political networks

Partition Decoupling for roll call data

Scott PaulsDepartment of MathematicsDartmouth [email protected]

5th Annual Conference on Political NetworksJune 13-16, 2012University of Colorado at Boulder and the University of Denver.

5th Conference on Political Networks June 13-16, 2012

Partition Decoupling for roll call data

This is joint work with Greg Leibon, Dan Rockmore, and Robert Savell, all from Dartmouth.

http://arxiv.org/abs/1108.2805

http://arxiv.org/abs/1108.2805


Inference from roll call data

Aye!Aye

Nay!Aye


A legislator is merely a bundle of votes.

Votes:

Motivations are vote profiles associated with a coherent ideological position.


Motivational model

If we have a complete set of motivations, then a legislator is represented as a linear combination of motivations:


Partition Decoupling Method (PDM)

1. Construct a similarity matrix of legislators from the roll call data.

2. Using this similarity, cluster the legislators together. The mean voting profile of each cluster defines a motivation.

3. Let be the collection of motivations and, using least squares, determine the .

4. Our first layer approximation of the roll call data is then given by:

5. Create residual data and repeat to create etc.

6. Iterate until is indistinguishable from a random model.

NETWORK

COMMUNITY

LEARNING

LOW DIMENSIONAL REPRESENTATION

ITERATION

Comparisons Minority

modelRandom model

Poole-Rosenthal: 1 dim.

Poole-Rosenthal: 2 dim.

% of residual captured

PDM: one layer

PDM: two layer

% of residual captured

House APRE 0 0.4561 0.534 0.593 13 0.839 0.856 11

Percent correct (House)

67.3 [72,88] 84.5 86.5 13 94.7 95.3 11

Senate APRE

0 0.4834 0.476 0.563 17 0.809 0.822 7

Percent correct (Senate)

66.6 [70,90] 82.3 85.2 16 93.6 94.1 8



Example: 108th Senate

Zell Miller (D-GA) “Liberal Democrats”: e.g. Kennedy, Feingold, Boxer, Leahy, Reed, etc.

“Conservative Democrats”: e.g. Pryor, Lincoln, Bayh, Breaux, Landrieu, etc.

Fitzgerald, Gregg, McCain, Sununu, Warner

“Moderate Republicans”: e.g. Snowe, Chaffee, Collins, Specter, etc.Frist, Lott, Brownback,

Hagel, etc.

“Con

serv

ative

Rep

ublic

ans”

Sessions, Kyl, Cornyn, Santorum, etc.

“tax cuts”



Outer shape: red=midwest, blue=northeast, green=south, black=southwest, yellow=west

Part

y

Civil Rights


Layer two

Regional identification dominates highest correlations (particularly in recent years).

Clustering on the residual data provides a new partition of network which is (often) completely different than the first layer.

In particular, clusters are not dominated by party identification.



Three clusters of mixed party.

Four sets of issues distinguish the clusters effectively:1. Infrastructure: Three amendments (86, 214 and 230) to H.J. Res. 2,

the Appropriations Bill, relating to infrastructure projects.2. Energy: Seven amendments (515, 843, 844, 851, 853, 856, 884

and 1386) to Senate Bill 14, a bill concerning the energy security of the United States. One amendment (272) to S. Con. Res. 23, relating to drilling in the Arctic National Wildlife Refuge.

3. Homeland Security: Two amendments (515 and 3631) pertaining to Homeland Security.

4. Trade: The passage of the US-Chile Free Trade Agreement

The first and second clusters are well separated by the Energy votes, the first and third by Energy and Infrastructure votes and the second and third by one energy vote, Homeland Security and Trade votes.


Interaction of the two layers


Conclusions

• PDM decomposition reveals multiple layers of structure associated to roll call voting.

• Taken together, these form a mathematical description of ideology.

• The coarse version of the first layer is close to the results of spatial models but even the first layer significantly outperforms spatial models with respect to standard metrics.

• The use of multiple layers allows us to capture a more nuanced picture of ideology while still retaining the parsimony of the NOMINATE-type models.

• Our dimensionality results confirm those of Poole-Rosenthal while simultaneously incorporating contradicting evidence (e.g. Heckman-Snyder) – the dimensions appear at different scales.


Distinguishing clusters: 108th Senate

• Coarse picture: one dimensional ideology (“liberal/conservative”).

Y N N N N N N

N N Y Y N N N

Y Y Y Y Y Y N

Y/N Y/N Y/N Y/N N/Y N/Y N/Y

Y Y Y Y Y N N

Y Y Y N N Y N

Democrats Republicans


Distinguishing clusters 108th Senate

• Coarse picture: one dimensional ideology (“liberal /conservative”).

Y N N N N N N

N N Y Y N N N

Y Y Y Y Y Y N


Y Y Y Y Y N N

Y Y Y N N Y N


An amendment to an appropriations bill which would eliminate tax cuts.



• Coarse picture: one dimensional ideology (“liberal conservative”).

Y N N N N N N

N N Y Y N N N

Y Y Y Y Y Y N


Y Y Y Y Y N N

Y Y Y N N Y N


An amendment to repeal authorities and requirements for a base closure




Y N N N N N N

N N Y Y N N N

Y Y Y Y Y Y N


Y Y Y Y Y N N

Y Y Y N N Y N


Three votes:1. Sense of the

Congress re: global AIDS funding

2. Cloture: Safe, Accountable, Flexible and Efficient Transportation Act of 2004

3. Amendment to provide a brownfields demonstration for qualified green/sustainable design projects




Y N N N N N N

N N Y Y N N N

Y Y Y Y Y Y N


Y Y Y Y Y N N

Y Y Y N N Y N


Two votes:1. Extend

Unemployment Benefits

2. Sense of the Senate re: imposition of an excise tax on tobacco lawyer’s fees that exceed $20,000/hr




Y N N N N N N

N N Y Y N N N

Y Y Y Y Y Y N


Y Y Y Y Y N N

Y Y Y N N Y N


Amendment to protect US workers from foreign competition for performance of Federal and State contracts.




Y N N N N N N

N N Y Y N N N

Y Y Y Y Y Y N


Y Y Y Y Y N N

Y Y Y N N Y N


Amendment to vest sole jurisdiction over Federal budget process in the Committee on the Budget


I suspect that some of the issues raised by the referees reflect disciplinary differences. For a paper like this to be attractive to a political science audience, it is necessary to motivate the method theoretically. This can be of the type "this model is based on these behavioral axioms" (like the Nominate and Clinton-Jackman-Rivers model) or "this method allows us to answer an important and previously unanswered question." Either of these frames would make the paper of greater interest to political scientists. If the method doesn't provide stand on its own substantively, then it's not something that will have much traction in our discipline, nor, in my mind, should it.

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