History of Roll

Call Voting. New York: Oxford University Press.

Poole, K. T. (2012). Voteview. http://voteview.com (retrieved 2012).

Tufte, E. R. (2001). The Visual Display of Quantitative Information, 2nd

edition.

Cheshire, CT: Graphics Press

Wasserman, S. & Faust, K. (1994). Social Network Analysis. Cambridge: Cambridge

University Press.

Waugh, A. S., Pei, L., Fowler, J. H., Mucha, P. J., & Porter, M. A. (2009). Party

Polarization in Congress: A Network Science Approach SSRN

(http://ssrn.com/abstract=1437055).

White, H. C., Boorman, S. A., & Breiger R. L.. (1976). Social Structure From Multiple

Networks I. American Journal of Sociology, 81, 730-780.