partition decoupling for roll call data (2)

Partition Decoupling for roll call data

Scott PaulsDepartment of MathematicsDartmouth [email protected]

University of Massachusetts, AmherstDecember 7, 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!

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

Random Model

The null model we use is a bootstrap null model – one generated by randomly permuting the data.

This preserves the basic structure of outcomes of the votes, but destroys any structure of association between legislators.

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“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

“Conse

rvati

ve

Repub

licans”

Sessions, Kyl, Cornyn, Santorum, etc.

“tax cuts”

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

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N/Y

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Y Y Y N N Y N

Democrats Republicans

Distinguishing clusters 108th Senate


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


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



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/N

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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


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

Application to UN roll call voting

This is work in progress – joint with Skyler Cranmer (UNC, Chapel Hill) and Bruce Desmarais (UMass, Amherst).

Goal: Can methods, such as the PDM, be used to construct meaningful categories which capture the positions of states in the world political system?

Test Case

UN roll call votes from the 60th session through the 66th session (2005-2011).

Consider, as with the U.S. House and Senate, two layers of the PDM.

First Layer

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US, Israel

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First Layer: GDP per capita

Quantiles 25% 50% 75% Cluster 1: $1,181 $3,923 $9,484Cluster 2: $12,374 $28,218 $53,118

Kolmogorov-Smirnov 2 sample test, .

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Adaboost resultsCuba:3 votes: Necessity of ending the economic, commercial and financial embargo imposed by the United States of America against Cuba : resolution

Human Rights:Human rights and unilateral coercive measures : resolution Human rights and cultural diversity : resolution Globalization and its impact on the full enjoyment of all human rights : resolution

Nuclear Weapons:Follow-up to the advisory opinion of the International Court of Justice on the Legality of the Threat or Use of Nuclear Weapons : resolution

Palestine:The right of the Palestinian people to self-determination : resolution Palestine refugees' properties and their revenues :

Economic Development:International trade and development : resolution The right to development : resolution

Vote splitsCluster 1 Cluster 2 Cluster 3

(World) ((Europe) (US/Israel)

Cuba 1 1 -0.5

1 1 -0.5

1 1 -0.16

Human Rights 1 -1 -1

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0.98 1 -1

Nuclear 0.95 095 -1

Palestine 0.95 0.97 -1

0.98 1 -1

Economic Dev. 0.97 0.97 -1

1 -1 -0.33

Second layerDark Blue:Ireland LiechtensteinSwitzerlandAustriaSan MarinoMaltaSerbia Bosnia and HerzegovinaCyprusFinlandSwedenNew ZealandMarshall Islands

Black:UKNetherlandsBelgiumLuxembourgFranceSpainPortugalPolandHungaryCzech RepublicSlovakiaItalyAlbaniaSloveniaBulgariaRussian FederationEstoniaLatviaLithuaniaGeorgiaAzerbaijanDenmarkTurkeyTajikistanKyrgyzstanKazakhstan

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Adaboost resultsHuman Rights:Situation of human rights in the Democratic People's Republic of Korea : resolution

Situation of human rights in the Islamic Republic of Iran : resolution

Death Penalty:2 votes: Moratorium on the use of the death penalty : resolution

Racism:Inadmissibility of certain practices that contribute to fuelling contemporary forms of racism, racial discrimination, xenophobia and related intolerance : resolution

Vote splits1 2 3 4 5 6 7 8

HR -0.4 0.09 0 -0.7 0.45 -0.1 0 0.4

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0.31 0.08 -0.46 0.54 0.04 -0.2 -0.54

DP 0.97 -1 0.1 -0.6 0.7 -0.02 0.2 -0.54

0.94 -1 0.1 -0.53 0.59 0.02 0.2 -0.48

Racism 0.83 -0.92 0.13 -0.6 0.6 -0.1 0.23 -0.27

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1: red2: green3: blue4: yellow5: magenta6: cyan7: black8: white

W-NOMINATE

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W-NOMINATE Coordinates

First Dimension

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Scree Plot

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W-NOMINATE:

% votes predicted correctly: 98.56% (1 dim)98.98% (2 dim)99.42% (3 dim)

PDM :% votes predicted correctly: 99.11% (1 layer)99.66% (2 layers)

W-NOMINATE vs. PDM

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Polity

Polity IV scores (Marshall, Jaggers and Gurr) provide a measure of the authority characteristics of states in the world political system.

It is often used as a proxy for political similarity between states, and hence the potential for cooperation on different issues. E.g. two democratic states are more likely to cooperate than one democratic and one authoritarian state.

Polity in layer one

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Polity-10 -5 0 5 100

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State classifications

Can the segmentation given by the layers in the PDM replace polity for use as a covariate in, for example, models in international relations?

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SummaryPDM 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.

This labeling given by the clusters at various levels provide a novel, and potentially useful, set of explanatory variables for use in political science models.

partition decoupling for roll call data (2)

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