Three Essays in Political Methodology
byArthur Peter Andrew Spirling

Submitted in Partial Fulfillmentof theRequirements for the Degree
Doctor of Philosophy

Supervised byProfessor Curtis Signorino
Department of Political Science
The College
Arts & Sciences

University of Rochester
Rochester, New York

2008

ii

For my mother and for my father.

iii

Curriculum Vitae
The author was born in Carshalton in the London Borough of Sutton, United
Kingdom, on August 26, 1979. He attended the London School of Economics
from 1997 to 2001 and graduated with a Bachelor of Science degree in 2000.
He received a Master of Science degree in 2001 from the same institution, andthen attended Nuffield College, Oxford University, from 2001 to 2003. Hecame to the University of Rochester in the Fall of 2003 and began graduate
studies in Political Science. He pursued his research in political methodology
under the direction of Professor Signorino and received the Master of Arts
degree from the University of Rochester in 2007.

iv

Acknowledgements
Social reformer Sir Thomas Fowell Buxton once modestly observed that“with ordinary talents and extraordinary perseverance, all things are attainable.” Those things apparently include my completion of a dissertationin political science at the University of Rochester, although even Sir Thomaswould be surprised to learn quite how ordinary one’s talents can be in practice. With this in mind, there are several individuals who I wish to thankfor their contribution to my education, work and emotional well-being overthese last several years.

Chronologically, the story begins at Nuffield College, Oxford, where Iain
McLean was a sage source of counsel and helped me garner admission to the
University of Rochester in 2003. David Firth tried patiently to teach mesome statistics, and has been a constant source of helpful advice since thattime. Working and coauthoring with both these individuals has taught memuch about our related interests, and the travails of getting published.

At Rochester, Curtis Signorino, my advisor, allowed me the flexibility andsupport to explore new avenues of methods research without the micromanagement that would have pained us both. Preferring to gently steer
rather than direct, Curt provided much needed pastoral care when I felt
particularly frustrated and anxious—especially in the last year of my dissertation writing, which coincided with the stress of the market. Emphasizing
the ‘grand plan’ as well as the details, Curt has taught me a great deal

v
about how to ‘play the game’ of our discipline. Also serving on my committee, Tasos Kalandrakis is one of the hardest working men in the business,and his diligence in reading and commenting on my papers is second-tonone. Our projects together have been the most challenging and rewarding
experiences of my career to date, and I expect our cooperative efforts willcontinue for some time yet. Larry Rothenberg stepped forward when I
needed an extra body on my committee for bureaucratic reasons, but he has
become an important member of my team in the meantime. I thank him
for his time and advice. Though not on my committee, I am very gratefulto Michael Peress and Tony Lenzo who both supported my work in quite
different ways. Michael’s deep understanding of econometrics allowed him
to provide valuable technical feedback on my papers. Tony, who managed
the star lab during the writing phase of my dissertation, ran a very tightship and ensured that both the hardware and software I had access to wasin the best possible working condition.

In the broader methods community, I am very grateful to Jeff Gill and Andrew Martin at Wash U, Michael Herron at Dartmouth and Kevin Quinn at
Harvard. All these people kindly spent time helping me improve my papers
with lengthy and valuable comments.

My comrades in the department were constant sources of amusement andencouragement throughout the writing of this dissertation; in my cohort,
I thank Matthew Platt, David Carter, Michael Epstein, Arnd Plagge andSubhashish Ray. Peter Loewen spent an all too short visit at Harkness,viduring which time we became firm friends. In the early days, Justin Fox,
Antoine Yoshinaka and Kris Ramsay were a strong influence on my outlook
and behavior as a graduate student.

I wish to convey a very special thanks to my family that loved me whether
my research was progressing or stagnating: my mother, my father, my sisterand my brother. They were constant in their support, affection and financial
assistance; I hope I can, one day, repay these debts. Finally, perhaps mostof all, I thank Sonia Tasbas: without her love and kindness, I know onlythat my outlook—academic or otherwise—would be the poorer. I remain
truly grateful that I have found such a wonderful woman to spend my life
with.

vii

Abstract
This political methodology dissertation consists of several distinct essaysthat apply three new estimation techniques to all three subfields of thediscipline—international relations, American politics and Comparative politics. The first is an application of reversible jump Markov chain montecarlo, a more general form of MCMC popular for model search problems
in statistics. We apply RJMCMC to the current Iraq conflict in order to
identify change points in terms of civilian casualty numbers. The second
chapter uses the Bradley-Terry model for pairwise contests to estimate the‘power’ of actors in legislatures. We apply this generalized linear modelto the United States Senate. We use both an unstructured and covariate
based model to show that, inter alia senators’ party identification, ideological tendency, leadership rank, service length and gender all affect theirability to influence others in the chamber. The third chapter shows that
British Members of Parliament’s voting decisions on roll calls can affecttheir constituency performance at election time. In particular, ‘rebeling’on government bills apparently hurts them, while voting independently on
less important matters tends to benefit them. We use a non-parametric,
random forest algorithm to estimate the relationship, since the number ofparameters (the number of roll calls) far exceeds the number of observations(constituency performances) to be predicted.

viii

Contents
1 Introduction: Purpose and Plan
1.1

1

Plan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3

2 ‘Turning Points’ in the Iraq Conflict: Reversible Jump Markov
Chain Monte Carlo in Political Science6

2.1

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . .

6

2.2

Background and Data . . . . . . . . . . . . . . . . . . . . . .

8

2.3

Estimation Problem . . . . . . . . . . . . . . . . . . . . . . .

10

2.4

Results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

15

2.5

Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

18

3 Measuring Power in Political Science: A New Method with
Application to the Senate

22

3.1

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . .

22

3.2

Problems with Traditional Approaches to Measuring Power .

24

3.3

Statistical Theory and Model . . . . . . . . . . . . . . . . . .

26

3.4

Application: 108th Senate . . . . . . . . . . . . . . . . . . . .

32

3.5

Structured Modeling . . . . . . . . . . . . . . . . . . . . . . .

36

ix

3.6

3.5.1

Party and Ideology . . . . . . . . . . . . . . . . . . . .

38

3.5.2

Committee and Agenda Control . . . . . . . . . . . .

42

3.5.3

Geographic Factors . . . . . . . . . . . . . . . . . . . .

46

3.5.4

Career Factors . . . . . . . . . . . . . . . . . . . . . .

50

3.5.5

Summary of Findings . . . . . . . . . . . . . . . . . .

52

Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

54

Appendix to Chapter 3

61

3.7

The “Busy” Senator Problem . . . . . . . . . . . . . . . . . .

61

3.8

Logit Model with Order Effect . . . . . . . . . . . . . . . . .

62

3.9

Amendment Proposers . . . . . . . . . . . . . . . . . . . . . .

63

3.10 Goodness-of-Fit . . . . . . . . . . . . . . . . . . . . . . . . . .

63

4 Rebels with a Cause? Legislative Activity and the Personal
Vote in Britain, 1997–2005

70

4.1

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . .

70

4.2

Members, Constituents and the Personal Vote in Britain . . .

74

4.3

Formalizing Intuitions . . . . . . . . . . . . . . . . . . . . . .

77

4.4

Data and Method. . . . . . . . . . . . . . . . . . . . . . . .

81

4.4.1

Data: 1997–2001, 2001–2005 . . . . . . . . . . . . . .

83

4.4.2

Estimation Problem: p > n . . . . . . . . . . . . . . .

84

4.4.3

Tree-based Regression and Random Forests . . . . . .

85

4.4.4

Estimation Plan . . . . . . . . . . . . . . . . . . . . .

93

Results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

96

4.5.1

First term: 1997–2001 . . . . . . . . . . . . . . . . . .

96

4.5.2

Second term: 2001–2005 . . . . . . . . . . . . . . . . . 104

4.5

x
4.5.3
4.6

Summary of Results . . . . . . . . . . . . . . . . . . . 109

Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110

Appendix to Chapter 4

113

4.7

Regression Tree Split Criteria . . . . . . . . . . . . . . . . . . 113

4.8

Model Fit, Variable Importance and Effect

4.9

Imputing Missingness . . . . . . . . . . . . . . . . . . . . . . 116. . . . . . . . . . 114

5 Discussion

117

Bibliography

122

xi

List of Tables
2.1

Change point median dates [90% HPD] in Iraq casualty data, with rates
between breaks. Comments note political and other activities approximately contemporaneous to break.

3.1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

57

Effect of majority party and senior leadership status on power in the
Senate. Asterisked coefficients (***) imply p < 0.01. AIC: 11052.

3.3

21

Baseline results for model of power for US Senators in the 108th
Senate.

3.2. . . . . . . . . . . . . . . . . .

. . .

58

Effect of majority party membership and any leadership status on powerin the Senate. Asterisked coefficients imply p < 0.01 (***), p < 0.05(**). AIC: 11152.

3.4. . . . . . . . . . . . . . . . . . . . . . . . . .

58

Effect of conservatism, distance from median and majority status on
power in the Senate. Asterisked coefficients imply p < 0.01 (***), p <0.05 (**). AIC: 11169.

3.5. . . . . . . . . . . . . . . . . . . . . . . .

58

Effect of extremism, distance from median and majority status on powerin the Senate. Asterisked coefficients imply p < 0.01 (***), p < 0.05(**). AIC: 11136.

. . . . . . . . . . . . . . . . . . . . . . . . . .

59

xii
3.6

Effect of committee membership, majority party membership and chairstatus on power in the Senate. Asterisked coefficients imply p < 0.01(***), p < 0.05 (**). AIC: 9434.9. . . . . . . . . . . . . . . . . . . .

3.7

59

Effect of incomes, southern state representation, land area (state size)and state population on senator’s power. Asterisked coefficients imply
p < 0.01 (***), p < 0.05 (**). AIC: 10954. . . . . . . . . . . . . . . .

3.8

60

Effect of incomes, southern state representation, land area (state size)and state population on senator’s power. Asterisked coefficients imply
p < 0.01 (***), p < 0.05 (**). AIC: 10205. . . . . . . . . . . . . . . .

3.9

60

Baseline results for model of power for US Senators in the 108th

. . .

68

3.10 Number of amendments per senator. . . . . . . . . . . . . . . . . .

69

Senate, logit with ‘order effect’ (party advantage) estimated.

4.1‘Most important’ parliamentary votes for predicting electoral performance by backbench Labour MPs in 2001 general election. First column
is data code for the division with date after point: so, div323.001107 isdivision 323 taking place on November 7, 2000. Name of bill in column
2; random forest ‘coefficient’ in column 3 for being a ‘rebel’(in the minority and/or frustrating the Government’s ambitions); OLS coefficientin column 6; p-value for that coefficient in column 7. . . . . . . . . . . 100

xiii
4.2

‘Most important’ parliamentary votes for predicting electoral performance by backbench Labour MPs in 2005 general election. First column
is data code for the division with date after point. Name of bill in column
2; random forest ‘coefficient’ in column 3 for being a ‘rebel’(in the minority and/or frustrating the Government’s ambitions) ; OLS coefficientin column 6; p-value for that coefficient in column 7. . . . . . . . . . . 107

xiv

List of Figures
2.1

Iraq Casualty Incidents, May 2003–May 2007. Solid line represents cumulative counts; solid dots are jittered incident occurrences; various
dates of interest demarcated.

. . . . . . . . . . . . . . . . . . . .

11. . . . . .

16

2.2

Posterior of k: number of change points, Iraq casualty data.

2.3

Change in rate of casualty incidents over time: rate on y-axis, actual
incidents as jittered points. Dates correspond to breaks found. . . . . .

3.1

19

NOMINATE score versus power (λi ); open squares are Republicans,closed circles are Democrats; solid line is loess. Top figure is for all
senators; bottom figure is for all proposing senators.

3.2. . . . . . . . .

43

Extremism versus power (λi ); open squares are Republicans, closed circles are Democrats; solid line is loess. Top figure is for all senators;
bottom figure is for all proposing senators.

3.3. . . . . . . . . . . . . .

44

Boxplot showing relative power of committee chairs, non-chairing Republicans and Democrats who propose amendments.

. . . . . . . . .

47

xv
3.4

Map of contiguous United States with shading proportional to ‘power’
given by coefficients in Table 3.7: lighter states are associated with more
powerful senators.

. . . . . . . . . . . . . . . . . . . . . . . . . .

51. . . . .

53

. . . . . . . . . . . . . . . . .

64

3.5

Boxplot showing relative power of male and female senators.

3.6

Amendment numbers: distribution.

4.1

Percentage of respondents naming different qualities as “important for
an MP to have”: solid line is percentage naming ‘independent minded’,broken line is percentage naming ‘loyal to party’. Multiple choice, morethan one choice permissible; survey dates are 1983, 1994, 1996, 2000,
2005. Source: Johnson and Rosenblatt (2007, 166, Table 1).

4.2. . . . . .

75

Example of a classification tree for American states, predicting (categorizing) the percentage of vote for George Bush in the 2004 Presidential
election. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4.3

89

Example of a tree that uniquely classifies American states, in terms thepercentage of vote for George Bush in the 2004 Presidential election.
Node labels removed for clarity of presentation.

4.4. . . . . . . . . . . .

90

Random forest schematic. Here the data set consists of ten observations
labeled 1 through 10. These are ‘bootstrap sampled’ into bags (1 thorough B). For each bag, some observations are ‘left out.’ A tree is grownfrom each bag, and the results aggregated.

4.5. . . . . . . . . . . . . .

94

Variable importance plot for 1997–2001 data. Controls and ‘important’roll calls used in subsequent analysis shown as subsets of all variables.
x-axis gives the increase in the regression performance from including
each variable.

. . . . . . . . . . . . . . . . . . . . . . . . . . . .

97

xvi
4.6

Variable importance plot for 2001–2005 data. Controls and ‘important’roll calls used in subsequent analysis shown as subsets of all variables.
x-axis gives the increase in the regression performance from including
each variable.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . 106

1

Chapter 1

Introduction: Purpose andPlan
As befits its title, the following dissertation is composed of three self-contained
essays within the broad rubric of ‘political methodology.’ For current purposes, this term refers to the use of quantitative techniques that can give
scholars insights into political phenomena. The stress on ‘quantitative’ isimportant since the chapters below all make claims that attributes of political events and actors can be measured and compared. In line with this,the essays develop tools that other political scientists can use to analyze thedata scenarios they face. Though these themes are consistent threads, thedissertation is eclectic: in terms of the models of inference, the nature of
the techniques used, the substantive topics of investigation, and the questions that are actually answered. To this end, one of the papers is avowedly
Bayesian, while two are not. Two papers utilize parametric methods, while

Section 1.0

2

the third uses non-parametric techniques. The papers cover the three broad
areas of substance seen in the discipline: International Relations, American
and Comparative politics respectively.

Pursuing such a diverse agenda in one work is not uncontroversial; King
(1989), for example, argues for a ‘unified’ methodology (in practice, maximum likelihood) in political science that would facilitate the applicationof consistent standards, communication and the cumulation of knowledge
within the discipline. With good reason, he warns against techniques whichare “imported intact and without adaptation” from other disciplines (King,
1989, 3). The current dissertation is more sanguine about such endeavors: it borrows techniques more commonly seen in bio-statistics, patternrecognition and market research literatures. The contention is that, if assumptions (and thus limitations) are clearly described, readers may judge forthemselves whether or not the model is appropriate. In any case, in reviewing the technical literature in each essay, an argument is made for the absenceof an existing method to solve the specific problem addressed. Moreover,as will be explored, the particular problems here are neither uniquely rare
nor trivial—that is, the chapters are not ‘solutions in search of applications’.

A second concern for work in political methodology is that of specifying
appropriate ‘theory’. Achen (2002, 424), for example, argues that “we have
yet to give most of our statistical procedures legitimate theoretical microfoundations.” For Achen (2002, 437), a micro-foundation is “a formal modelof the behavior of the political actors under study. The model might emerge

Section 1.1

3from decision theory, game theory, or some other formalism. Then the statistical setup is derived from the model, with no further ad hoc adjustments.”
In the second chapter, this prescription is broadly followed: a model of human behavior is suggested and an estimator derived directly. In the first andthird chapters it is not. That is in part because these other essays are moreconcerned with data exploration and summary, rather than establishing “reliable empirical generalizations.” In statistics, such endeavors are common
and their usefulness is in part derived from the fact that they simplify anddescribe (for the analyst) an otherwise complex picture of information. As afirst pass on the data they are helpful: previously hidden regularities emerge
and help scholars (including the present author) to think more systematically about what is driving behavior ‘under the hood.’ Of course, it is a thinline between ‘data mining’ and ‘data dredging’ but these essays make a goodfaith attempt to avoid the latter. In any case, as argued above, introducing
new techniques to the discipline where current ones simply cannot be used
is a fruitful exercise.

1.1

Plan

The first essay (Chapter 2) uses a reversible jump Markov chain monte carlo
approach for examining structural breaks in the current Iraq conflict. Theinterest is in identifying patterns of violence, especially as they relate topolity building. We find four ‘turning points’—all of which correspond toincreased civilian casualties. These are arguably congruent with insurgent
responses to widely publicized events including the arrest of Saddam and theSection 1.1

4

holding of elections. Thus the chapter makes a contribution to the systematic study of international conflict and comparative political development.
Methodologically, the chapter adds to the political science toolkit by suggesting a more general Bayesian approach to change point detection that isphilosophically appealing.

The second essay (Chapter 3) suggests a new way of measuring ‘power’
for actors in structured settings like legislatures and courts. In contrast toa priori pivotality indices (of which Shapley-Shubik and Banzhaf are most
famous) which have been criticized for their measurement of ‘luck’ rather
than ‘power’, this essay introduces a data-driven Bradley-Terry approachthat proceeds directly from a theoretical model of (pairwise) actor behavior. We apply the model to the 108th Senate. In its unstructured form, weare able to produce a valid rank ordering of senators, with individuals suchas John McCain, Bill Frist and Robert Byrd appearing in the power top
ten. When a structured, covariate model is used, we show that, empirically,
chamber centrists lack power relative to party medians. Moreover, we areable to demonstrate that, contrary to some expectations, female senators
tend to be as powerful (on average) as males.

The third essay (Chapter 4) uses a non-parametric regression approach to
examine the relationship between a member of the British parliament’s legislative activity and their constituency electoral performance. In contrast to
assumptions of no effect, we show evidence of a subtle reward/punishment
dynamic, contingent on the nature of the roll calls in question. This pa-

Section 1.1

5

per combines quantitative and qualitative research on roll calls in the years
1997–2001. Methodologically, we describe a new ‘random forests’ approachfor political scientists interested in problems for which the number of parameters far exceeds the number of observations, and for which the causal
story is potentially complex and non-linear.

We conclude in Chapter 5 with a discussion of future applications and extensions to the work here, along with some comments on the role and futureof political methodology more generally.

6

Chapter 2‘Turning Points’ in the Iraq
Conflict: Reversible Jump
Markov Chain Monte Carloin Political Science
President Bush believes that the region is at a true turning point.
He believes that the people of the Middle East have a real chance
to build a future of peace and freedom and opportunity.
—Condoleezza Rice, National Security Advisor (2003)

2.1

Introduction

The study of inter – and intra– state conflict is a mainstay of political science. As an international conflict that increasingly resembles a civil war,
the current situation in Iraq provides both a testing ground for theories on
the duration and termination of different types of conflicts (e.g. Filson andWerner, 2004; Stam and Bennett, 2006), as well as a rich source of data
for empirical work. This is quite separate from its obvious importance as apolitical, military and economic event in progress. In part due to its contem-

Section 2.1

7

poraneous nature, political scientists have access to carefully, daily recorded,
military and civilian casualty information: an unusual and excitingly finelevel of detail. Of course, the utility of any data is only as good as the way
it is explored and analyzed. Here, we suggest that a fruitful approach forpolitical scientists lies in examining the time series for (potentially multiple)
structural breaks and their effects. For scholars of American politics andpublic policy, the way that these change points correspond with administration statements on the progress of the war may be particularly intriguing.
This notion extends to Comparative institutions scholars interested in thepotentially pacifying effect of various post-war ‘state-building’ activities. In
keeping with the increasing acceptance and popularity of Bayesian methodsin political science, in undertaking our study we justify and adopt a novel (topolitical science) approach that uses a more general form of Markov chainmonte carlo (MCMC) techniques, well-known to statisticians as ‘reversible
jump’ MCMC (Green, 1995). We do so primarily for computational reasons.

Examining civilian casualty data from the official cessation of hostilities(May 2003) to May 2007, we find evidence of four change points. These
breaks are approximately contemporaneous with (1) the capture of Saddam, and the emergence of the Abu Graib scandal (late 2003 to Spring2004); (2) the installation of the Iraqi Interim Government, and the subsequent handover of power to the Iraqi Transitional Government (Summer
2004 to early 2005); (3) the legislative elections for, and negotiations toform, the first full-term Iraqi government (the early months of 2006); (4)the assumption of security and some military responsibilities by the Iraqi

Section 2.2

8

government (August/September 2006) . In every case, the frequency withwhich such incidents occur is increasing after the break.

2.2

Background and Data

The United States and allied forces attacked Iraq with aerial bombardments,
followed by a land invasion, on March 20th, 2003. By mid-April, Iraq’s capital city, Baghdad and Saddam Hussein’s home region of Tikrit was underallied control—bringing a de facto end to the war. A fortnight later, on May
3rd, 2003, President Bush declared that allied combat operations would now
officially cease. As with all conflicts, the war has not been costless. Whatmarks the Second Iraq War though, is the continued loss of life after the Iraqi
army was formally defeated. At the time of writing, some 3,000 coalition
force members had died in addition to at least 57,000 civilian fatalities sincemilitary operations began (sources are http://icasualties.org/oif/ andhttp://www.iraqbodycount.org/ respectively. Some studies have placed
the number of civilian fatalities at a much higher number. For example,
Burnham et al. (2006) claim up to 600,000 deaths). Violence has not yet
abated despite the passing of some presumably important landmarks in whatsome characterize as the development of Iraq’s polity and stability: for example, the capture of Saddam (December, 2003), the placing of the former
dictator on trial from ‘crimes against humanity’ (July 2004) and his execution (December 2006); the killing of Saddam’s sons, Uday and Qusay (July
2003); National Assembly elections (January 2005); the drafting (December
2003–March 2004) and subsequent referendum approval (October 2005) of a

Section 2.2

9

constitution; the election of a new president (April 2005) and the forming ofa governing coalition (May 2006); the execution of an Al-Qaeda ringleader,
Abu Musab al-Zarqawi, thought responsible for planning many terrorist attacks (June 2006); the assumption of security responsibility by the Iraqi
government (September 2006). We are interested in violence for the post(official) war period: although we certainly cannot make firm causal claims,
our study will enable us, for example, to make statements about the plausibility of various events as “turning points” and allows us to pass some
exploratory comments on how new democratic institutions and state apparatus developments are effecting Iraqis. Hence our study focuses on May
3rd 2003 through to the present time of writing (May 2007).

Our data are drawn from iraqbodycount.org a (online) data base thatrecords civilian deaths in Iraq “that have resulted from the 2003 militaryintervention by the USA and its allies. The count includes civilian deaths
caused by coalition military action and by military or paramilitary responses
to the coalition presence (e.g. insurgent and terrorist attacks)” (Dardagan
and Sloboda, 2006). The data in raw form record deaths at the day level,from January 2003 through to the present and are compiled from (primarily
Western) media reports and other sources. Since uncertainty often exists
on precise numbers, especially when different agencies have conflicting figures for the same incident, the data base reports a range of possible death
numbers from a ‘minimum’ to a ‘maximum.’ Potential ‘over-counting’ isa concern, so we use the ‘minimum’ and define a ‘casualty incident’ as involving five deaths or more (our findings below are similar when we defineSection 2.3

10

the incident threshold at ten or twenty deaths). For the purposes of thispaper, we focus on the (changing) frequency of attacks, rather than theirsize (above our minimum). In part this is a behavioral assumption: wewould contend that, at least initially, terrorists were able to control how
often they planned to inflict casualties, rather than how many. There were1682 such incidents in our time series, and we graph their occurrence inFigure 2.1; there, the solid line is the cumulative incident count, the solid
dots are simply jittered incident occurrences (for which the y-axis is not
the scale). We also report various dates that may of interest and to give
readers a sense of timing perspective. Although univariate time series work
is not regularly encountered in political science, it is valuable in the current
context as a ‘first glance’ exploration before covariate information becomes
available. We think that such work helps to prompt both theorizing anddata gathering for more nuanced and sophisticated analysis.

2.3

Estimation Problem

The single change point problem, estimated using Markov chain monte carlo
techniques, has been discussed for and by political scientists elsewhere (seeWestern and Kleykamp, 2004). That treatment is similar to the (hierarchical) presentation given by Carlin, Gelfand and Smith (1992): suppose y =(y1 , . . . , yT ) is a vector of observations of the random variable Y (casualty
incidents) over time and let f and g be unknown densities in the same parametric family with yi ∼ f (Y |λ1 ), i = 1, . . . , k, yi ∼ g(Y |λ2 ), i = k + 1, . . . T .
We wish to estimate k the (single) change point which takes (discrete) values

11

1500

Section 2.3

1000

Constitution writing finishedElections for transitional govt

500

Cumulative CountFirst full term govt takes power

Transitional Admin Law
Saddam captured

0Uday, Qusay killed

0

500

1000

Time (days after May 03, 2003)
Figure 2.1: Iraq Casualty Incidents, May 2003–May 2007. Solid line represents cumulative counts; solid dots are jittered incident occurrences; various dates of interest
demarcated.

1500

Section 2.3

12

in {1, 2, . . . , T }. A frequentist approach proceeds by maximizing

L(y) =kY
i=1

f (yi |λ1 )TYg(yi |λ2 )

(2.1)

i=k+1

to obtain k and the parameters λ1 and λ2 (which for the count case arearrival rates for a Poisson) if they are of interest. A Bayesian approachproceeds by placing a prior τ (k) on the change point. There are computational advantages of a Bayesian MCMC approach here since (a) maximizing(2.1) requires optimization in a space that is not continuous (recall that k is
discrete) which, say, Gibbs sampling does not; (b) the resultant non-nested
models may be straightforwardly compared using Bayes factors (Chib, 1998);(c) missingness in y is handled systematically. This is quite apart from thephilosophical appeal of Bayesian approaches of which political scientists are
increasingly aware (see, for example, Gill 2002, 1–6 and Jackman 2004, 486).

Here, we are interested in exploring multiple change point and such work
(Bayesian or otherwise) is much less common in political science. In part thisis because, with respect to the logic above, there are profound computationaldifficulties in generating proposals for situations where we suspect there are
more than a couple of change points. One approach, suggested by Chib
(1998) and applied to American politics by Park (2006), treats the change
point model as a type of time series Markov mixture model, where the observations are (assumed) drawn from latent state variables. Notice that thisapproach requires separate Markov chain monte carlo runs for the different
numbers of change points hypothesized (Leonte, Nott and Dunsmuir, 2003).

Section 2.3

13

An alternative solution is to use reversible jump Markov chain monte carlo
which allows us to complete the computational operations in one ‘go’ as well
as allowing us to be a priori agnostic over the number of parameters to be
estimated.

Typically when MCMC is used in political science the parameter vector
θ has a known number of components, denoted n. For the single change
point problem n = 3 (these are k, λ1 and λ2 ). Now consider a very different
scenario which arises for an unknown number of k change points: for every
possible k, we need to estimate 2k + 1 parameters—the change points themselves and then parameters of the densities before, between and after them.
That is, we have a set of Mk = {1, . . . , K} candidate models of our data
generating process, each with a different number of parameters. Otherwise
put, the number of parameters is, of itself, a parameter. More formally,
the k th model in Mk has associated parameter vector θk which contains nk
parameters such that θk ∈ Rnk .

Continuing to denote our data vector y, the joint distribution becomes:p(k, θk , y) = p(y|k, θk )p(k, θk )= p(y|k, θk )p(θk |k)p(k).

(2.2)

Section 2.3

14

Since we have a constant of proportionality we can rearrange and reexpress(2.2) into the more familiarp(k, θk |y) ∝ p(k)p(θk |k) p(y|k, θk ) .
| {z } |{z} | {z }posterior
prior(s) likelihood(2.3)

Notice that p(y|k, θk ) is simply the likelihood, while p(θk |k) is the prior forthe parameter vector, given a particular data generating process and p(k)is the prior on the model itself. We wish to generate samples from (2.3).
Setting up a Markov chain to do this may be difficult though, because it isrequired not simply to move around the parameter space for any particularθk , but to also ‘jump’ from space to space (from model to model) dependingon the k in question.

This type of problem is given a general formulation by Green (1995), known
as reversible jump MCMC (RJMCMC), of which standard MCMC algorithms are special cases. Green explicitly discusses a Poisson count change
point problem and we followed his approach for our application (though wevaried the priors somewhat to ensure that our results were robust to suchalternative specifications). Although well known to statisticians, the details
somewhat technical, and readers are guided to Brooks (1997) who gives anaccessible overview for political scientists.

The implementation of RJMCMC, in particular the efficiency of proposals, can be problematic in practice and Hastie (2005) devotes considerable

Section 2.4

15attention to designing a technique to do this. We used his Automix sampler (with a maximum of ten possible change points) for our estimation.
Though the full details are somewhat technical, drawing on Hastie (2005,
202–203), it is instructive to summarize the way that the model of the data
generating process is selected. The first two stages of the sampler producea Normal mixture distribution for every possible value of k. In the third
stage, assuming the Markov chain is currently in state (k, θk ), Automix allocates the parameter vector θk to a component lk of the mixture and uses
it to standardize θk . Then a new model k 0 is proposed, along with a commensurate (new) mixture which has component lk0 . To obtain the new statevector θk0 0 , the standardized vector is transformed using the mean and thecovariance matrix of the mixture component lk0 0 . Automix then accepts the
proposed state (k 0 , θk0 0 ) with some specified acceptance probability. A particularly pleasing feature of this software is that issues such as burn in andthe requisite number of post-burn iterations are handled automatically.

2.4

Results

There are three sets of (posterior) distributions that interest us here:
1. the posterior of k: this enables us to answer the question “how manychange points in the data?” This will have support k = 1, . . . , kmax
where kmax = 10.
2. the posterior of change point positions conditional on some estimatedk. More intuitively, this enables us to answer the question “given a
particular number of change points, when did they occur in the data?”

16

0.0

0.1

0.2

0.3

0.4

0.5

0.6

Section 2.4

1

2

3

4

5

6

7

8

9

10

k

Figure 2.2: Posterior of k: number of change points, Iraq casualty data.
3. the posteriors of the rates for each period, conditional on some estimated k: that is, given the number of change points, and when theyoccurred, we can answer “what were the effects of the change points?”
In Figure 2.2 we display the posterior for k, the number of change points.
The strongest evidence (in the sense of Kass and Raftery (1995)) is for k = 4
and we will explore this possibility exclusively. In Table 2.1 we summarize
the results for k = 4 model in a way that answers questions 2 and 3 above.
The first break, in late January 2004 occurs between incidents that may beof import. The first was the capture and arrest of Saddam at a farmhousenear Tikrit in December 2003. The subsequent months saw both an insurgency uprising lead by rebel Shia cleric Muqtada al-Sadr in Baghdad and the
diffusion of abusive photographs taken at the Abu Graib prison where coali-

Section 2.4

17tion forces were holding Iraqi detainees. The political fallout of the latter
was profound, and criticism of the Bush administration by allied, Arab andother politicians was widespread. This event, arguably, rallied and spurredsectarian hatreds and violence. The break marks a sharp increase in thecasualty rate, doubling from one incident every four days, to one every twodays.

The second break occurs in August of 2004, a little while after the Iraqi
Interim Government assumed power from the Coalition Provisional Authority (in June 2004). This new entity, under the Premiership of Iyad Allawi
was subsequently recognized as the legitimate sovereign government of Iraq
by both the United Nations and the Arab League (an important regional
player). Allawi quickly announced new security measures to tackle insurgency forces and was criticized by some for their draconian nature. As partof this offensive, the Iraqi Interim Government began to censor the criticalreports of media outlet al Jazeera. Included in the highest posterior density
interval for this break is the January 2005 democratic elections for the Iraqi
Transitional Government. This change point saw an increase in violencefrom one incident every two days, to four incidents every five days.

The third break itself, in February 2006, occurs not long after the elections
for the first full term Iraqi government (December 2005) and at around thetime of the protracted negotiations to form a new coalition government.
These talks were deadlocked for some time, lasting from December throughto April of the following year. Jawad al-Maliki, leader of the Islamic Dawa

Section 2.5

18

Party would become Prime Minister after the original candidate Ibrahim
al-Jaafari proved unacceptable to the Sunni and Kurdish representatives inparliament. Once again, violence surged after this point with, on average,
five incidents occurring every three days.

The fourth and final break occurs in September of 2006, a time when the
Iraqi government assumed control of national security for approximately 70
percent of the country. The first specific task of the Iraqi Security Forces
was, and is, to tame insurgency (with coalition logistical and medical support). By now incident rates were approaching three per day. In Figure
2.3 we summarize our findings in a different way: the open circles represent
the median incident rate between the relevant breaks which are demarcatedby the broken lines. For reference, we again draw the jittered incidents
themselves on the plot.

2.5

Discussion

Our study—to our knowledge the first that uses RJMCMC in a political science context—suggests that violence is increasing and that important state-building activities, like democratic elections, are contemporaneouswith upticks in casualties. Apart from this rather grim substantive conclusion, we found that investigating time series on violence to be an interesting
and fruitful exercise. If a Bayesian approach is pursued, then reversible
jump techniques seem most helpful. We hope that our discussion here willencourage others in political science to consider such methods in future.

19

3

Section 2.5

λ2

Sep 2006

1

Feb 2006

Aug 2004

0

Jan 2004

0

500

1000

1500

Date
Figure 2.3: Change in rate of casualty incidents over time: rate on y-axis, actual incidents as jittered points. Dates correspond to breaks found.

Section 2.5

20

As noted above, we do not establish causation in any sense: the events
we noted were simply occurring at around the same time as the breaks inthe time series and it is speculative that they may be of direct importance.
This suggests some interesting avenues for future research: for example, one
possibility is that increasing violence is a product of an increasingly organized insurgency. On this point, notice that the solid line in Figure 2.1
resembles a exponential curve of form F (t) = aert + ² (we are indebted to an
anonymous TAS referee for this observation). Modeling—both theoreticaland statistical—of this apparent pattern would allow us to think about thedevelopment of the conflict in Iraq in a more systematic way. We leave thisfor future research.

Sept 4, 2006
[Aug 23, 2006–Sept 20, 2006]

Feb 22, 2006
[Feb 16, 2006–Mar 24, 2006]

Aug 7, 2004
[Jul 10, 2004–May 4, 2005]

Jan 26, 2004
[Jul 18, 2003–Apr 30, 2004]

Time

2.850

1.660

0.814

0.476

0.283

Rate (λ)

8 incidents every 3 days

Iraqi govt assumes control of counter-insurgency
operations for much of country (Sept 2006)

5 incidents every 3 days

elections for first full term Iraqi government (Dec 2005)

4 incidents every 5 days

Iraqi Interim Government assumes power (Jun 2004)
elections for Iraqi Transitional Govt (Jan 2005)

1 incident every 2 days

Capture of Saddam (Dec 2003)
Abu Graib scandal (Apr 2004)

1 incident every 4 days

Comments

other activities approximately contemporaneous to break.

Table 2.1: Change point median dates [90% HPD] in Iraq casualty data, with rates between breaks. Comments note political andafter break 4

break 4btwn break 3 and 4

break 3btwn break 2 and 3

break 2

btwn break 1 and 2

break 1

before break 1

PeriodSection 2.5
21

22

Chapter 3

Measuring Power in Political
Science: A New Methodwith Application to the
SenatePower is not revealed by striking hard or often, but by striking
true.
—Honoré de Balzac

3.1

Introduction

Scholars have long conceptualized politics as a process of conflict over resources. To determine “who gets what, when and how” (Lasswell, 1936), political scientists have invoked notions of ‘power’ (Dowding, 1996, 1–8). Early
positive political theory made the case that median voters—be they in theelectorate or in parliaments—were particularly decisive and hence ‘powerful’(Black, 1948; Downs, 1987; Riker, 1962). Later theorists—particularly those
associated with the ‘Rochester school’ (Amadae and Bueno de Mesquita,

Section 3.1

231999)—have focused on the role of institutional rules and norms in giving‘players’ advantages over one another in settings like Congress. This literature is, by now, enormous, and includes foundational work by Riker (1982,1986) and others (e.g. Shepsle (1979), Shepsle and Weingast (1987), Krehbiel (1991)). Despite this theoretical work, the empirical investigation andmeasurement of power—even in structured settings like parliaments, committees and courts—has proved difficult and contentious, concentrating ona priori metrics that are removed from the data that we have regarding
agents’ actual actions and decisions (Felsenthal and Machover, 1998, 2004).

This paper is an attempt to address this problem and to bridge a gap between the theoretical treatments of power familiar to positive political theorists and the empirical work of political methodologists. Following Dowding(1996), we suggest an actor-based, data driven approach. Thus, we treat‘power’ as a latent variable or ‘ability’ possessed to varying extents by actors
like Congressmen (Senators in particular). We demonstrate that this trait
is straightforwardly uncovered by studying easily available voting records.
A strength of this approach is that the definition of power is theoreticallyremoved from factors that influence how powerful individuals actually are.
Methodologically, our contribution to the discipline is the introduction of a
new version of the Bradley-Terry (Bradley and Terry, 1952) model for pairwise comparisons, which includes regressors that are thought to covary withactors’ power. We show the utility of both the conceptual and empiricalsuggestions by studying ‘power’ in the 108th United States Senate where
we show the role that ideology, institutional arrangements, geography andSection 3.2

24

personal factors play in determining the power of its members. To wit, inSection 3.2 we discuss the problems with traditional voting index measuresof power; in Section 3.3 we suggest, derive and discuss a new data driven
model; in Section 3.4 we apply the model to the 108th Congress and produce a ‘power list’ of Senators therein; in Section 3.5 we show how the power
can be predicted by its proposed ‘causes,’ and we discuss the impact of, inter alia, party, committee assignment, geographic and personal factors. In
Section 3.6 we conclude and suggest future avenues for research.

3.2

Problems with Traditional Approaches to Measuring Power

Scholars have been interested in measuring the power of actors in structured
settings for over half a century.1 Beginning with Shapley and Shubik’s seminal 1954 contribution, with extensions most famously by Banzhaf (1965),
this branch of positive theory has failed to find widespread acceptance inpolitical science for at least three reasons. First, when voters have different
weights, different indices yield different results for the same data and, generally, the resulting ambiguity cannot be resolved because there is no objective
evidence on the actual distribution of power (Leech, 2002a,b). Second, for
institutions with large numbers of actors, there are computational difficulties with performing the requisite calculations (Leech, 2002a,b). Third, there
1

Social scientists have discussed ‘power’ in various ways for well over a century: at least
since, for example, Marx and Das Kapital. The American Political Science Association felt
it was sufficiently important and unresolved even in 2006 to devote their annual meeting
to “Power Reconsidered.”Section 3.2

25

is much sceptism on the question of whether the indices actually measure‘power’ at all (Barry, 1991; Dowding, 1996; Riker, 1964).

The third criticism is the central issue here. Barry (1991) argues that,since power indices are based on the probability that an actor is pivotal,they measure something akin to ‘luck’ or ‘decisiveness’ rather than power.2
The point is that any definition or measurement of power must incorporate
the notion of getting one’s preference in the face of resistance from otheractors. Moving on from this notion, Dowding (1996) considers pivotality asa resource among many.3 The implication is that one’s power index score issimply one of several independent variables explaining or ‘causing’—but theoretically distinct from—an individual’s ‘power’ (which might be thought ofas a latent variable). Thinking this way enables political scientists to breakaway from some nonsensical statements such that the power of the Chief
Justice in the Supreme Court is ( 19 ), or that the Chairman of the FinanceCommittee in the United States Senate is is equal in power terms to a fresh1
man senator who has never held a committee post ( 100).

In sum: power indices whatever their hue, are not ideal tools for studying
what political scientists conventionally think of as ‘power.’ A new method
is needed which, inter alia,
2

A natural defence is that power indices are intended for a priori analysis; that is,
power indices tell us about the distribution of power before we consider the preferencesof actors or their ability to set an agenda (see Felsenthal and Machover (1998) for acomprehensive review. See also: Lane and Berg (1999) and Holler and Widgren (1999) intheir response to Garrett and Tsebelis (1999)).
3
See also Krehbiel (1998) for a development of ‘pivotality’ with respect to US legislatures.

Section 3.3

26

1. defines power as the capacity to get what an actor wants in the faceof resistance. . .
2. treats power as a (latent) capability. . .
3. estimates an actor’s power as a function of independent variables. . .
4. incorporates commensurate statements of uncertainty and. . .
5. allows for explicit comparison of the effects of different predictors.
In the next section, we show one way to achieve these aims.

3.3

Statistical Theory and Model‘Power,’ as considered here, is a latent variable. Since we cannot measure
it directly, we need a statistical model that takes observable data, estimates
an unobservable trait, and outputs a metric. We made the case above that,in the broadest sense, power is an actor’s ability to obtain his preferredoutcome. In the case of legislatures, which are our concern here, members
require majorities to pass bills and an actor’s power in these settings willturn on his capability to form legislative coalitions for the issues he cares
most about. There is resistance, in the form of actors who vote against thebill, precisely because they stand to lose from its passage. After introducing a little notation, we now provide a way to systematically measure actors—in fact, senators’—capabilities to achieve their preferences in such settings

Let i = 1, . . . , I index the senators and j = 1, . . . , J index the bills on

Section 3.3

27

which they vote. For any particular j, there exists a senator who proposes
the bill, denoted ipj . In any session of the Senate, there will be not morethan J such individuals, since all bills are proposed by someone, but not all
senators propose. The proposer of bill j, ipj , is assumed to seek a coalition
to vote for the bill and we denote that coalition cipj which has |cipj | members (one of whom is the proposer). It is natural to assume that ipj prefersa coalition that is a majority of all senators voting on j, but this is notstrictly required here.4 For now, we suppose that the benefits of passing
j—be they pork, credit, news headlines—will accrue only to ipj and that
other legislators pay some cost in supporting the bill, perhaps because thetotal size of the pork or publicity ‘pie’ available is now decreased for themand their home districts. Else, there is some simple opportunity cost of thetime they take to vote. In attempting to form the coalition, we say thatipj ‘convinces’ a senator to join cipj if she subsequently votes in favor of thebill (and hence in favor of ipj ’s ideal point relative to the status quo). The
nature of the convincing could take many forms: the proposer may attempt
to reason, argue, threaten or bargain with his colleagues explicitly, or elsethe inducement may be implicit. In subsequent votes, say j + 1, the situation may well be reversed with the previous proposer now joining a coalition
ci+1pj+1 backing a senator i + 1 who had been a member of cipj . We say that
two senators ‘interact’ in a particular session of Congress if one proposes abill and the other joins its backing coalition. Notice that for any particularbill j proposed by i, there are cipj − 1 interactions.
4

We assume rather that a proposer is coalition size maximizing: his utility is increasingin |cip |. We could think of this as increasing the probability that j is passed.
jSection 3.3

28

For each senator, the statistical model we discuss below will determine ascore λi such that if we know only that Senator A and Senator B are involved in an interaction, the probability that it is A convincing B (i.e. B isbacking A’s proposal) rather than B convincing A, is the difference of thescores λA − λB :logodds(A convinces B|A and B interact ) = λA − λB .

(3.1)

The interpretation is then straightforward: the greater the value of λi relative to other senators, the more powerful we hold that senator to be.

The derivation of the estimator begins by assuming that there exists a latentand hence unobservable power for each senator denoted αi . For any given interaction (any particular bill) between a pair of senators, let πAB ∈ (0, 1) be
the probability that the interaction involves Senator A convincing Senator
B. Since an interaction must involve either A convincing B or B convincing
A it must be true that πAB + πBA = 1.5 Write the odds that A convinces
B as a function of their latent powers, such that
π AB
π AB
αA
=
=
.
π BA
1 − π AB
αB

(3.2)

5
An objection may be that party or some other factor compels senators to vote one
way or the other, in which case this equality will not hold. By studying personal amendments in Section 3.4 we ameliorate these concerns somewhat but see also our ‘order effect’
specification below.

Section 3.3

29This formulation has the obvious consequence that, if αA > αB , in any given
interaction, πAB > πBA . That is, for any given interaction between A and
B, A is more likely to be forming the coalition (and gaining his preferredoutcome) than B is.

The problem of estimating αi can be approached via a logistic regression.
To see how, first let αi = exp(λi ). Then, some rearrangement yields6
π AB =

exp(λA ).
exp(λA ) + exp(λB )(3.3)

Suppose that A and B interact a total of NAB times. Of these interactions,let nAB —where nAB ≤ NAB — be the number of times that A convinces B.
Then, so long as the NAB interactions are independent of one another, andthe same probability πAB applies to each interaction, nAB has a binomial(NAB , πAB ) distribution. If we are also willing to assume that all the otherinteractions between the other senators are also independent, we have a logit
model that can be estimated via maximum likelihood:

logit[Pr(A convinces B)] = λA − λB .

(3.4)

We can then compare the relative size of λA and λB to see which senator ismore powerful.7
αA
αA
B
From Equation (3.2), it is obvious that π AB (1 + α)= α; substitute α
for 1 and
αB
B
B
note that αi = exp(λi ) to obtain (3.3).
7
Importantly, the model does not require that the matrix of interactions is ‘complete’in the sense that every senator interacts at some point with every other. The model
implicitly assumes transitivity: if Senator A is more powerful than B, and B is more
powerful than C, then A is also more powerful than C.
6

Section 3.330

A concern with this formulation might be that, in fact, party pressuresand thus a priori similar preferences between senators, obviates the need to‘convince’ other legislators in any real sense. Otherwise put, some senators
are disposed to supporting others like them, whatever the proposers power.
We will tackle this issue head-on by estimating a version of our logistic
regression as

logit[Pr(A convinces B)] = λA − λB + δw

(3.5)

where w is an indicator taking the value 1 if the proposer’s party is the sameas that of an individual he convinces and −1 otherwise. Hence, δ will capture the ‘natural advantage’ of proposing to someone in a senator’s party,
and the λi will reflect the ability absent this advantage.

Notice that our method here is very different to that of previous endeavors
to measure power. Unlike index methods, it is an a posteriori in the sensethat we infer ‘power’ after observing actor’s actual decisions—rather than
before. Hence the terms ‘data driven’ and ‘actor based.’ Second, unlike
subjective rankings it is objective and relies on a clearly defined definitionof power. This means, in contrast to ‘panel of expert’ surveys, that ourfindings (below) are exactly replicable by any other political scientist whochooses so to do. Moreover, it is much cheaper and faster to calculate.

This estimator is not new to this paper; it is the Bradley-Terry (BradleySection 3.4

31

and Terry, 1952) pairwise comparison (with equation 3.5 representing an‘order effect’ specification) method in a novel setting. This approach is wellknown and well studied by statisticians working in fields as diverse as sport
team rankings (Agresti, 2002), journal citation patterns (Stigler, 1994) andcompetition for mates in the biological sciences (Stuart-Fox et al., 2006).8This is not the first paper in the discipline to suggest thinking of somepolitical phenomena as pairwise interactions: for example, Groseclose andStewart (1998) study the value of Congressional committee assignments using (dyadic) transfers of representatives.9 The paper is perhaps closest in
spirit (though not in execution) to work by Wawro (2000) who studies legislative entrepreneurship in the House. Designing a novel “entrepreneurshipscales score” based on five observables of behavior, Wawro shows that partybased career prospects are strongly linked to a representative’s records ofactively introducing legislation. Below, we build on this work by presenting
congruent findings—though with a different causal direction: in particular,that party and committee advancement aids senators in their quest to pass(potentially controversial) legislation. Also, like Wawro we provide scholars
with a metric that may be used for further research.
8
Such models can be fitted with many standard statistical packages. For this paper, R(R Development Core Team, 2006) was the environment of choice in conjunction with the
BradleyTerry library (Firth, 2005).
9
See also King (2001) who discusses some possible extensions of standard international
relations models that assume dyadic interactions, and Fowler (2006) who studies the ‘connectedness’ of legislators in both chambers—though not in an explicitly pairwise way.

Section 3.4

3.4

32

Application: 108th Senate

We use data from the 108th Senate, that met between January 2003 andDecember 2004. The universe of cases for the present analysis is the 255
amendments, by 74 different senators, proposed and voted upon during thistime. Amendments are preferred to bills as a whole since they “tend toreflect more specific changes to a bill that are less susceptible to deviations
from the sponsor’s original intent” (Fowler, 2006, 9). That is, they are
more amenable to the notion of personal coalitions formed to achieve an
individual’s goals. Studying the Senate in particular has the further benefit that, subject to some constraints negotiated via Unanimous Consent
Agreements, its members may propose amendments at essentially any time,in any order, without permission from a Committee of the Whole. Thismeans that, unlike the House, the status quo is afforded less protection—an
ongoing concern for those studying power (see Bachrach and Baratz, 1962,
for example). There are 101 actors in the current data set: 74 proposing
senators, 26 non-proposing but voting senators and the President (where
his views on the amendments are known). Of the amendments, 112 were
winning, 139 were losing, and four were tied votes. Recall that the numberof observations is the number of interactions, and is thus well in excess ofthe number of amendments: otherwise put, each amendment corresponds tomultiple interactions and hence multiple observations.

One concern might be that senators vote strategically: against their firstpreferences for an alternative that is a priori less preferred. They might

Section 3.4

33

also propose strategically, to ensure their preferred alternative is selected bymajority rule (Riker, 1982, 1986). However, it is not immediately apparent
that strategic (let alone ‘killer’) amendments are common. Second, strategic voting on amendments, as opposed to bills, should be relatively rare:
we can generally assume that those voting for an amendment want it topass. Third, strategic voting is presumably a product of the organizational
structure—like the timetabling procedures—of the Senate: but this is precisely the sort of consideration that ought to be included in the calculationof our metric. Lastly, votes in the Senate are part of the public record, so
we expect senators to treat their vote seriously and think through its consequences.10

In Table 3.1, we report a selection of the power estimates for this specification. Recall that there is no sense in which the power measure is absolute,and all the coefficients are scaled relative to zero which is assigned to President Bush.

Examining the table, we note that the long serving (since 1979) John Warnerof Virginia (senior senator) is ranked first. Second is Mitch McConnell of
Kentucky (senior senator). In the 108th Senate he was elected as the majority whip by the Republicans and, at the time of writing, was the leader
of Republicans in the Senate. Judd Gregg, the senior (Republican) sena10

Notice that simply proposing (and forming coalitions) for more amendments cannot
in and of itself increase a senator’s power in this model: see Appendix 3.7 and Appendix
3.9.

Section 3.4

34

tor from New Hampshire is at third. Gregg chaired the Health, Education,
Labor and Pensions Committee in the 108th Congress, and became chairof the Budget Committee in the 109th. Robert Byrd, the longest serving
senator in history is the first Democrat on this power list. From West Virginia, Byrd is, at the time of writing, the President Pro Tempore—a role hehad previously held in the 1980s and 1990s. John McCain of Arizona, thenchair of the Commerce committee, is followed by Bill Frist of Tennessee, theSenate Majority leader for the Congress in question. Thad Cochran andCharles Grassley, chairs of the Appropriations and Finance Committees respectively (in the 109th Congress) hold the 7th and 8th spots. Barbara
Boxer, the junior senator from California is the first woman to feature on
the list. At the bottom of the ranking, we see both senators from Hawaii(Daniel Akaka and Daniel Inouye) along with Jim Jeffords (Republican to2001, Independent thereafter).11 Fitting an ‘order effect’ model such thatthe ‘natural advantage’ of proposing to like-minded partisans is controlled
for—as specified in equation 3.5—makes little appreciable difference to thisrank order: see Appendix 3.8 for more details.

Subjective rankings—published in magazines such as Time and by consultancy groups like Knowlegis—reach very similar conclusions to ours. The
Knowlegis power list for 2005 for example, one session after the 108th, places
Thad Cochran at 1 (7 in our ranking), Mitch McConnell at 4 (2), Charles
Grassley at 7 (8), John McCain at 8 (5), Bill Frist at 10 (6), Arlen Spec11

Importantly, the rank ordering is very different to that which might be garnered fromlooking solely at the number of amendments proposed by each senator. See Appendix 3.9
for this rank ordering.

Section 3.4

35

tor at 9 (15) and Orrin Hatch at 2 (19). This similarity to our ranking isremarkable given that (a) they are discussing a different Congress and that(b) our approach is based on a simple, model-based voting metric that is
relatively straightforward to compute. The Knowlegis list, by contrast, isbased upon a vast and expensive survey incorporating what is theoreticallymuch more information.12

As noted above, a pleasing feature of the current estimator is that the power
estimates λi have meaning outside of a simple rank ordering. Recall that
λA − λB is the (anti-logged) probability that, conditioned on two senatorsinteracting, it is A that convinces B to back his amendment rather than theother way round. Consider, for example, John McCain and Russ Feingold(Wisconsin), coauthors of the Bipartisan Campaign Reform Act of 2002.
The probability that, in any interaction between these two, it is McCain
proposing the bill and Feingold backing it isexp(λMcCain )exp(21.58)=≈ 0.85.
exp(λMcCain ) + exp(λFeingold )(exp 21.58) + exp(19.85)
By contrast, the same calculation for McCain and Rick Santorum yields a
probability of (very close to) 1. This is hardly surprising given that the senator from Pennsylvania did not offer an amendment in the 108th Congress,
12

According to their website, “Knowlegis staff carefully researched, sorted and considered thousands of data points to determine . . . power. . . reviewed thousands of media articles, hundreds of bills that passed out of committee . . . over a thousand amendments. . . We collected data on the leadership, committee, and caucus positions of each
Member . . . researched relevant campaign contributions, and considered any characteristic
or action that could contribute to their Sizzle-Fizzle factor. . . there are more than 10,000
data points and variables that were considered in the 2006 Knowlegis Power Rankings”
source:http://www.congress.org/congressorg/power rankings/backgrounder.tt

Section 3.5

36

but it lends some validity to the estimator.

A further factor in favor of the new approach concerns the goodness offit: in contrast to standard methods this is at least meaningful (what is the
goodness of fit for a subjective survey?) and, in fact, respectable, at some
85% of interactions correctly predicted. This figure is within the ballpark ofsimilar statistics for industry standards like NOMINATE (see Poole and Rosenthal, 1997), though given the structure of the underlying statistical model
it is calculated somewhat differently. Appendix 3.10 reports more details.

In sum, Table 3.1 seems to be a reasonable ‘influence list’ both in termsof its underlying statistical model and its actual contents; it tells us little,
however, about the causes of power, a subject to which we now turn.

3.5

Structured Modeling

We usually have theories about what explains the power of different individuals; indeed, sometimes we treat characteristics that are causes of power as
if they were synonymous with power itself: consider, for example, the notionthat ‘the rich are powerful.’ A pleasing feature of the current approach andestimator is that we can separate these notions and explicitly incorporate
individual specific explanatory variables as predictors of power. We estimate

λi =

p
X
r=1

βr xir(3.6)

Section 3.5

37

and thus we predict the power of each senator as a (linear) function of explanatory variables xi1 , xi2 , . . . xip with coefficients β1 , β2 . . . , βp (see Firth(2005) and Springall (1973) for details). Since the approach here is essentially a logistic regression, we can interpret coefficient estimates as positiveor negative, in terms of their marginal effects on power, and we have commensurate standard errors. We can thus make uncertainty statements about
our predictors.

We used institutional and personal information to explain power in the
Senate. Collecting such data is straightforward: the Senate itself, the Government Printing Office and the United States Census Bureau provided all
the relevant variables below in electronic form. We break the findings into
four subsections dealing with ‘Party and Ideology,’ ‘Committees and Agenda
Control,’ ‘Geographic Factors’ and ‘Career Factors.’ The intention here is
not to provide an exhaustive account of power, but to demonstrate thestrength of the approach and possible avenues for future research. Before
describing the results, notice that the nature of ‘power’ now being considered is altered somewhat. In the previous section, power was an ability to
be ascribed to individual senators—it was a ‘personal’ characteristic. Now
though, power is a function of variables and is being treated in an ‘institutional’ sense, separate from the individuals who wield it. Otherwise put, it is
now a maintained assumption that institutional (and other) characteristics
make individuals powerful.13
13

Notice that a potential endogeneity concern—that individuals already endowed withlatent power ipso facto obtain important institutional advantages—is being avoided byconstruction.

Section 3.5

3.5.1

38

Party and Ideology

In contrast to the ‘textbook Congress’ of Fenno (1973), there is increasing
evidence that Congressional voting is ideological and party driven (McCarty,
Poole and Rosenthal, 2006).14 This is more true of the House than the Senate, but nonetheless it suggests some testable hypotheses. As noted above,
senators must assemble majorities to obtain their own preferences. If a majority party exists (the Republicans for the 108th Congress) we might expect
those from the majority party to be more powerful than those from the minority (Democrats). A refinement on this theme is that we expect leaders ofCongressional parties to be especially powerful: the Senate Majority Leader(Bill Frist for the 108th Congress), for example, has the ability to scheduledebate. Other officials—which we refer to as ‘junior leaders’—such as Policy Committee Chairs have powers to design and execute policy ideas. In
Table 3.2 we give the results of the model for a Majority dummy variable
and SeniorLeadership, a dummy that denotes either the senior Senator
for each party, or the whips for each party. We also interact these variables.
The positive and significant effects of being a Republican and being partof the Senate’s senior leadership are evident from Table 3.2. From the interaction term it is evident that being a Republican and a leader adds anextra fillip to one’s power. To be clearer here and recalling equation (3.6),
consider the power of some senator A who is a member the majority party
14

See also Huitt (1957) who discusses cross cutting tensions of ideology and party as it
applies to senators.

Section 3.5

39

and also a senior leader. By Table 3.2,

λA = 0.286 × 1 + 0.205 × 1 + 0.754 × 1 = 1.245.
The power of Senator B who is a rank-and-file Republican is

λB = 0.286 × 1 + 0.205 × 0 + 0.754 × 0 = 0.286.
The probability that, if these two interact, it is the Republican leader proposing and B supporting is
exp(1.245)= 0.72.
exp(1.245) + exp(0.286)
If B is a rank-and-file Democrat, then this probability rises toexp(1.245)= 0.78.
exp(1.245) + exp(0)In Table 3.3 we estimate the same model with AllLeadership, a dummythat includes all senior leaders (as in Leadership) in addition several othercategories: Conference Chairs, Party Committee Chairs, Conference Secretaries and Senatorial Campaign Chairs. This model fits the data as wellas the previous model (note the similar values of the Akaike Information
Criterion (AIC)). Interestingly though, general leadership status does notconfer the power that senior leadership does—notice that the coefficients for
AllLeadership and the interaction are now smaller than the commensurate
ones in Table 3.2.

Section 3.5

40

To demonstrate how American politics has become increasingly polarized,
McCarty, Poole and Rosenthal show that legislators’ ideological positions,and the median positions for parties, have become increasingly disparate
along a liberal-conservative dimension. As politics becomes more polarized,
we might have several conflicting expectations. On the one hand, senators
who occupy the center ground—are close to the legislative median— mayfind it easier to broker deals with others to their left and right, and hence
will be more powerful. On the other hand, if voting is strongly party based,
then perhaps the most ideologically extreme in each party will be able tomotivate their ‘core’ supporters into backing their preferred positions. This
will be a fortiori true for relatively radical senators from the majority party.
At base, this is one version of the ‘party versus floor median’ debate welldiscussed in literature elsewhere (Cox and McCubbins, 1993; Rohde, 1991,
cf. Krehbiel, 1998).

We can measure ideological extremism via senators’ NOMINATE scores (Pooleand Rosenthal, 1997).15 In particular, the score for the senator in one dimension is treated as their ‘conservatism’ (we label this ‘Conservatism’ andthe higher the score, the more conservative and less liberal they are). ‘Extremism’ is a different concept and can be ascertained by taking the absolutevalue of this score (Extremism): a very high score now implies a senator very
far to the left or to the right, while a low score reflects a senator in the centerof the chamber. We add Distance from Median that records the absolute
15

In particular, DW-NOMINATE scores, available from http://voteview.com/dwnomin.htm

Section 3.5

41value of senators’ distances from their party median in terms of NOMINATE
scores. In Table 3.4 we report the effects of conservatism (controlling for
majority party membership and distance from the median) and in Table 3.5
we report the effects of extremism.

The lessons from Tables 3.4and 3.5 are interesting. Once we control for
majority party membership, conservatism and distance from the medianhave a negative impact on power. Consider, for example, Senator A who
is a moderate Republican with a NOMINATE score of 0.2 (the scale runs -1
through 1). By contrast Senator B is deeply conservative with a NOMINATE
score of 0.8. Their powers are

λA = −0.591 × 0.2 + 0.844 × 1 + × − 0.702 × |0.2 − 0.441| = 0.557
and

λB = −0.591 × 0.8 + 0.844 × 1 + −0.702 × |0.8 − 0.441| = 0.119.
In any interaction, the probability that A proposes some coalition, while
B joins it, is around 0.61. To see more of the interplay between ideology
and power, consider Figure 3.1: here, we plot the Senator’s power estimatesagainst their NOMINATE scores, and then impose a solid loess curve. The
top graphic displays the plot for all senators, and the one below is thesame graphic for senators who proposed amendments in the 108th Senate.

Section 3.5

42

Notice that, in the top panel of Figure 3.1, the extremes of the Senate are
rewarded in power terms: the loess dips slightly as it crosses the middle of theideological spectrum. But, interestingly, in the lower panel (which represents
the most powerful senators), we see two things: first, majority party status
boosts one’s power—notice that the loess rises as it moves right. Within
the majority party (the Republicans) though, the most powerful senators
are not drawn from the far right wing: notice the high λi recorded for thosewith a NOMINATE score around 0.4. In Table 3.5, the positive coefficienton Extremism suggests once again that senators towards the middle of thechamber lack power. Interestingly, it is also evident while being in the
majority party is beneficial, it does not pay to be a right wing Republican:
rather, the powerful are from the median of the party. Figure 3.2 confirms
this idea: in the first panel, the power ratings for all senators are shown,and in the bottom panel, the analysis is restricted to the proposers only.
Notice that the bulk of the mass occurs around 0.4 for both parties, withthe most powerful senators of both parties occurring just above and below
this scaling. Otherwise put, it does not pay to be the median of the chamber,but it does pay to be the median of your party.

3.5.2

Committee and Agenda Control

Positive political theorists, especially those of the ‘Rochester school’ (Amadaeand Bueno de Mesquita, 1999), have suggested that it is the organization ofCongress in terms of its committees that confers power on actors. Indeed,
in a series of articles Shepsle and Weingast (1987) and Krehbiel (1991) discussed precisely why committees are powerful. Of course, not all commit-

5

10 15 20430Power (λ i)Section 3.5

−0.5

0.0

0.5

18 19 20 21 22Power (λ i)NOMINATE score

−0.5

0.0

0.5

NOMINATE score

Figure 3.1: NOMINATE score versus power (λi ); open squares are Republicans, closed
circles are Democrats; solid line is loess. Top figure is for all senators; bottom figure isfor all proposing senators.

5

10 15 2044

0Power (λ i)Section 3.5

0.0

0.2

0.4

0.6

0.8

0.6

0.8

18 19 20 21 22Power (λ i)Extremism

0.2

0.4
Extremism

Figure 3.2: Extremism versus power (λi ); open squares are Republicans, closed circles
are Democrats; solid line is loess. Top figure is for all senators; bottom figure is for all
proposing senators.

Section 3.5

45

tees are created equal, and they attract different memberships with different
motivations (Fenno, 1973). Nonetheless, there is general agreement that financial committee positions—those that have ‘power of the purse’ tend tobe the most coveted spots for ambitious senators. This is not least becausesuch positions enable members to channel substantial pork to their home
states. For example, Charles Grassley, Chairman of the Senate’s Appropriations Committee, used the 2004 appropriations bill to steer some $50m to
Iowa’s visionary complex of biomes, Earthpark (The Economist, 2006).

Committees themselves are, of course, hierarchical structures. As mentioned above, Grassley was the Chair of Appropriations, not simply a member. Chairs have several de jure responsibilities and rights pertaining totimetabling, hearings and the selection of bills to be considered. Other thanthe Chair, who must be a member of the majority party, committees areconstructed of minority and majority party members. Above, we discussed
reasons why majority party senators might be powerful, and presumably
this goes mutandis mutatis for majority party committee members.

Since space is limited, we only discuss some of the committees and theirmembers here. In particular, in Table 3.6 we report regression coefficientsfor the Appropriations, Armed Services, Commerce, Finance and Rules andAdministration committee all denoted with these names. We also include amajority party interaction term, and a term for Chairs (of any committee)
denoted Chair. Where Table (3.6) reports positive coefficients, the Committee assignment increases the power of a senator relative to one not onSection 3.5

46

the that committee. Majority party members get an extra boost in poweron the Armed Services, Appropriations and Finance committees, but noton the Rules and Administration or Commerce committees. Caution is required in interpreting the findings for some committees, such as Rules andAdministration, which are notoriously weak and generally involved in lessinteresting work. Indeed, senators may accept a role on such committees
as the ‘price’ for serving on more powerful committees elsewhere. Hence,
the magnitude of the coefficient maybe somewhat misleading: senators are
powerful because of their ‘good’ committee assignments which are correlatedwith weak assignments, not caused by them.16

From the perspective of a senator, the most powerful position is a role on the
Finance committee (notice that the addition of the Finance coefficient andthat for Majority×Finance is a larger number than for any other committee). Perhaps unsurprisingly, Chairs are more powerful than rank-and-filemembers; in Figure 3.3 we compare chairs to Democrats and non-chairing
Republicans who propose amendments. Notice that the median power ofchairs clearly exceeds that of the other groups and, in fact, their entire
inter-quartile range is more powerful than that of Democrats.

3.5.3

Geographic Factors

One of the results of the Constitutional Convention of 1787 was the socalled ‘Connecticut Compromise.’ Dealing with the creation of the UnitedStates’ legislative bodies, the Compromise proposed two houses: a lower
16

We are grateful to Antoine Yoshinaka for this suggestion.

47

20.5
18.5

19.0

19.5

20.0

Power

21.0

21.5

22.0

Section 3.5

Dems

Republicans

ChairsFigure 3.3: Boxplot showing relative power of committee chairs, non-chairing Republicans and Democrats who propose amendments.

Section 3.5

48

house elected in proportion to population, and a senate, in which each state
would have two representatives, regardless of its population. The fear oflarge state tyranny, though admonished as unlikely and illogical by the likes
of Madison and Hamilton, motivated small states—like Delaware, Maryland,
New Jersey and Connecticut—to seek institutional protection.

Of course, as argued with respect to the power indices approach above, thefact that voting resources are de jure equal across states should not imply
that all senators are equally powerful. One way to examine this notion moreformally is to use the present model with geographic factors as explanatory
variables. We do not have particularly strong priors about the effect of geographic factors on a senator’s power, but some vague ideas might be as
follows.

Historically, representatives from the South were very powerful actors. Up
until the 1960s, Southern states were solidly Democratic, and possibly dissenting voices—from blacks and poor whites—were excluded from voting(Key, 1949). As a result, Southern senators faced few challenges in theirhome states and could use the committee seniority system—that rewarded
long service irrespective of party affiliation—to obtain powerful chairmanships. In the ‘post-reform’ period, this systematic concentration of power inSouthern hands was much reduced Rohde (1991). Moreover, the South isno longer under hegemonic Democratic control as demonstrated by George
Bush with victory in every Southern state in his 2004 Presidential reelection. Nonetheless, we might still expect, for historical or other reasons, that

Section 3.5

49

senators from the South—Texas, Louisiana, Arkansas, Mississippi, Alabama,
Florida, Georgia, North Carolina, South Carolina, Virginia and Tennessee—
wield disproportionate power. We use a South dummy taking the value of
1 for senators from these states.

The expected effect of a state’s wealth on a senator’s power is arguably
ambiguous. On the one hand, senators from rich states may be able to procure greater ‘home-grown’ funding for their campaigns and causes, rendering
them more influential. On the other hand, senators from poorer places may
have more sway in Washington because they can point to underfunded public services and crumbling infrastructures in their home states as evidence
that they have a more urgent claim to the nation’s resources. Combinedwith suitably deployed rhetorical skill, we could imagine poverty may boost
a state’s representative’s powers. We measure wealth use the Census Bureau’s Median Household Income statistics for each state in dollars (Median
Income).

We have similarly vague priors viz the effect of population density on power.
On the one hand, small, primarily urban, densely populated states have senators who literally represent ‘more’ citizens (we measure this with Census
Bureau’s population estimate for 2003, Population), which may aid rhetorical appeals. On the other, sparsely inhabited, primarily agricultural states
may increase the power of senators who represent them, in part because,for historical reasons, farm-based financial aid—an important componentof rural states’ federal funding—is easier to deliver than other types of sup-Section 3.5

50

port. We use the land area of the states and denote this variable Land Area.

The significant, negative coefficients in Table 3.7 suggest that poorer,smaller, more densely populated, non-Southern states will yield senatorswith more power. Of course, this might not correspond to any particularstate. To help interpretation, in Figure 3.4, we color a map of the contiguous United States according to the predicted λi that a senator from thatstate based on the coefficients of Table 3.7. Based only on geographicalfactors, the most powerful state—in terms of its Senators—is California andit is shaded lightest. New York and West Virginia are similarly light colored. ‘Weaker’ states are dark colored. There are no particular regional
patterns discernable from Figure 3.4, except perhaps a band of states fromNew York west through Missouri which appear disproportionately light (andthus powerful) relative to their neighbors.

3.5.4

Career Factors

For most politicians, a position in the Senate is a career ambition (Brace,
1984; Rohde, 1979). But, once attained, senators have strong incentives
to seek reelection (Mayhew, 1974). As implied above, this is in part because long service is linked to promotion in terms of committee and otherassignments. Here we calculated the years of service since first entering the
Senate through 2004 and denoted this variable Service. Though not formally associated with greater rights or responsibilities, longevity of service
for a particular state makes a senator the ‘senior’ representative of his constituency. We use a Senior dummy to check for any extra power effect that

Section 3.5

51

Figure 3.4: Map of contiguous United States with shading proportional to ‘power’ given
by coefficients in Table 3.7: lighter states are associated with more powerful senators.

Section 3.5

52such status confers.

From a career perspective, sociologists have long argued that being malestrengthens advantages one in the work place, and this is no less true in politics. Consider, for example, the comment and excitement drawn by Nancy
Pelosi’s ascension to the Speakership of the House in 2006.17 For this reason,
we add a dummy variable for Male here.

The coefficients for Service and Senior status are much as we might
anticipate in Table 3.8: longer time served in the Senate, as well as seniority makes for a more powerful senator. The coefficient for sex though isperhaps not as expected. Being male is actually associated with a lower
power than being a female. In Figure 3.5 we report a boxplot for males andfemales, in terms of their power. Interestingly, though the median powerof the sexes is approximately equivalent, the distributions are very different: while male senators are counted among the most powerful, they arealso some of the weaker members of the Senate. Females, by contrast, areheavily concentrated in the upper power ranges.

3.5.5

Summary of Findings

In summary, a senator is more powerful if the senator is:- a member of the majority party, and has a leadership position within
17
Pelosi herself seemed well aware of her exceptionism and, in her acceptance speech
noted that “[i]t is an historic moment for the Congress, and an historic moment for the
women of this country. . . For our daughters and granddaughters, today we have broken themarble ceiling. For our daughters and our granddaughters, the sky is the limit, anythingis possible for them.”

53

10
0

5

Power

15

20

Section 3.5

FemaleMale

Figure 3.5: Boxplot showing relative power of male and female senators.

Section 3.6

54

the party;- from the center of the ideological distribution of her party;- a majority party member of the Finance and Appropriations committees;- chair of a committee;- is from a relatively poor, densely populated non-Southern state;- is female, long serving and is the Senior Senator from her state.

3.6

Discussion

This chapter proposed a new way to measure power in structured settings.
Rather than relying on a priori metrics that arguably measure something
akin to ‘luck’ or ‘pivotality’ rather than power, we suggested an approachthat assumes the powerful have a greater capability to form coalitions inorder to pass bills that they care about. This method is straightforward to
implement, and allows the separation of ‘power’ from its ‘causes’ in a standard generalized linear model framework. Thus, we can talk of predictedprobabilities and make statements of uncertainty regarding the ‘effects’ of
certain variables. We applied the statistical model to the 108th Senate, using (personal) amendments as the bills around which Senators attempt toform coalitions and we found that inter alia majority party membership,
moderation within a party, chairing of committees, long service records andseniority all make for more powerful senators. These findings in and of

Section 3.6

55

themselves are perhaps not shocking, but they do demonstrate the strengthand flexibility of the approach, along with establishing some validity of themethod.

In terms of future avenues of research, there are obvious ‘cross section’ and‘time series’ extensions to this work. Here, we choose to study the Senate:
its 100 members are a manageable number of observations for which to ascertain biographical and other data. There is no reason why, with moretime, political scientists could not execute a similar model for the House ofRepresentatives. Temporally, we studied one Congress and thus the results
here are something of a ‘snapshot.’ Studying actors’ power over time may
allow a more complete picture: certainly we could imagine that changing
rules in Congress, along with the prevailing political climate, might alter
the power of say, chairs and party leaders.

Taking the model outside of the United States Congress is a possibility
too, though any such extension requires knowledge of actors’ preferences ininteractions. The United Kingdom House of Commons, for example, may
provide another test ground for the model via private members bills. Unfortunately, due to strong party whipping and strategic voting, deciding
actors’ preference in this circumstance is not always straightforward. Thereis a similar caveat for the US Supreme Court, though in that case it is simply unclear who ‘leads’ a coalition. Outside of American and Comparative
politics, International Relations with its concentration on specifically dyadic
interactions may be amenable to such an approach. We leave this for futureSection 3.6
work.

56

Section 3.6

57

Senator
1
2
3
4
5
6
7
8
9
10
..
.
22
23
..
.
29
..
.
33
..
.
45
..
.
54
57
..
.
93
..
.
99
100
101

Warner, John
McConnell, Mitch
Gregg, JuddByrd, Robert
McCain, John
Frist, Bill
Cochran, Thad
Grassley, Charles
Boxer, Barbara
Graham, Lindsey..
.
Kennedy, Edward
Daschle, Tom..
.
Kerry, John..
.
Lott, Trent..
.
Clinton, Hillary..
.
Feingold, Russ
Lieberman, Joe..
.
Santorum, Rick..
.
Inouye, Daniel
Jeffords, Jim
Akaka, DanielPower (λi )
22.10
22.09
21.84
21.63
21.58
21.57
21.44
21.44
21.39
21.36
..
.
20.79
20.79
..
.
20.58
..
.
20.48
..
.
20.13
..
.
19.85
19.74
..
.
-0.34
..
.
-0.73
-0.74
-0.82

Table 3.1: Baseline results for model of power for US Senators in the 108th Senate.

Section 3.6

58

Estimate

Std. Error

Majority

0.286∗∗∗

0.034

SeniorLeadership

0.205∗∗∗

0.072

Majority×SeniorLeadership

0.754∗∗∗

0.104

Table 3.2: Effect of majority party and senior leadership status on power in the Senate.
Asterisked coefficients (***) imply p < 0.01. AIC: 11052.

Estimate

Std. Error

Majority

0.304∗∗∗

0.035

AllLeadership

0.118∗∗

0.047

Majority×AllLeadership

0.373∗∗∗

0.073

Table 3.3: Effect of majority party membership and any leadership status on power in
the Senate. Asterisked coefficients imply p < 0.01 (***), p < 0.05 (**). AIC: 11152.

Conservatism
Majority
Distance from Median

Estimate

Std. Error−0.591∗∗∗0.080

0.844∗∗∗

0.073−0.722∗∗∗0.122

Table 3.4: Effect of conservatism, distance from median and majority status on powerin the Senate. Asterisked coefficients imply p < 0.01 (***), p < 0.05 (**). AIC: 11169.

Section 3.6

59

Estimate

Std. Error

Extremism

1.14∗∗∗

0.107

Majority

0.783∗∗∗

0.075

Majority×Extremism−0.9636∗∗∗

0.168

Distance from Median−0.702∗∗∗

0.123

Table 3.5: Effect of extremism, distance from median and majority status on power in
the Senate. Asterisked coefficients imply p < 0.01 (***), p < 0.05 (**). AIC: 11136.

Estimate

Std. Error

0.596∗∗∗

0.042−1.055∗∗∗0.089

Appropriations
Majority×Appropriations

0.245∗∗∗
1.376∗∗∗

0.040
0.100

Armed Services
Majority×Armed Services

0.189∗∗∗
1.353∗∗∗

0.042
0.102

Commerce
Majority×Commerce

0.264∗∗∗−0.737∗∗∗

0.040
0.068

Finance
Majority×Finance0.482∗∗∗
1.445∗∗∗

0.046
0.104

Rules Admin
Majority×Rules Admin

0.440∗∗∗
0.312∗∗∗

0.039
0.068

Chair
Majority

Table 3.6: Effect of committee membership, majority party membership and chair statuson power in the Senate. Asterisked coefficients imply p < 0.01 (***), p < 0.05 (**). AIC:
9434.9.

Section 3.6

60

Estimate

Std. Error

Median Income−2.199 × 10−5South−0.256∗∗∗

Land Area−1.668 × 10−6

Population

2.488 × 10−8∗∗∗2.003 × 10−6
3.390 × 10−2

∗∗∗

∗∗∗

2.135 × 10−7
1.723 × 10−9

Table 3.7: Effect of incomes, southern state representation, land area (state size) andstate population on senator’s power. Asterisked coefficients imply p < 0.01 (***), p < 0.05(**). AIC: 10954.

Estimate

Std. Error

Service0.029∗∗∗

0.001

Senior0.543∗∗∗

0.029

Male

−0.521∗∗∗

0.035

Table 3.8: Effect of incomes, southern state representation, land area (state size) andstate population on senator’s power. Asterisked coefficients imply p < 0.01 (***), p < 0.05(**). AIC: 10205.

61

Appendix to Chapter 3
3.7

The “Busy” Senator Problem

The concern is that a senator could increase his influence score by simply
proposing more amendments. That is, by being ‘busy’ in a legislative sense,
he would appear more powerful. Here we show this to be untrue.

First, consider three proposing senators A, B and C. Suppose that A andB decide to somehow combine their efforts such that only one of them willpropose and form coalitions for all amendments jointly that they formerly
worked on separately. Whether A will have B do all the proposing and coalition forming, or whether B will delegate his work to A, write the senator
who does the proposing and forming as SAB .

Clearly, SAB is busier—in that he now proposes more amendments—than either A or B. Importantly, though, the probability that any randomly drawninteraction involving SAB and C has C convincing SAB , will be simply theweighted average of the former probability that C convinces A and C con-

Section 3.8

62

vinces B: there is no fillip from proposing more amendments. Hence, ‘business’ alone cannot yield a higher power rating. To show this, let “CconSAB ”
be the event that C convinces SAB . The probabilities for the constituent
senators are:
A

Pr(AconC)
Pr(CconA)

B

Pr(BconC).
Pr(CconB)

Pr =
and
Pr =

The probability for the joint, ‘busy’ senator is:
SAB

Pr

=
=
=

Pr(SAB conC)
Pr(CconSAB )Pr(AconC) + Pr(BconC)
Pr(CconSAB )conC)
Pr(B conC)
Pr(CconA) Pr(A
Pr(C conA) + Pr(CconB) Pr(C conB)
Pr(CconSAB )A

B= γ Pr +(1 − γ) Pr .
Pr(C conA)
where γ = Pr(CconSAB ) .

Thus, business cannot itself increase a senator’s influence.

3.8

Logit Model with Order EffectWe estimate the ‘order effect’ model as described in equation 3.5 and present
the results in Table 3.9. Inspection suggests that the rank order is closely
similar to that of the model without an order effect. In fact, performing aSection 3.10

63

Spearman rank correlation test between the sorted lists yields a ρ = 0.144
with a p-value (on the null hypothesis that ρ ≤ 0) of 0.08. We estimate
δ—the advantage of proposing to someone in one’s own party—at 0.52 (andis significant at the 1% level). That is, there is a ‘home advantage’, but it
does not disturb our earlier findings greatly when accounted for.

3.9

Amendment Proposers

Table 3.10 gives the rank ordering of senators in accordance with the numberof amendments they proposed. Clearly, simply proposing more amendments
does not make you more powerful: for example, Grassley proposes only 3
times yet is ranked in the top 10. For completeness, Figure 3.6 displays thefrequency information from Table 3.10.

3.10

Goodness-of-Fit

Recall that the method calculates a (maximum likelihood) value of λA andλB for all senator pairs who interact. Above, we defined an ‘interaction’ as
an amendment in which either A proposed and B supported or B proposed
and A supported. Then, as in 3.3, the λi have the interpretation that
Pr(A convinces B|A and B interact) =exp(λA ).
exp(λA ) + exp(λB )(3.7)

The conditioning of the probability in (3.3) implies that we need not consider the counterfactual of non-proposing senators as proposers. Hence, thematrix of votes to be predicted denoted Yact , is of dimension I p × I where

64

10
5
0

Frequency

15

20

Section 3.10

1

2

3

4

5

6

7

8

9

10

Number of Amendments

Figure 3.6: Amendment numbers: distribution.

15

Section 3.10

65

|I p | is the number of proposing senators (74 for this case) and |I| is thenumber of senators in total (here, 101, since we included President Bushto aid interpretation). Yact then, is the actual interactions, and is of thefollowing form:
Akaka Alexander Allard . . .
Allard

1

1

0

...

Baucus

3

0

0

...

Bayh

1

0

0

...

Biden

4

2

1

...

Bingamen
..
.

9
..
.

4
..
.

2
..
.

...
..
.

where the proposers lie to the left and all the voting senators form thecolumns. So, for example, Joe Biden proposed and was backed four times
by Daniel Akaka, twice by Lamar Alexander and once by Wayne Allard.
Notice also that senators voting for their own amendments are not, in andof themselves, counted as backers.

For any particular cell of Yact , there exists an associated total numberof possible interactions (in either direction) for the senators. For example,
Joe Biden and Wayne Allard interacted a total of 3 times: once when Allard
was the proposer and Biden backed him, twice when Biden was the proposerand Allard backed him. This matrix has symmetric form when proposers
as compared to voting senators who were also proposers, but not otherwise.

Section 3.10

66

We denote this matrix Yposs and a similar segment to that above appears
as:Akaka Alexander Allard . . .
Allard

1

1

0

...

Baucus

3

0

1

...

Bayh

1

0

0

...

Biden

4

2

2

...

Bingamen
..
.

9
..
.

4
..
.

3
..
.

...
..
.

From the estimates of Table 3.1 via Equation (3.3), we can obtain predictedprobabilities of ‘convincing’ for any particular pair of senators A and B. For
example, consider the following subset of the matrix:
Akaka Alexander Allard . . .
Allard

1.00

1.00

0.50

...

Baucus

1.00

1.00

0.48

...

Bayh

1.00

1.00

0.21

...

Biden

1.00

1.00

0.52

...

Bingamen
..
.

1.00
..
.

1.00
..
.

0.74
..
.

...
..
.

where the incidence of 1 implies that the proposer on the left is the one
convincing the voter in the column to back the amendment (rather than theother way round) essentially with certainty. We denote this matrix Opred .
Since we have direct estimates of the underlying latent abilities, we do notdichotomize this matrix to zeros and ones as may be seen in standard logis-

Section 3.10

67

tic (and probit) regression predicted probability contexts.

The expected votes matrix is the element-by-element multiplication Yposs ×
Opred yielding another matrix of dimensions I p × I. Note that every element of Yposs × Opred is non-zero valued. Subtracting this matrix fromYact yields a matrix of both positive (the model over predicts) and negative
entries (the model under predicts). The absolute sum of these columns yields
the total number of misclassifications which is (when rounded) 2062 of some
13,869 total interactions. Hence, the percentage of interactions correctly2062
predicted is 1 − 13,869= 0.85.

Section 3.10

68

Senator
1
2
3
4
5
6
7
8
9
10
11
..
.
21
..
.
25
..
.
30
..
.
33
..
.
46
..
.
52
53
..
.
94
..
.
98
99
100
101

McConnell, Mitch
Warner, John
Gregg, Judd
Frist, Bill
McCain, John
Cochran, Thad
Byrd, Robert
Graham, Lindsey
Grassley, Charles
Nickels, Don
Boxer, Barbara..
.
Kennedy, Edward..
.
Daschle, Tom..
.
Kerry, John..
.
Lott, Trent..
.
Clinton, Hillary..
.
Feingold, Russ
Lieberman, Joe..
.
Santorum, Rick..
.
Akaka, Daniel
Jeffords, Jim
Inouye, Daniel
Johnson, Tim

Power (λi )
19.63
19.59
19.36
19.10
19.09
18.98
18.97
18.97
18.96
18.87
18.84
..
.
18.30
..
.
18.19
..
.
18.10
..
.
17.97
..
.
17.49
..
.
17.30
17.25
..
.
-0.89
..
.
-1.20
-1.34
-1.51
-1.53

Table 3.9: Baseline results for model of power for US Senators in the 108th Senate,
logit with ‘order effect’ (party advantage) estimated.

Byrd
15
McCain8
Leahy
5
Hutchison
4
Conrad3
Kerry
3
Bunning2
Lott2
Brownback
1
Hagel
1
Smith
1

Bingaman
10
Daschle7
McConnell
5
Levin
4
Corzine3
Kyl3
Dayton2
Murray2Campbell1
Kohl
1
Stabenow
1

Dodd
9
Dorgan6
Breaux4
Reed
4
Feingold3
Nickles3
Hollings
2
Rockefeller
2Collins1
Nelson (FL)
1
Wyden
1

Feinstein
9
Harkin6
Cantwell4Specter
4
Graham (FL)3
Schumer3
Inhofe2Snowe2
DeWine1
Roberts
1

Lautenberg
9Durbin5
Clinton4
Baucus3
Graham (SC)3
Thomas3
Landrieu
2
Allard1
Ensign1
Sarbanes
1

Table 3.10: Number of amendments per senator.

Boxer
10
Warner7
Biden
4
Mikulski4
Edwards3
Lincoln
3
Hatch
2
Reid
2
Carper1
Murkowski
1
Voinovich
1

Kennedy
8
Gregg
5
Frist
4
Cochran
3
Grassley3
Bond2
Lieberman
2
Bayh
1
Enzi
1
Sessions
1

Section 3.10
69

70

Chapter 4

Rebels with a Cause?
Legislative Activity and the
Personal Vote in Britain,
1997–2005
The first duty of a member of Parliament is to do what hethinks in his faithful and disinterested judgement is right andnecessary for the honour and safety of Great Britain. His second
duty is to his constituents, of whom he is the representative but
not the delegate. Burke’s famous declaration on this subject iswell known. It is only in the third place that his duty to party
organization or programme takes rank.
—Sir Winston Churchill, 1954

4.1

Introduction

At least since the time of Burke and his Speech to the Electors of Bristol(1774/1975), scholars of politics have debated the proper ‘model’ for elected
representation. While much of the discussion has been normative in nature, country-comparativists are able to distinguish quite different practices

Section 4.1

71

across polities. At one extreme of these stylized facts, House members in the
United States are perhaps closest to Burke’s ‘delegates’: primarily concernedwith delivering (federal spending) ‘pork’ to their constituents and, indeed,
consciously acting in line with the general ideological preferences of theirdistrict (e.g. Fiorina, 1974; Mayhew, 1974). The nation, or even the party
with which they identify, is thought to exert a relatively weak pull on theirdecision calculus (Jacobson, 1989). By contrast, akin to a ‘trustee’ conception, members of parliament in the United Kingdom House of Commons areelected on a party ticket, are thought to have a negligible ‘personal’ vote,and make policy according to some notion of ‘national interest’, broadly
construed. In particular, members of the governing party generally support
the executive’s bills, regardless of any constituency or personal concern.

In that they hold representatives to account, elections are identical mechanisms in all systems (Riker, 1982). But contingent on the model of representation in place, the policy-making behavior for which citizens will reward or
punish their legislators should vary markedly. Analysts of American politics
have devoted considerable attention to this issue and there is a voluminous
theoretical and empirical literature that investigates the legislative determinants of individual office-holders’ electoral performances (e.g. Canes-Wrone,
Brady and Cogan, 2002). Congruent with the ‘delegate’ assumption, thefindings generally suggest that more ‘maverick’ incumbents—those who votewith their party least often—tend to do better come polling time.

Despite its Burkean vintage though, equivalent research for the United King-

Section 4.1

72

dom House of Commons—or any ‘Westminster’ system—has been much lessdeveloped. That the study of British politics has generally neglected the fundamental link between constituents, their expectations of behavior and theirelected agents is unfortunate, but unsurprising. It is unfortunate because
ignoring Britain (and Westminster systems more generally) has resulted in
an asymmetrical development of political science understanding of representation and accountability. While we know much about the United States
where parties are weak, we can say little concerning polities where parties
and party voting are strong forces.

The lacuna is unsurprising: with some important exceptions (Kam, 2007;
Pattie, Fieldhouse and Johnson, 1994), scholars have assumed away the potential importance of legislative activity, and looked elsewhere for personalvote effects (see, for example, Cain, Ferejohn and Fiorina, 1987; Norton andWood, 1993). In any case, with over a thousand votes to consider in a given
parliamentary session, and no convenient ideal point summary available (seeSpirling and McLean, 2007), scholars have not been able to conduct systematic studies that analyze MP legislative behavior as a whole—that is, every
decision on every vote. It has not helped that public opinion studies point
to seemingly inconsistent preferences and contradictory expectations, withcitizens claiming that both party unity and ‘independent-mindedness’ matter (Johnson and Rosenblatt, 2007).

We seek to rectify this theoretical and empirical deficit in the current chapter: using a new data set that incorporates some 2200 parliamentary votes

Section 4.2

73

cast by around 200 backbench Labour MPs between 1997 and 2005, withcommensurate constituency controls, we explain ballot box performance asa function of personal voting decisions in the House of Commons. We show
that, all else equal, MPs that disrupt important government business arepunished by their constituency voters while those that show freedom ofthought and action on less important matters tend to be rewarded for their
independence. This effect is worth up to 2.5 percentage points at election
time. In pursuing our study we suggest a novel theoretical model of partisan voter behavior in Britain and new non-parametric, statistical methods
as yet unseen in political science. Our findings extend the growing literaturethat emphasizes the importance of seeing MPs as individual and accountable representatives, at least partly responsible for their own electoral fates.

We proceed as follows: in Section 4.2 we give the substantive backgroundfor our study, and report on previous efforts in the literature. In Section
4.3, we give a simple formal expression describing the actions of (partisan,
Labour) voters in response to different actions on various roll call types at
Westminster. In Section 4.4 we describe and use a “random forest” classification technique that allows us to include essentially every vote as a possible
independent variable, along with suitable controls, for predicting subsequent
electoral performance. In Section 4.5 we report results consistent with ourmodel, and show that several bills have a small but significant effect on
performance with signs as predicted. Section 4.6 concludes.

Section 4.2

4.2

74

Members, Constituents and the Personal Vote
in Britain

Party voting by the electorate, either based on national Cabinet—i.e. executive—
policy positions and performance (see Budge, 1999; Crewe, 1983; Norris,
2001) or on cruder partisan loyalties (see Butler and Stokes, 1974) is thought
to be the norm for Westminster systems like Britain. Congruent with thisprincipal, almost all legislative business is directly controlled by the executive, and party pressure or ‘whipping’ is commonly used by the government
to herd its ‘backbench’ MPs into supporting the Cabinet’s programmatic
agenda when required (e.g. Cowley, 2002, 3–7).1 By conventional wisdom
then, since voters don’t (and have no reason to) care about parliamentary behavior, there is little an individual backbencher has to offer her constituentsaside of her party label at election time.

Interestingly though, when the public was recently asked to name the qualities that an MP ought to possess, while two-fifths claim that a representative should “be loyal” to her party, some 60 percent also claim that sheshould “be independent-minded” (Johnson and Rosenblatt, 2007, 165–167).
In Figure 4.1 we show the changing nature of public opinion on this subject:
clearly freedom of thought seems increasingly important, while loyalty is
falling away as a requirement. This is a fortiori true for the period in which
Labour has held large majorities of seats in government i.e. post-1997.
1

Whipping typically includes offers or threats related to ministerial promotion: see
Kam (2006) for a discussion of the Canadian case.

Section 4.2

75

50
45
40

Important Characteristic (%)

55’Independent−minded’’Loyal to the party’

1985

1990

1995

2000

2005

Year

Figure 4.1: Percentage of respondents naming different qualities as “important for an
MP to have”: solid line is percentage naming ‘independent minded’, broken line is percentage naming ‘loyal to party’. Multiple choice, more than one choice permissible; survey
dates are 1983, 1994, 1996, 2000, 2005. Source: Johnson and Rosenblatt (2007, 166, Table
1).

On the one hand, such a diversity of views might imply that voters fail tounderstand the nature of parliamentary government and the importance ofparty dominance and discipline therein (e.g. Paltzelt, 2000). On the other
hand, it is not impossible to rationalize both preferences, especially for voters who lean towards the governing party: united governments are more
efficient, and able to respond rapidly to crises (see, e.g. Alesina and Drazen,

Section 4.2

76

1991; Tsebelis, 2002); they also exhibit greater longevity and thus are moreable to deliver benefits to their supporters. On the other hand, perhaps‘maverick’ representatives are more able and willing to impose their constituents’ views and concerns on the government at large when the attentionof national politics—and national parties—is elsewhere (see, e.g., CanesWrone, Brady and Cogan, 2002; Pattie, Fieldhouse and Johnson, 1994), or
perhaps they avoid dangerous ‘group think’ (in the sense of Janis, 1972)
behind the scenes. But whether different voters hold different preferences,or voters are internally divided, it is not difficult to see the potentially tricky
balancing act this presents for MPs involved in Commons roll calls.

Despite—or perhaps because of—the complicated dynamics this suggests,
previous work has tended to examine other MP-voter links. A series ofstudies, for example, examine constituency service as both a goal of members and its effects at election time (see Cain, Ferejohn and Fiorina, 1987;
Norton and Wood, 1993; Searing, 1994). Others look to local campaigning activity (e.g. Denver and Hands, 1997; Pattie, Johnston and Fieldhouse,1995), with some suggesting that, whatever the truth may be, MPs increasingly believe they enjoy a personal vote dependent on their appearances,
statements and legislative behavior (Cowley, 2005).

When scholars have examined parliamentary votes as a predictor of performance, they have tended to be limited in scope: in the case of Pattie,
Fieldhouse and Johnson (1994), they deal with just six ‘key’ votes with various levels of attendant whipping, while Kam (2007) uses ‘dissent’ on allSection 4.3

77

whipped bills (in the aggregate) to predict voter familiarity with their MP’sname.2 These strategies are not unreasonable given the specific questions
that were to be addressed, and the studies are important in that they arerare breaks with the orthodox thinking on voting in Britain. Nonetheless, if
we could be agnostic about the potential bills of interest, and thus include
all votes as possible predictors, we would garner the best of both investigations: we would have a survey of parliamentary behavior that is deeper
in terms of both the number of votes in the sample and broader in termsof their content and the pressure applied in each case. We would thus capture the totality of legislative behavior, rather than a potentially misleading
small sample. Before doing so, we need to be clear about what voters desire
and expect from their representatives. We outline our intuitions in the next
section.

4.3

Formalizing Intuitions

As with other scholars in the field, our work here will concentrate on the
behavior of government (i.e. Labour) party MPs: the ‘power’ of the government relative to other parties in a Westminster system means that these
representatives receive more media attention, and are more likely to be held
accountable for the state of the polity at election time. Thus these are themembers for whom the stakes are highest—for whom party unity and/or
independence matter most.

2
Though for New Zealand, rather than Britain, Kam (2007, 135) does show that dissent
is an effective vote-winning strategy.

Section 4.3

78

Our intuition is that on almost all issues (whipped or unwhipped) debatedin the House of Commons, voters are uninformed. The bills and proposals
are too technical and it is too time-consuming to review and understandtheir contents. Thus, voters rely on heuristics. For the reasons cited above,
party unity is prized on issues that are most important to the government’s
legislative agenda. Notice that this effect will be strongest for bills which
exhibit “government-versus-opposition” voting: that is, on roll calls where
the non-government parties attempt to foil the executive for the sake of opposition, rather than because they actually have some different and sincere
policy preference (see Spirling and McLean, 2007). The reason is that thesevotes most starkly test the Cabinet’s ability to govern; indeed losing on sucha roll call would typically trigger a vote of confidence.3

By contrast, when votes are relatively free of party pressure, precisely because they do not endanger a government agenda, maverick, independentminded voting is welcomed. Indeed here, ‘dissent’ from the MP’s party as
a whole is a ‘good thing.’ However, on the rare occasion that free votes
arise whose contents and consequences are simple to grasp for the public atlarge, voters reward MPs on a spatial basis. That is, left-leaning partisan
voters want their MPs to plump for the more ‘socialist’ option while rightpartisans prefer the more ‘conservative’ choice.
3

Such votes dangerously undermine Prime Ministerial authority: John Major called
such a vote in 1993 in response to sustained rebellion over a series of European integration votes. Major was compelled to resign his position as party leader—though hesubsequently won reelection—in response to the continual sniping. Fifteen years earlier,James Callaghan was forced to call a general election (which he subsequently lost) after
suffering defeat in Commons in March 1979.

Section 4.3

79

More formally, suppose there are 1, . . . , i, . . . N voters in constituency j,
for which MPj is the incumbent governing party member of parliament. For
any particular bill (or proposal, or amendment) b that is to be voted upon,
there are two possible responses by MPj —‘aye’ or ‘no’. We will write thechoice of MPj as a point oj in p-dimensional space: oj ∈ Rp . For a bill thatis essential to government business, denote the Cabinet’s preferred outcome
as og . There are q1 such bills of a total of B that come to be voted upon in
House of Commons. Since the government essentially never loses on parliamentary business it cares about, in a slight abuse of notation, we will use
og to also refer to the outcome voted for by the majority of the governing
party. This extends to the B − q1 bills that are not essential to government
business. Finally, denote the median voter of constituency j as having an
outcome preference on any particular roll call as oi ∈ Rp . Notice that weassume she voted for the incumbent at the previous election. We can now
write her utility from MPj ’s voting record in the Commons as
unwhippedunwhipped

whipped
z
z
}|
}|
}|
z
{
{

Ã
!{
q
q
B
2
1
X
X
X
Ui (·) = − w1d(oj , og ) +w2 d(oj , og ) − (1 − w1 − w2 ) d(oj , oi )

|

b=1

{z

q1 +1

voter uninformed

}

|

q2 +1

{z

voter informed(4.1)

where 0 ≤ w1 , w2 ≤ 1 refer to the ‘weights’ that voter i places on eachlegislative activity component and d(·, ·) is the Euclidean distance between}

Section 4.3

80

two points in p dimensions.4 With no loss of generality we assume that voter
i compares the utility from (4.1) with some constant c—say, zero—and casts
her ballot for MPj at the subsequent election if Ui (·) ≥ c, else she abstains
or votes for a competitor. Several simple comparative statics, consistent
with our reasoning above, follow:• for (heavily) whipped government business in Equation (4.1), so long
∂Ui (·)
as w1 > 0, ∂d(o< 0. In words: for bills that deal with imporj ,og )tant government business, (partisan, government party) voters will
disapprove of fractious, rebellious MP behavior. Moreover, the further away the MP’s vote (oj ) places him relative to the government(og ), the worse he does.
• for unwhipped roll calls on which voters are uninformed, so long as∂Ui (·)> 0. In words: on these bills, voters reward ‘inw2 > 0, ∂d(oj ,og )

dependent thinking’ insofar as it manifests itself as choosing options
different (far from) the party majority option.
• for unwhipped roll calls for which voters are informed, so long as w1 +∂Ui (·)
w2 < 1, ∂d(o< 0. That is, the voter’s utility is decreasing thej ,oi )

further the MP’s choice is from her ideal (outcome) point.
For reasons that we will discuss below, it is not possible to ‘test’ this theory
directly. Nonetheless, this model will give us a structured way to think about
our findings. Before leaving the theoretical discussion here, it is helpful to
4

Recall that the Euclidean
pPn distance between two points X = (x1 , x2 , . . . , xn ) and Y =2(y1 , y2 , . . . , yn ) is simply
i=1 (xi − yi ) . It is thus always positive, and caters for points
in any number of dimensions in space.

Section 4.4

81clarify three issues. First, this is an as if model: we are not contending thatmost voters directly examine voting records to ascertain their representative’s performance. Rather, they receive media and elite reports summarizing these patterns. What matters then is the types of MPs and the types ofvoting behavior in a broad sense. Second, there is a potential contradictionin the voter calculus: punishing a rebellious MP also hurts the party by potentially denying them an admittedly unreliable seat in the Commons. We
do not doubt that such reasoning occurs, but we will assume that at somepoint an MP’s actions are sufficient to merit voting against them, even if itsuperficially damages the national party in the short term.5 Third, to theextent that a time trend exists, Figure 4.1 implies that independent thought
ought to be increasingly rewarded, in addition to (or perhaps in place of)loyalty. Otherwise put: (relatively) free votes should be better predictors of
performance in 2005 than in 2001.

4.4

Data and Method

Ideally, we would test our predictions from Section 4.3 with constituency
level data recording citizens’ preferences for their MP’s specific legislative
actions, in addition to partisan, government party voters’ views on the desirability of party unity and favored positions on various free-vote issues. We
would compare these predilections to their representative’s actual record
5

As a case in point, consider the fate of Neil Hamilton, Conservative MP for Tatton in
Cheshire. Accused by The Guardian newspaper of taking bribes to ask questions in theHouse of Commons, Hamilton proclaimed his innocence, sued for libel and went on to fightfor his seat in the 1997 General Election, the then 5th safest Tory district in the country
with a previous majority of 16,000 votes (27.6 percent). Hamilton lost to an independent
challenger, by some 11,000 votes on a 18 percent swing away.

Section 4.4

82

and calculate the effect that this divergence had on the MP’s subsequent
electoral performance. No such data exist so, instead, we will try to infer
micro-behavior from aggregate level findings.

In the Americanist context, scholars have summarized Congress members’legislative behavior using ideal point estimation, and then contrasted thiswith metrics purportedly capturing the underlying political orientation of
citizens in their home district. Thus ‘divergence’ and the degree to which amember is ‘out-of-step’ with his constituents may be assessed (e.g. CanesWrone, Brady and Cogan, 2002). But such a strategy is fraught with difficulty for the United Kingdom case: the sheer preponderance of strategic,‘government-versus-opposition’ voting in the House of Commons makes interpreting industry-standard tools for summary very difficult (Spirling and
McLean, 2007).

The analysis of British parliamentary voting in the context of our theoryis hampered by two further considerations. First, it is not publicly obvious
how much whipping is applied on individual roll calls. While parties certainly acknowledge that strong pressure is present at Westminster, they do
not typically publish details of its intensity and, in any case, whipping may
take the form of informal threats and offers.6 Moreover, the fact that a rollcall is ostensibly ‘free’ is no guarantee that it is completely undirected.7 So,
6
In practice, party whips contact party members with a schedule concerning upcoming divisions. They literally underline the requirement that members attend and voteappropriately according to the importance the party places on the roll call in question.
7
See McLean, Spirling and Russell (2003) for a specific incidence of this phenomenon.

Section 4.4

83

though we will use terms ‘whipped’ and ‘unwhipped’ below, they are meant
only as broad-brush shorthand for the general environment in which the billis being considered: this is especially true when the parties differ in theirapplication of their whip. The second problem is that, within the parliamentary record, Hansard, missingness is endemic and unexplained. Since
there is no way to formerly record absences, there is no way of knowing if a
missed vote was due to indifference, principled abstention, illness, ministerial
business, etc.

4.4.1

Data: 1997–2001, 2001–2005

For each data set, our dependent variable is the difference in electoral success (vote percentage in their home constituency) for each of the MPs in
the study between the respective elections. As noted above, we restrict theanalysis to government party—i.e. Labour party—MPs for whom we think
the theory predicts the strongest effect. Further, we deal solely with MPs
who hold seats in England and who did not hold ministerial office at any
time during the parliamentary terms. The location restriction avoids including MPs whose electoral fates may be the product of nationalist party
dynamics that are difficult to control for. The next avoids the potential endogeneity problems inherent in ‘good behavior’, front-bench promotion andconstituency popularity. Simply put, MPs are given ministerial responsibilities contingent on toeing the party line,8 but that same status makes themmuch more recognizable in their home districts, increasing the possibility
8

See Benedetto and Hix (2007) for a discussion of this issue and its consequences fordiscipline.

Section 4.4

84

their subsequent vote share is influenced by factors other than their roll callrecord. For obvious reasons, we also drop MPs who choose not to fightthe subsequent election, or who joined the parliament mid-way through via
by-elections (and thus for whom we are missing some dependent variable
information). These data cuts leave some 225 backbench Labour MPs for
1997–2001, and 194 for 2001–2005.

Our approach is to predict, i.e. to regress, the vote shares on every single
roll call vote the MP casts in the relevant parliament, data which was compiled from (online) Hansard reports.9 This way, we know that the totalityof MP legislative behavior is being captured. We have also collected numerous (standard) controls which include the difference in electoral spending
by Labour between the elections (a reasonable proxy for campaign ‘effort’—
see Pattie, Johnston and Fieldhouse (1995)), the difference in turnout, andthe proportion of constituency residents falling into several traditionallymarginalized groups that might be disproportionately sympathetic towards
a Labour government.10

4.4.2

Estimation Problem: p > n

The dependent variable of interest is (essentially) continuous. Hence, ordinary least squares (OLS) might seem attractive as an estimation procedure.
9
See Firth and Spirling (2006) for a discussion of this data. We impose the requirementthat at least 50 percent of all the MPs in the sample voted on that roll call for it to enter
the data. This avoids including divisions where the majority of MPs were missing.
10
Compiled from the Census 2001 Report for Parliamentary Constituencies. In particular, the percentage of pensioners, of non-whites, of individuals living with a limiting longterm illness (which includes disability), of unemployed, and the proportion of households
headed by a lone parent.

Section 4.4

85

Unfortunately, on the ‘right hand side’ there are around 1300 variables—
predominantly parliamentary divisions—which we wish to use as regressors(or ‘predictors’). That is, the number of parameters to be estimated, p far
exceeds the number of observations, n: we have negative ‘degrees of freedom’, p > n. The consequence is that the standard OLS solution,β = (x0 x)−1 x0 y,(4.2)

is unavailable; moreover, the equivalent of Equation (4.2) for essentially any
parametric model—discussed in more detail below—is elusive.

One unsatisfactory solution is to re-specify the regression problem with fewer
variables, but this requires an entirely arbitrary a priori restriction on themodel. A better option is to employ systematic exploration methods that
uncover structure and reduce the data down to its ‘important’ component
variables. Moreover, because our theory is somewhat vague, we would likea flexible approach that assumes as little as possible about the precise functional form of the relationship between the y and x we alluded to above.

4.4.3

Tree-based Regression and Random Forests

OLS is a special case of ‘regression’ which we can write more generally
as y = m(x) + ² where m() describes an unknown model for the data weobserve. Depending on the assumptions we make about m()—in particular, what we believe we ‘know’ about the function that it represents—wecommit to a parametric or nonparametric approach. In parametric models,Section 4.4

86

the functional form of the relationship between the dependent and independent variables is assumed known, but it contains parameters whose values
are unknown and to be estimated. Political scientists are most familiar
with generalized linear models (GLM) where y is linearly associated withx profiles but in which the functional relationship between them can be
non-linear.11 Examples include logit or Poisson regression. When analysts
have a strong grasp of the underlying physical causal process (and thus,
for example, the potentially subtle ways that variables interact), parametric models are a good choice. They are of limited use, however, when thedata are not well understood, or theory is not easily forthcoming—especiallywhen the number of independent variables is large and thus the causal story
complex. This is precisely because the assumptions that make parametricmodels straightforward to fit also restrict the variety of relationships thatthey can adequately describe: and if the model is ‘incorrect’ for the data
(e.g. linearity is assumed when non-linear relationships are more apt), results will be less than satisfactory. Notice that the goodness of fit criteria
may be misleading in these circumstances. In any case, for problems inwhich we have p > n, standard parametric models cannot be fit to the data.

In contrast to parametric models, nonparametric models make very few
assumptions about the functional form between the dependent and independent variables. While parameters of the model are estimated, they do
not necessarily have a clear interpretation in terms of the physical causal
11

That is, E(y|x) = G(βx) where E() is the expectations operator, G() is some function
and β are the parameters to be estimated.

Section 4.4

87

process thought to underlie the data: instead the concern is with function
estimation and good prediction.

A simple nonparametric method, popular in biostatistics, is that of regression trees (Ripley, 1996, 213). Within this literature, the task of optimizing
predictive performance is performed by classifying cases according to their
independent variable values via a series of logical splits. Typically, at eachsplit, or ‘node’, the algorithms divide one independent variable into (binary) disjoint subsets into which the cases can be placed. Further splits
are then proposed for any cases that are not in terminal nodes (known as‘leaves’ of the tree). There are lots of different rules that may be used to‘cut’ the independent variables (Ripley, 1996, 216–220), and hence several
different ways to assess how well the tree classifies the problem in question.
The general idea is to split the data so that cases within the subsets are
as like each other as possible; in regression contexts, this literally means
choosing to split a ‘parent’ node such that the resulting two ‘child’ nodes
have the minimum possible within node variance in terms of their values ofthe dependent variable.12 By seeing which variables—when split—best predict the cases, we obtain some notion of ‘importance’ in a regression context.

To see how this process might work, consider the following toy example:
we have data on the 2004 Presidential election, in terms of George Bush’s
percentage of the vote in any given state. We also have ‘explanatory’ variables for each state, including its population density, its median household
12More details may be found in Appendix 4.7.

Section 4.4

88

income, and the proportion of its population that are black. In Figure 4.2
we report a tree grown for this data using the split criterion defined above.13
At the top of the tree, we see the first split was on population density, withthose having a value of lower than 206.8 sent ‘to the left’ and those thatare more dense than this cutoff sent ‘to the right.’ On the left, these relatively rural states were once again split on population, with the least dense(< 35.2) sent to the left. The next split for those states occurs in termsof their black population. If it was less than 1.5 percent (0.015 to the leftof the figure), they were dropped in the bin of states with a mean value of
65 percent for Bush. Literally, these are large, rural, predominantly whitestates such as Utah and Wyoming. Each leaf (end value) in the figure corresponds with a different bin, and states are placed there contingent on theirvariable values.

Several comments are in order here. First, the variables are not all of thesame ‘importance’: different variables at different nodes do better in reducing the variation in the subsequent (split) data sets than others (here,
population density does particularly well). Second, there is no guaranteethat ‘important’ variables will be statistically significant in a regression context or vice versa: classification and/or tree-regression are not synonymouswith OLS. Third, we made a judgement call as to when the tree would stop
growing. Clearly, there are 50 states, but only 8 bins as terminal nodes—
65.00, 57.17, 46.00, 51.00, 59.78, 54.60, 48.20, 42.29. In this case, the tree
13

Implemented in the R (R Development Core Team, 2006) statistical language andenvironment using the tree package: see Ripley (1996).

Section 4.4

89

popn.density < 206.848|

popn.density < 35.2142

popn.density < 361.186
48.20

black.popn < 0.015

65.00

42.29

black.popn < 0.065

57.17

black.popn < 0.025
46.00

51.00

median.income < 40418.5
59.78

54.60

Figure 4.2: Example of a classification tree for American states, predicting (categorizing)
the percentage of vote for George Bush in the 2004 Presidential election.

Section 4.4

90|

Figure 4.3: Example of a tree that uniquely classifies American states, in terms thepercentage of vote for George Bush in the 2004 Presidential election. Node labels removed
for clarity of presentation.

is grown until no more than 10 cases reside in a terminal node. In this toy
instance, we could have, in fact, insisted on a perfect fit to the data: 50
terminal nodes with one for each state. Such a tree is given—without the
distraction of node labels—in Figure 4.3. Its complexity should be obvious.

For most purposes, fitting a large data set with lots of independent variables
in a way that resembles Figure 4.3 won’t be helpful: we will ‘overfit.’ That

Section 4.4

91

is, we will essentially reproduce the complexity of the data by fitting its
random (‘noisy’) features which are not part of the causal process in which
we are interested. Such trees have high variance, in the sense that altering
the data on which they were grown (by, perhaps, adding new points outof the sample) would result in very different findings. This is undesirable
given that we want to know about the general structure of the data at hand.
To reduce this variance, we can ‘prune’ the tree back after it is grown, andthere are various methods for doing so (Ripley, 1996, 221–231). Alternatively, we can ‘stop’ growing at some pre-defined point. But less complex
trees introduce a new problem of bias: simpler models may not be goodenough to correctly represent the subtleties of the data we are interested
in. Though we can make the selection of ‘right-sized’ trees automatic using
various cross-validation procedures, there may be a better way to proceed.

One solution is to grow multiple trees—each potentially classifying the cases
differently—and find some way to aggregate the results from all of them. A
popular and powerful way to do this is Breiman’s (2001) random forests
algorithm.14 The key idea is that each tree will be unpruned and thus have
low bias. And, while the individual trees will have high variance, for reasons
noted below, there will be a low correlation between them. Combining thetrees will give the best of both worlds: low bias and low variance.

Random forests actually builds on an earlier technique—also proposed by
14

Implemented in R by Liaw and Wiener (2002).

Section 4.4

92

Breiman (1996)—called ‘bagging’.15 Bagging is an abbreviation of bootstrap
aggregating and, like most tree methods, it begins by splitting the data intoa ‘training’ and ‘test’ set. In random forests, we do not need to make thissplit. We proceed as follows:
1. take a bootstrap sample from the data, D. In practice, this means
taking a sample of size N —with replacement—from D (see Efron andTibshirani, 1993, for a general discussion). Denote this sample as Dk
and notice that the same observations can therefore appear multiple
times in Dk , and others from D might not appear at all. In fact,
approximately one third of the cases will not appear in the sample(called ‘out of bag’).
2. train the predictor using Dk . That is, grow one tree from that sample
until the cases reside in sufficiently small nodes (commonly, five cases).
These trees are not pruned.
3. repeat steps 1 and 2 1, . . . , b, . . . B (say, 500) times.
4. aggregate the results of the B trees. In a regression context, we average
across the trees.
Random forests get their name from the randomness employed at each nodein each tree: rather than employing the best split among all variables to continue to grow the tree, a random forest splits a randomly chosen subset of all
the predictors; in practice this subset is approximately one-third of the total
number of independent variables (around 350 here). This strategy results in
15

See Ruger et al. (2004) for a political science application of an earlier contribution by
Breiman et al. (1984).

Section 4.4

93

low correlation between the trees, and yet the predictive performance generally exceeds that of related techniques—such as neural nets (see Beck, Kingand Zeng, 2000; de Marchi, Gelpi and Grynaviski, 2004)—without overfitting. A schematic diagram describing random forests is given in Figure 4.4.

We will be interested in several quantities from our models: first, the goodness of fit, which is calculated in a similar way to the R2 for a standard
regression with the difference that we explicitly attempt to predict datathat was not involved in fitting the trees. Second, we want to know how‘important’ different variables are; to do this, we will inspect a residual sumof squares measure for trees where the variable is involved, relative to thosewhere it is not. Third, the marginal effect of any given variable on y will bea concern. Broadly, we obtain this by comparing the predicted y when thevariable is in the (aggregate) random forest model, to when it is not. Appendix 4.8 gives more technical details. Notice that because random forests
are not attempting to estimate regression coefficients in the usual, GLM,
way there is no requirement that n > p.

If random forest classification is successful, we expect observations whichare ‘alike’ to end up in the same terminal nodes across trees. We can use
this fact to impute missing observations, and Appendix 4.9 explains how.

4.4.4

Estimation Plan

Given the above explication, our investigation now proceeds in several steps,
which combine both quantitative and qualitative methods:

Section 4.4

94

Data D1 2 3 4 5
6 7 8 9 10

’out−of−bag’ 2 5 8

1 5 7

1 4 8

3 4 9

4 10 66 2 3

10 2 56 8 1

7 5 8 32 5 5 10

7 9 7

7 8 7

’in bag’

4 9 4 1 10 9 8 8
7 3 10

2 4 6

bag 1

bag 2

bag B − 1tree 1tree 2tree B−1

bag B
tree B

Figure 4.4: Random forest schematic. Here the data set consists of ten observations
labeled 1 through 10. These are ‘bootstrap sampled’ into bags (1 thorough B). For eachbag, some observations are ‘left out.’ A tree is grown from each bag, and the results
aggregated.

Section 4.5

95

1. impute values for the missingness in the divisions using a random forestclassification
2. use imputed data and random forest to calculate relative ‘importance’of different controls and roll calls in predicting electoral success.
3. using 2 as a guide, obtain and report the (random forest) marginal
effect of some important variables (roll calls)
4. use narrative histories (such as Cowley (2002) and Cowley (2005)) toestablish nature of bills—whipped/unwhipped, etc.
As a further comparison we will also report OLS coefficients for the variablesfrom 2 (using each variable with all controls to predict performance). To
reiterate, we will use data classification techniques to find the most ‘important’ variables (which will involve a judgement call on our part) and thensee if and how they fit our theory. Because the method fits by maximizing
prediction, concern will focus on the types of roll calls that matter (‘heavily
whipped’, ‘free’, ‘issue of conscience’, ‘programmatic concern’, etc.), rather
than their precise content. In other words, we will identify those bills thatbest predict the dependent variable in question and then describe their broad
characteristics in terms of our interest in party discipline versus independence. Because essentially all votes are used, there is thus no danger that
we are looking in the ‘wrong place’ when predicting electoral performancefrom legislative behavior.

Section 4.5

4.5

96

Results

The results are in two parts, first for 1997–2001 and then, separately, for
2001–2005. Of course, for both data sets, we follow the stages set out in theprevious section.

4.5.1

First term: 1997–2001

For our first data set, recall that the dependent variable is the differencein vote share that the backbench Labour MP’s garnered in their home constituency for the 1997 versus 2001 election. In fact, both events were landslides for the Labour party as a whole, and Labour lost just six seats (ofa 179 seat majority) in the latter. Nonetheless, there was quite significant
variation in terms of the performance differences of individual MPs with amean change of −1.59 percent (variance of 14.77), and a maximum loss of-12.5 percent recorded by Khabra Piara (Ealing Southhall), and a maximum
gain of 12.7 percent recorded by Michael Jabez Foster (Hastings and Rye).
In Figure 4.5, we graph the most important 30 variables from the random
forest regression where, x-axis scale refers to the decrease in the average
residual sum of squares when the variable is in the tree, as opposed to when
it is left out. The (mean) pseudo-R2 goodness of fit measure for the model
was around 0.06.

Note first that the controls are seemingly essential and all contribute morethan any roll call in accounting for differences in the dependent variable. In
particular, the percentage of citizens in a district with a debilitating illness

Section 4.5

97’important’ roll calls

controls

Illness
DiffT
EthnicSpend
PensionLoneParent
Unemploy
div323.001107
div162.010321
div312.980622
div281.991102
div307.001023
div303.001023
div186.000509
div111.971210
div012.001219
div294.980608
div299.001023
div300.001023
div046.990125
div311.980622
div079.990301
div078.971103
div243.990714
div290.000725
div191.990520
div134.010227
div071.000210
div063.990210
div302.001023
0

100

200

300

400

IncNodePurity

Figure 4.5: Variable importance plot for 1997–2001 data. Controls and ‘important’ rollcalls used in subsequent analysis shown as subsets of all variables. x-axis gives the increasein the regression performance from including each variable.

Section 4.5

98(Illness in the graphic) is most important, followed by turnout differential(DiffT), the proportion of non-whites (Ethnic), the proportion of Pensioners (Pension), the proportion of lone parent households (LoneParent), theproportion of citizens unemployed (Unemploy) and then the electoral spending differential (Spend). The following points on the graphic refer to theimportance of the roll calls and have labels beginning with div. Deciding
which of these bill votes are worthy of further inspection is essentially ajudgement call, and here we consider the top 9, below which there is a slight
drop off in importance.

In Table 4.1 we report our results: for each variable, we give the marginal
effect from the random forest: literally, this is the difference in the predictedconstituency performance when an MP votes with the minority of his party
as opposed to when he votes with the majority. We also report an OLS coefficient (with p-value) from including that predictor in a regression—with allcontrols. In both cases, a positive number means the MP did better at election time while a negative one means he was worse off. Since the controls are
not the focus of the study, they are left out of the table. As noted above, it
can be quite difficult to know for sure how much party pressure was appliedin the various votes, but column 3 gives a casual author-based coding of
the discipline imposed for that vote, ascertained from a qualitative readingof the relevant House of Commons debate and surrounding literature; thewhipping is one of four ordinal levels: ‘free’ (essentially no whipping), ‘weak’(little whipping, perhaps timetabling concerns), ‘moderate’ (some pressure,government has preference for outcome), ‘strong’ (tight whipping, govern-

Section 4.5

99

ment has strong, programmatic concerns).

Beginning first with bills which Cowley (2002) discusses as central to theGovernment’s post-1997 legislative agenda, we note that the signs are in the
expected direction. That is, rebeling on the Transport Bill (row 7) leads
to MPs being punished at election time—i.e. a negative coefficient—that is
statistically significant. This roll call dealt with the Government’s attempts
to privatize the National Air Traffic System. The rebels on this roll callwere backing an (non-Government) amendment that would have substantially delayed the denationalization.

The vote on the Crime and Disorder Bill (rows 3) was concerned with lowering the age of homosexual consent from 18 to 16, such that it would be on aparity with heterosexual consent. They were ostensibly unwhipped, yet thisbelies some potential party pressure on MPs. For this bill, voting for anamendment to enforce a minimum age of at least 18 in certain circumstances
was punished by the electorate. Within the realms of the model we advanced
above this suggests two possibilities: first, that voters were sympathetic tosuch social equality issues, and the MPs that vote for them. For gay rights,
such preferences seem to be the case: some 93% of British respondents ina recent survey supported laws to protect gay people from discrimination(Cowan, 2007), while the legalization of same-sex civil partnerships appears
to have occasioned much less heated debate in the UK than their potential
introduction in the US. Certainly, those taking the more conservative position here did worse. Second, note that though the government was formallyWeights and Measures (S.I.)
Crime and Disorder Bill
City of London (Ward Elections) BillElection of Speaker
Election of Speaker
Transport Bill
Doctor Assisted Dying
Human Fertilisation and Embryology

div162.010321

div312.980622

div281.991102

div307.001023

div303.001023

div186.000509

div111.971210

div012.001219

free

free

strongfree

freemoderate

free

weak

Discipline
weak+0.171-0.147-0.271+0.142+0.213-0.176-0.011+0.291‘Rebel’ Effect (RF)+0.179+0.822-0.472-1.287+1.165+1.743-0.845-0.391+0.827‘Rebel’ Effect (OLS)+1.144

0.132

0.360

0.031

0.075

0.006

0.092

0.460

0.256

p-value
0.038

election. First column is data code for the division with date after point: so, div323.001107 is division 323 taking place on November
7, 2000. Name of bill in column 2; random forest ‘coefficient’ in column 3 for being a ‘rebel’(in the minority and/or frustrating theGovernment’s ambitions); OLS coefficient in column 6; p-value for that coefficient in column 7.

Table 4.1: ‘Most important’ parliamentary votes for predicting electoral performance by backbench Labour MPs in 2001 general

Name
Programming of Bills

Code
div323.001107

Section 4.5
100

Section 4.5

101

uncommitted to the amendment, it allowed it time for consideration and,
when the House of Lords rejected it, the government reintroduced it via theseparate Sexual Offences (Amendment) Bill. Indeed, when the Lords once
again refused its assent, the government threatened to enact it directly over
the wishes of the upper chamber. In short then, the executive was clearlycommitted and sympathetic to this issue—suggesting that rebels might beconsidered at least ‘out of step’ if not ‘troublemakers’ per se.

Votes that concerned the election of a new House of Commons Speakeroccupy rows 5 and 6 of the table. Unlike, say, the United States House ofRepresentatives, the Speaker of the House of Commons is a non-partisan
referee of parliamentary debate. Selected from back-bench MPs, Speakercandidates do not usually receive official endorsements though MPs fromthe same party often vote similarly in the elections. Ultimately then, theseare free votes, and the whip is not present. Moreover, these are votes forwhich voters are uninformed: the candidates are not typically a priori wellknown, nor do they have particular ‘policies’ beyond their general personal
reputations. We would predict then, that rebeling—in the sense that MPs
vote in a way that contrasts with the majority of their party—would be aboon to electoral performance. In fact, both coefficients—OLS and random
forest—are in the correct direction (positive), and they are statistically significant.

The other roll calls in the table have a slightly more complicated status interms of the party pressure applied to the vote. For example, consider theSection 4.5

102

June 2000 “Programming of Bills” motion that concerned the Modernisation
Committee’s recommendations for changes to the way that parliamentarybusiness be conducted. Usually, ‘House business’ issues are seen as free
votes, not least because they emanate from non-partisan Select Committees
that are designed to hold the government to account. Interestingly, and asa break with standard practice, the Modernisation Committee was chairedby the Leader of the House, a cabinet member. Both in committee andduring the ensuing Commons debate, MPs accused the Government—via
the Leader of the House—of promoting its own agenda (see Kelso, 2007,
140–141). In particular, several MPs felt that the proposed reforms madeit more difficult for parliament to oppose the executive and hold it to account. Thus, members backing an amendment to these plans that would
have extended debating time were de facto frustrating Government ambitions. There are thus two consequences: first, the vote was ‘free’ for Labour
backbenchers but pressure was surely present and second, the ‘rebels’ wereactually the majority of the party on this vote (note that the Leader of theHouse opposed the amendment). With all this in mind, the sign is essentially as predicted: those showing independent-mindedness on a bill thatwas not an explicit part of the Government’s agenda did better at the polls.

The City of London (Ward Election) Bill appears in row 4: the coefficient
is significant. By this private bill, the City of London intended to reform
its self-governing arrangements as a municipality. Unusually for an authority in a democratic state, the City gives businesses votes, and the proposed
legislation would have extended this right to more businesses. For many left-Section 4.5

103

leaning MPs in the Labour party, such a plan was anathematic. It is unclear
exactly how or even if the Government asserted pressure on its MPs though.
Certainly, the Leader of the House claimed it was an explicitly free vote,though Salter (2004) argues that the Government may have pressured MPs
to at least pass something that could be considered ‘reforming’, just to bedone with the issue. In July of 1999, the ideological components of the plans
came under attack, with Labour backbenchers in the minority condemningthem. In November of the same year, the bill was not yet passed and there
was lively debate as to whether or not the proposals should be reconsideredin the next parliamentary session which, without explicit Government involvement they would not have been. To the extent that the rebels were
now holding up procedural Government business, it is perhaps understandable that the sign is negative and they were punished for their intransigence.

The votes concerning “Weight and Measures” (row 2), “Human Fertilisation and Embryology” (row 9) have signs as predicted, though not at significant levels. The first vote dealt with a particular “statutory instrument”,
a method of delegated legislation that allows a minister to make changes
to rules and laws without the requirement that the proposals be passed asa separate parliamentary bill. In this particular case, the vote dealt withhow long Imperial measurement units would be allowed to continue as a‘supplement’ to the metric units required by European Union legislation. Itshould be clear that such a vote should not fall into the category of essential governmental programmatic business as defined above—and we see that‘rebels’ did better when they opposed this vote. The Human Fertilisation

Section 4.5

104vote pertained to cloning as a medical research practice. Again, we see rebels
garnering a (minor) uptick in support for their ‘independent-mindedness’ ona free vote for which the public is presumably fairly ill-informed.

The final case to consider concerns a vote on “Doctor-Assisted Dying” (row8). Euthanasia is not generally a salient issue for most British voters at theballot box (unlike, say, abortion for US voters), and the debate has beencharacterized by its cross-cutting dimensions. For example, conservative,
religious groups, the British Medical Association (the main doctors’ tradeunion) and several prominent left-wing MPs oppose doctor assisted dying.
It is thus not precisely clear where the average Labour voter places herself
on the issue, so it is hard to know what to make of the fact that ‘rebels’(those who voted in favor of euthanasia) did worse at election time. In any
case, the effect is apparently not significant.

4.5.2

Second term: 2001–2005

The 2005 election saw most Labour MPs do worse than in 2001, with amean loss of 7 percent in our data set (variance was 12.32). Given that
Labour entered the election with 30 seats where the majority was less than
7 percent, this was clearly a more competitive election. The national swing
was a commensurate 6 percent away from the governing party, though theiroverall performance was sufficient to garner a workable majority of 66 seats.
The biggest (Labour) loser of the election was Roger Godsiff who suffered a
reduction in his vote total of some 21 percent (primarily to a candidate fromthe new anti-war Respect party) and the biggest gains were made by Shaun

Section 4.5

105

Woodward, a Conservative defector who left his original party in 1999. In
Figure 4.6 we graph the most important variables for this regression fromthe random forest technique. The (mean) pseudo-R2 goodness of fit measurefor the model was around 0.04.

Once again, we note that the controls are certainly important, though theirrelative ranking has been permutated from that in Figure 4.5. And, again,
we make a judgement call as to which of the bills are worthy of further
inspection. Here, it is just 10, and we report their effects in Table 4.2. Asin the 1997–2001 session, we see that the ‘Programming of Bills’ is an apparently important predictor, occupying rows 1 and 8 of the table. In bothcases, ‘rebeling’—in the sense of voting with the minority—was beneficial forMPs (and this effect is statistically significant). These votes were explicitly
free though, once more, knowing precisely how much pressure was appliedin practice is difficult to gauge. With this in mind, as with our previous
findings, our theory predicts the positive sign we see in practice.

Unlike the programming matters of the previous paragraph, the “Children
Bill” was part of the Government’s legislative plans for the session and wastherefore whipped appropriately. The vote in row 2 of the table actually concerned a backbench amendment (from David Hinchliffe, Chair of the HealthSelect Committee) that would have struck out part of the Government’s
bill that allowed parents to use “reasonable physical chastisement” in disciplining their children. The result would be a bill that essentially outlawed
all such spanking. Somewhat unusually—given that it proffered a change

Section 4.5

106’important’ roll calls

controls

PensionEthnicUnemploy
Illness
Spend
LoneParent
DiffT
div278.041026
div306.041102
div044.011025
div283.041026
div208.040628
div358.031110
div011.010705
div279.041026
div048.050126
div240.020514
div336.021029
div281.041026
div045.050125
div093.011129
div180.030508
div237.020514
div311.041108
div316.020724
div059.040225
div241.030618
div307.041103
div239.020514
div244.020516
0

50

100

150

200

250

IncNodePurity

Figure 4.6: Variable importance plot for 2001–2005 data. Controls and ‘important’ rollcalls used in subsequent analysis shown as subsets of all variables. x-axis gives the increasein the regression performance from including each variable.

Programming of Bills
Children Bill: Reasonable Punishment
Social Security
Removal of References to Strangers
Human Tissue Bill: consent for removal
Fluoridation of Water Supplies
Members’ Allowances, Insurance
Programming of Bills
Modernization of the House
Liaison Committee: Power to Take Evidence

div278.041026

div306.041102

div044.011025

div283.041026

div208.040628

div358.031110

div011.010705

div279.041026

div048.050126

div240.020514

free

free

free

free

free

weak/mod

free

weak

moderatefreeDiscipline+0.082+0.047+0.250+0.100+0.141+0.240+0.288+0.256-0.130+0.535‘Rebel’ Effect (RF)+0.586+2.517+1.263+0.243+1.233+1.335+1.297+0.931-1.113+1.660‘Rebel’ Effect (OLS)

0.197

0.634

0.046

0.630

0.013

0.024

0.043

0.130

0.039

0.005

p-valueelection. First column is data code for the division with date after point. Name of bill in column 2; random forest ‘coefficient’ incolumn 3 for being a ‘rebel’(in the minority and/or frustrating the Government’s ambitions) ; OLS coefficient in column 6; p-value forthat coefficient in column 7.

Table 4.2: ‘Most important’ parliamentary votes for predicting electoral performance by backbench Labour MPs in 2005 general

Name

Code

Section 4.5
107Section 4.5

108

to government legislation—the vote was ‘free’ in theory. Nonetheless, theGovernment clearly had a preference on the vote, and we see a negativeand significant coefficient implying that ‘rebels’ did worse after ‘defying’ theexecutive. The other piece of Government legislation in the table is the “Human Tissue Bill” (row 5) but, once again, the substantive circumstances ofthe vote are quite odd by Westminster standards. In particular, the roll callconcerned a Liberal Democrat amendment to a government bill that would
have made organ donation automatic unless the deceased had previously
registered an objection. While this was a free vote for both the main Opposition parties, it was whipped by the government, on the philosophical basisthat such an amendment would, by presuming consent, be denying individuals the right to exercise their conscience. Clearly then, this bill was not a
cut and dried “government-versus-opposition” case and the low turnout adds
fuel to this argument. With this in mind, the significant and positive coefficient for rebel behavior is perhaps less anomalous than it might first appear.

Several of the remaining entries in Table 4.2 are free votes, primarily that
dealt with internal House issues. For example, the “Removal of References
to Strangers” (row 4) dealt with changes to parliamentary language, “Members’ Allowances, Insurance” referred to various MP compensation concerns,“Modernization of the House” (row 9) referred to the sitting hours of theCommons and “Liaison Committee: Power to Take Evidence” (row 10) dealt
with procedural issues for cross-party committees. In all cases, we see thesign is positive, as predicted for ‘rebeling’ on such unwhipped votes, though
it is only significant in one case.

Section 4.5

109

The last two votes to consider from Table 4.2 are quite obscure. The first,
on “Social Security” (row 3) actually refers to a statutory instrument that
regulates unemployment services in the UK. The Conservatives abstainedon the issue and, though not technically a free vote, it was not a crucial partof the Government’s agenda. Thus the sign for ‘rebeling’ is in the correct
direction (i.e. it is positive) but it is not significant. Finally, row 6 deals
with “Fluoridation of Water Supplies”, a perennial debate in the Commons.
The free vote concerned whether or not local authorities could force waterproviders to add fluoride to residential and other supplies. As predicted,
the sign is positive—rewarding the minority on a free vote—and, in fact,
significant.

4.5.3

Summary of Results

We found that controlling for various other factors,- For both 2001 and 2005, MPs rebeling against important government
legislative business (‘trouble-makers’) were punished by voters, andthis effect was sometimes statistically significant.
- For both 2001 and 2005, MPs dividing with the minority on free votes(being ‘mavericks’) which involved issues on which voters were illinformed tended to be rewarded by voters- For 2001, Labour MPs voting against popular social justice legislation—in particular, gay rights—in free votes were generally punished by theelectorate

Section 4.6

110- the OLS effects, when significant, were on the order of 1 to 2 percentof the vote differential from the previous election. The random forest(marginal) effects were generally of a much smaller magnitude, though
the signs generally agree.

4.6

Discussion

It seems that old certainties about British politics are changing: government party MPs are now more rebellious than they have been in a generation (Cowley, 2002, 2005), and there is increasing evidence that local
factors matter at election time (Denver and Hands, 1997; Pattie, Johnston
and Fieldhouse, 1995). The current paper was concerned with connecting
the two trends and systematically assessing the evidence for voter reaction to patterns of MP activity in Parliament. Using new non-parametrictechniques and roll call records in their totality, we found that (Labour) voters do indeed seem to respond to overall patterns of activity: they punish‘trouble-making’ rebellion on heavily whipped government business, while
rewarding more maverick legislators when party unity is not per se at stake.
Moreover, this finding makes sense of seemingly inconsistent public opinion preferences for both party loyalty and free thinking, and adds a layerof intuitive, though subtle, depth to our understanding of accountability inWestminster systems. This perhaps allows some ‘catch up’ with Americanist efforts, while producing new directions for future research.

As was explicitly noted above, the model of voter behavior was ‘as if’ inSection 4.6

111

nature: we would not contend citizens have a sufficiently advanced knowledge of policy making or parliament to directly reward or punish legislatorson certain bills. Rather, we think that voters receive signals from a possibly
media-based elite, who digest and then describe overall patterns of MP behavior as ‘rebellious’, ‘loyal’, ‘fractious’, ‘conforming’ and so on. So, while
our data and method tapped the generalities of this dynamic, it could not
trace the causation path precisely. Further work in this area might thus
profitably gather media or other data on the messages that voters receivein order to disentangle what exactly are the triggers that change the labels
MPs receive.

Finally, this paper has potentially important ramifications for institutional
reform in the United Kingdom. At the time of writing, the House of Commons Modernisation Committee is engaged in an attempt to strengthen therole of backbenchers in terms of their dealings with the executive, and issoliciting expert opinion on these matters (see, e.g., Cowley, 2006). It is
hoped that this will resurrect public engagement in politics after two general election turnouts of around 60 percent (very low numbers by Western
European standards). We have suggested that voters are already either heterogenous or discerning in their responses to backbench behavior, and further independence for MPs will presumably make them more so. Whether
MPs supporting these reforms understand that their electoral fortunes will
be increasingly tied to their legislative performance and choices—and not
the party’s overall popularity—is unclear. Given that institutional norms—
whipping and unity—appear to both affect and be affected by ‘what voter’sSection 4.6

112

want’, changing those norms ought to have interesting and complex consequences.

113

Appendix to Chapter 4
4.7

Regression Tree Split Criteria

Consider a ‘parent’ node t containing some number of cases N (t) that is tobe split. We measure the ‘impurity’ of t via the least squares deviation (alsocalled the ‘deviance’), written R(t), which is

R(t) =

X(yi − y(t))2

(4.3)

i=t

where yi is the dependent variable value for the ith case at node t, and y(t)is the mean of all the cases in node t. Notice that Equation (4.3) is simply
the residual sum of squares at t.

We will split the cases from t into two distinct subsets such that the subsequent ‘child’ nodes have summed deviations that are as small as possible. In
particular, we require that our split s (on some value of one of the covariates)
maximizes
R(t) − R(tL ) − R(tR )(4.4)

Section 4.8

114

where R(tL ) is the within node variance of the left child and R(tR ) is thewithin node variance of the right child. This is equivalent to choosing a split
maximizing the reduction in deviance.

As an example, suppose our parent node t has a variance of 20. Two possible splits in the covariates, s1 and s2 are proposed. These may be different
points in the same variable, or different splits in different variables. Suppose
s1 yields two children: one with a deviance of 11, the other with a devianceof 19. For s2 , the left and right child both have a deviance of 15. These
splits are considered equivalent since both result in an equal value of (4.4).

4.8

Model Fit, Variable Importance and Effect

Determining goodness of fit for random forests regression proceeds as follows.
Notice from step 1 in Section 4.4 above that in any given bootstrap sample(i.e. in any given tree grown) around one third of the cases from the original
training set will not appear there. These are called “out-of-bag” (oob) data.
Every time a particular case i is in the oob data with respect to a tree,
it is ‘run down’—that is, regressed—according to that tree and an (oob)prediction produced. Take the average of all those oob predictions for i (thatis, one for each tree where it is oob) and denote that value as ŷioob . Akin to
linear regression, we would like to know the percentage of the variance in ythat is explained by our model. For the current technique, this is computedas
1−

MSEoobσ̂y2Section 4.9

115

where

n

MSEoob =1X{yi − ŷioob }2ni=1where MSE is the mean square error (Liaw and Wiener, 2002, 20).

The importance of variable v is estimated by considering the decrease innode ‘impurities’ when v is split (i.e. it is part of a tree), averaged out over
all the trees in the forest. These impurities are measured via the residualsum of squares (RSS)—a formula we given in Appendix 4.7. We compare
the (average) value of RSS when v is in x and when it is not. Intuitively,
if the variable is ‘important’, it will be responsible for a better regression
performance: it will generally occur more often in the ‘best’ split and/or the
reduction in deviance when it occurs will be greater.

Finally, we will typically want to know the marginal effect that a variable v
has on y. Liaw and Wiener (2002) suggest estimating the function
˜ =
f (v)

n

1X
m(v, xiC )ni=1

where v is the variable of interest and xiC are all the other variables. The
element m(v, xiC ) is the (aggregated) random forest regression function (thepredicted y): the idea being that we vary the values of v (‘aye’ or ‘no’ in thecase of a roll call) to see the (predicted) effect on constituency performance.

Section 4.9

4.9

116

Imputing Missingness

Suppose that there is missingness in the underlying data (in the x). Beginby filling missingness in each column with the median (if continuous) ormodal (if discrete) category for that column. Then run a random forest
regression procedure and compute the proximity matrix: that is the fractionof times (across all the trees) that each i, j pair of cases ends up in thesame terminal node. For continuous missing data, the imputed value isthe weighted average of the non-missing data for that column, with theproximities as the weights. For categorical missingness—the case for ourwork here—the category with the largest average proximity (which will beeither ‘aye’ or ‘no’) is the imputed value. As a toy example consider avariable x = [0, 0, NA, 1]. Observation 3 is first filled with a 0 (since it is themost common category). Suppose that the resulting proximity matrix was




1
2
3
4





0.5 0.6 0.1
1|




2| 0.5

0.4
0.1




3| 0.6 0.4

0.2




4| 0.1 0.1 0.2
Observation 3 is with Observations 1 and 2 12 of the time, but with Observation 4 only 15 of the time: the largest average proximity is thus zero andwe impute this for the observation.

117

Chapter 5

Discussion
The preceding dissertation was concerned with three quite separate substantive areas, involving three somewhat different methods. What draws thechapters together is the focus on finding new solutions to ‘old’ problems:
identifying ‘turning points’ in conflicts; measuring the ‘power’ of politicalactors; describing the ‘effects’ of roll call voting on electoral support. The
essays all suggested thinking about these issues in new ways. In the firstchapter, we employed a change point identification technique that was notable for its flexibility: the number of parameters was, itself, a parameterto be estimated. In the second chapter, we argued that ‘power’ makes little
sense in the absence of ‘contests’ in which actors compete to garner finite
resources. Our statistical model reflected our (more realistic) assumptions
on this matter. In the third chapter, we argued that a very large numberof variables (i.e. roll calls) might collectively demarcate members of parliament in terms of their appeal to voters. Rather than employing an ad
hoc ‘thinning out’ of variables such that parametric models could be fit, weSection 5.0

118

decided to take a more systematic non-parametric approach.

In the individual chapters we made some comments about future uses ofthese techniques within their substantive areas, but it may be helpful tothink more generally about applications here. Reversible jump Markov
chain monte carlo, which we introduced in the first chapter, seems an intriguing tool for ‘cluster analysis’ in parliaments. Historically, ideal point
estimation (frequentist or Bayesian) has been a popular choice for analyzing legislatures (Clinton, Jackman and Rivers, 2004; Poole and Rosenthal,1997). A model of legislator behavior is posited in which elected members
compare the utility of the status quo relative to that the policy changed
potentially introduced by passing a new bill. A distribution for the error
terms is assumed—typically Type-1 extreme value or Guassian—to producea (parametric, random-utility) statistical model. On occasions, such models
produce misleading or unhelpful results. As noted in Chapter 4, Spirling and
McLean (2007) show that strong whipping in Britain’s House of Commons
produces rank ordering on an ‘agreement with the government’ dimension,
rather than an ideological spectrum. Clustering algorithms, which search forgroupings, are an alternative way to proceed. Some of these techniques—
optimal partitioning methods being among them (Venables and Ripley, 2002,316)— require an a priori commitment to a fixed number of clusters K towhich cases are then assigned. By contrast, other (typically ‘hierarchical’)methods fit numerous models (one for each value of k total clusters) whichmust then be compared. Since Bayesian procedures are philosophically appealing in terms of model comparison (see Gill, 2002, 199–224), they seemSection 5.0

119

a natural choice here. Moreover, because we would like to be flexible about
the number of clusters, RJMCMC would seem a particular good option.

The second essay (Chapter 3) made the case that we can consider political actors as players competing in contests. This is an idea with mileage
outside the current context. For example, at least since the time of theancient Greeks, scholars have studied the power of argument to convince
citizens. The earliest accounts were primarily interested in rhetoric as anart (e.g. Aristotle, 322BC/1991), though in more recent times, psychologists and economists have studied the consequences of ‘framing’ effects, especially with respect to risk-taking behavior (e.g. Tversky and Kahneman,
1981). In these cases, ‘arguments’ essentially ‘compete’ with respondents
either suggesting which they prefer directly, or voting commensurate with
their views. Using the Bradley-Terry model in the second chapter would
be one way forward here. Indeed, if one could properly separate competingarguments in, say, an election campaign, analysts could begin to model why
certain candidates win or lose. As constructed, the standard Bradley-Terrymodel assumes that contests involve two players, with one losing and one
winning. Over a series of (independent) contests, we make the reasonableassumption that success is binomially distributed. Of course, contests inpolitics are often more complicated. For example, US presidential primaries
and caucuses are typically three- or four-way competitions, at least in theearly stages. The same is true of British electoral contests, where Labour,
Conservative and Liberal Democrat candidates vie for success in parliamentary constituencies. Moreover, there are not always clear ‘winners’ andSection 5.0

120‘losers’: outcomes are often ‘tied.’ Paradoxically, this idea often holds inmajoritarian electoral systems where there is one winner and all others, in
effect, lose ‘equally’: for example, when candidates run for President of theFrance. An economic version of this holds when firms bid for public works
contracts. With these cases in mind, it would be helpful to think more generally about the Bradley-Terry model, perhaps facilitating the estimation ofabilities when contests have several players and when ties are possible.

The third essay (Chapter 4) claimed that, when the number of variables
to consider was greater than the number of parameters to be estimated,
one helpful way to proceed was the employment of a ‘random forests’ classification procedure. King (1989, 3) makes the case that political science“outdistances most other social sciences” in terms of data collection. For
data exploration purposes then, the model matrices are potentially verylarge. Moreover, translation from ‘theory’ to statistical model is typicallynot direct in political science: for example, a scholar may believe that ‘corruption’ has some systematic effect on citizen-to-citizen trust in a city , orthat ‘more proportional’ electoral systems give rise to fiercer intra-party
competition. In such cases, there are presumably several indicators andways of measuring the attributes of the independent variables and possibly
no way to a priori decide between them. Since non-parametric techniques
allow one to include literally hundreds more predictors than observations,these operationalization decisions can be refined within the (first) estimation‘round’ rather than on some ad hoc basis with knock-on effects for the study
as a whole. As data becomes increasingly available in massive amounts—

Section 5.0

121

especially via the internet—such work would seem important and valuable.
Of course, non-parametric fitting should not be considered the final stage
in any investigation of political actor behavior: nonetheless, it can help us
think more clearly about possible micro-mechanisms.

All told then, this dissertation has argued that our statistical solutions
should fit our problems, and has suggested several realms in which either
current practices might be improved, or where new profitable avenues of investigation exist. It would remiss of the author, however, to fail to addressa criticism of quantitative techniques that arises particularly in politicalmethodology. Phrased in various ways, typically implicit and casually suggested, the claim of some is that methodologists fetishize complexity in theirmodels; that is, much of political methodology is ‘complicated for the sakeof being complicated.’ This argument is imprecise, incorrect and unfair. It
is imprecise insofar as it can be applied—in its most basic form—to any
data analysis technique: logistic regression is ‘more complicated’ than OLS,
which is ‘more complicated’ than cross-tabs, which are ‘more complicated’
than frequency summaries. Otherwise put, it is unclear as to where theanalyst should draw the line: what extra utility must be garnered in order
to approve of a more complex technique? Moreover, such standards clearly
differ from scholar to scholar: reversible-jump Markov chain monte carlo
approaches might seem unaccessible to someone who know little of Bayesian
methods, but are a helpful and important extension for an analyst alreadyfamiliar with MCMC techniques. The claim is incorrect because it fundamentally misunderstands the goal of political methodology. The aim is toSection 5.0

122provide tools that help us understand political behavior; to the extent that
progress towards this goal remains incomplete (few if any would disagreewith this contention), ‘more’ or ‘better’ theory, methods and data are theway forward. It can surely never hurt to refine our techniques and our understanding of their capabilities. Note also that, in computational terms,
the costs involved with ‘complicated’ techniques have fallen precipitously
over time and will continue to do so. Finally, the claim is unfair because
it cynically assumes that methodologists either deliberately dissemble (andare thus dishonest in describing) their work, else they are simply incompetent in solving the problems that the discipline presents. Yet, one of thestrengths of work in methodology is that assumptions of models and techniques are both clearly laid out, and written in a language common to its
practitioners. It is certainly in this spirit that this dissertation is intended
as a contribution to the discipline.

123

Bibliography
Achen, Christopher H. 2002. “Toward a New Political Methodology: Microfoundations and ART.” Annual Review of Political Sience 5:423–50.
Agresti, Alan. 2002. Categorical Data Analysis. 2 ed. New York: John Wileyand Sons.
Alesina, Alberto and Allan Drazen. 1991. “Why are Stabilizations Delayed?”
American Economic Review 81(5):1170–1188.
Amadae, S. M. and Bruce Bueno de Mesquita. 1999. “The Rochester School:
The Origins of Positive Political Theory.” Annual Review of Political Science 2:269–295.
Aristotle. 322BC/1991.

Rhetoric.

New York: Oxford University Press(translation by George A. Kennedy).
Bachrach, Peter and Morton Baratz. 1962. “Two Faces of Power.” American
Political Science Review 56:947–952.
Banzhaf, John F. 1965. “Weighted Voting Doesn’t Work: A Mathematical
Analysis.” Rutgers Law Review 19:317–343.

Section 5.0

124

Barry, Brian. 1991. Is it Better to be Powerful or Lucky? In Democracy andPower. Oxford: Clarendon.
Beck, Nathaniel, Gary King and Langche Zeng. 2000. “Improving Quantitative Studies of International Conflict: A Conjecture.” American Political
Science Review 94(1):21–36.
Benedetto, Giacomo and Simon Hix. 2007. “The Rejected, the Ejected, andthe Dejected: Explaining Government Rebels in the 2001-2005 British
House of Commons.” Comparative Political Studies 40:755–781.
Black, Duncan. 1948. “On the Rationale of Group Decision-making.” Journal of Political Economy 56:23–34.
Brace, Paul. 1984. “Progressive Ambition in the House: A Probabilistic
Approach.” The Journal of Politics 46(2):556–571.
Bradley, R A and M E Terry. 1952. “Rank Analysis of Incomplete Block
Designs I: The Method of Paired Comparisons.” Biometrika 39:324–345.
Breiman, L., J. H. Friedman, R. A. Olshen and C. J. Stone. 1984. Classification and Regression Trees. Monterey, CA: Wadsworth and Brooks/Cole.
Breiman, Leo. 1996. “Bagging predictors.” Machine Learning 24(2):123–140.
Breiman, Leo. 2001. “Random forests.” Machine Learning 45:5–32.
Brooks, Stephen P. 1997. “Markov chain Monte Carlo Method and its applications.” The Statistician 47(1):67–100.

Section 5.0

125Budge, Ian. 1999. Critical Elections: British Parties and Voters in Longterm Perspective. London: Sage Publications.
Burke, Edmumd. 1774/1975. Speech to the Electors of Bristol. In Edmund
Burke: On Government, Politics and Society, ed. B.W. Hill. London:
Fontana.
Burnham, Gilbert, Riyadh Lafta, Shannon Doocy and Les Roberts. 2006.
“Mortality after the 2003 invasion of Iraq: a cross-sectional cluster sample
survey.” The Lancet (online) 10.1016/(S0140-6736(06)69491-9).
Butler, David and Donald Stokes. 1974. Political Change in Britain. 2 ed.
Macmillan.
Cain, Bruce E., John A. Ferejohn and Morris P. Fiorina. 1987. The Personal
Vote: Constituency Service and Electoral Independence. Cambridge, MA:
Harvard University Press.
Canes-Wrone, Brandice, David W. Brady and John F. Cogan. 2002. “Outof Step, Out of Offce: Electoral Accountability and House Members’ Voting.” American Political Science Review 96(1).
Carlin, Bradley, Alan Gelfand and Adrian Smith. 1992.

“Hierarchi-

cal Bayesian Analysis of Changepoint Problems.” Applied Statistics
41(2):389–405.
Chib, Siddhartha. 1998. “Estimation and comparison of multiple change
point models.” Journal of Econometrics 86:221–241.

Section 5.0

126

Clinton, Joshua, Simon Jackman and Doug Rivers. 2004. “The Statistical
Analysis of Roll Call Data.” American Political Science Review 98.
Cowan, Katherine. 2007. “Living Together: British Attitudes to Lesbianand Gay People.” Stonewall Poll by YouGov.
Cowley, Philip. 2002. Revolts and Rebellions: Parliamentary Voting Under
Blair. London: Politico’s Press.
Cowley, Philip. 2005. The Rebels: How Blair Mislaid His Majority. London:
Politico’s Publishing.
Cowley, Philip. 2006. “Strengthening the role of the backbencher.” Written
submission to the Select Committee on Modernisation of the House ofCommons Session 2006–07, no. 1.
Cox, Gary W. and Mathew D. McCubbins. 1993. Legislative Leviathan:
Party Government in the House. Berkeley: University of California Press.
Crewe, Ivor. 1983. The Electorate: Partisan Dealignment 10 Years On. In
Change in British Politics, ed. Hugh Berrington. London: Frank Cass
pp. 183–215.
Dardagan, Hamit and John Sloboda. 2006. “Iraq Body Count.”.
URL: http://www.iraqbodycount.net/
de Marchi, Scott, Christopher Gelpi and Jeffrey D. Grynaviski. 2004. “Untangling Neural Nets.” American Political Science Review 98(2):371–378.
Denver, David and Gordon Hands. 1997. Modern Constituency Electioneering. Portland, Oregon: Frank Cass.

Section 5.0

127

Dowding, Keith. 1996. Power. Minneapolis: University of Minnesota Press.
Downs, Anthony. 1987. An Economic Theory of Democracy. New York:
Harper.
Efron, Bradley and Robert Tibshirani. 1993. An Introduction to the Bootstrap. New York: Chapman & Hall.
Felsenthal, Dan S and Moshé Machover. 1998. The Measurement of Voting Power: Theory and Practice, Problems and Paradoxes. Cheltenham:
Edward Elgar.
Felsenthal, Dan S. and Moshé Machover. 2004. “A Priori Voting Power:
What Is It All About?” Political Studies Review 2:1–23.
Fenno, Richard F. 1973. Congressmen in Committees. Boston, MA: Little,
Brown and Company.
Filson, Darren and Suzanne Werner. 2004. “Bargaining and Fighting: The
Impact of Regime Type on War Onset, Duration, and Outcomes.” American Journal of Political Science 48(2):296–313.
Fiorina, Morris. 1974. Representatives, Roll Calls and Constituencies. Lexington, MA: Lexington Books.
Firth, David. 2005. “Bradley-Terry Models in R.” Journal of Statistical
Software 12.
Firth, David and Arthur Spirling. 2006. “tapiR and the Public Whip: Resources for Westminster Voting.” The Political Methodologist 14(2).

Section 5.0

128

Fowler, James H. 2006. “Connecting the Congress: A Study of Cosponsorship Networks.” Political Analysis 14(4):456–487.
Garrett, Geoffrey and George Tsebelis. 1999. “Why Resist the Temptation
to Apply Power Indices to the EU.” Journal of Theoretical Politics 11:291–
308.
Gill, Jeff. 2002. Bayesian Methods: A Social and Behavioral Sciences Approach. New York: Chapman & Hall/CRC.
Green, Peter J. 1995. “Reversible Jump MCMC computation and Bayesianmodel determination.” Biometrika 82(3):711–732.
Groseclose, Tim and Charles Stewart. 1998. “The Value of Committee
Seats in the House 1947–1991.” American Journal of Political Science42(2):453–474.
Hastie, David. 2005. Towards Automatic Reversible Jump Markov Chain
Monte Carlo PhD thesis University of Bristol.
Holler, Manfred and Mika Widgren. 1999. “Why Power Indices for Assessing European Union Decision-Making?” Journal of Theoretical Politics
11:321–330.
Huitt, Ralph K. 1957. “The Morse Committee Assignment Controversy: A
Study in Senate Norms.” American Political Science Review 51(2):313–
329.
Jackman, Simon. 2004. “Bayesian Analysis for Political Research.” Annual
Review of Political Science 7:483–505.

Section 5.0

129

Jacobson, Gary. 1989. “Strategic Politicians and the Dynamics of House
Elections, 1946-86.” American Political Science Review 83:773–93.
Janis, Irving L. 1972. Victims of Groupthink. Boston: Houghton Mifflin
Company.
Johnson, Catherine and Gemma Rosenblatt. 2007. “Do MPs have the ‘Right
Stuff’ ?” Parliamentary Affairs 60:164–169.
Kam, Christopher. 2006. “Demotion and Dissent in the Canadian Liberal
Party.” British Journal of Political Science 36:561–74.
Kam, Christopher. 2007. On Division: Cohesion, Discipline, and Intraparty Politics. University of British Columbia: Book manuscript underreview.
Kass, Robert E. and Adrian E. Raftery. 1995. “Bayes Factors.” Journal of
the American Statistical Association 90(430):773–795.
Kelso, Alexandra. 2007. “The House of Commons Modernisation Committee: Who Needs It?” British Journal of Politics and International
Relations 9:138–157.
Key, V. O. 1949. Southern Politics in State and Nation. New York: Knopf.
King, Gary. 1989. Unifying Political Methodology: The Likelihood Theory of
Statistical Inference. Ann Arbor: University of Michigan Press.
King, Gary. 2001. “Proper Nouns and Methodological Propriety: Pooling Dyads in International Relations Data.” International Organization
55(2):497–507.

Section 5.0

130

Krehbiel, Keith. 1991. Information and Legislative Organization. Ann Arbor: University of Michigan Press.
Krehbiel, Keith. 1998.

Pivotal Politics: A Theory of U.S. Lawmaking.

Chicago: University of Chicago Press.
Lane, Jan-Erik and Sven Berg. 1999. “Relevance of Voting Power.” Journalof Theoretical Politics 11:309–320.
Lasswell, Harold. 1936. Who Gets What, When and How. New York: Whittlesey House.
Leech, Dennis. 2002a. “Computation of Power Indices.” Warwick Economic
Research Papers (644).
Leech, Dennis. 2002b. “An Empirical Comparison of the Performance ofClassical Power Indices.” Political Studies 50(1):1–22.
Leonte, Daniela, David J. Nott and William T. M. Dunsmuir. 2003.
“Smoothing and Change Point Detection for Gamma Ray Count Data.”
Mathematical Geology 35(2).
Liaw, Andy and Matthew Wiener. 2002. “Classification and Regression byrandomForest.” R News 2(3).
Marx, Karl. 1967. Das Kapital. New York: International Publishers. English
Translation.
Mayhew, David R. 1974. Congress : the Electoral Connection. New Haven:
Yale University Press.

Section 5.0

131

McCarty, Nolan, Keith Poole and Howard Rosenthal. 2006. Polarized America: The Dance of Ideology and Unequal Riches. Cambridge, MA: MIT
Press.
McLean, Iain, Arthur Spirling and Meg Russell. 2003. “None of the Above:
The UK House of Commons Votes on Reforming the House of Lords,
February 2003.” The Political Quarterly 74:298–310.
Norris, Pippa. 2001. New Labour and Public Opinion: The Third Way as
Centrism? London: Macmillan pp. 32–44.
Norton, Philip and David M. Wood. 1993. Back from Westminster: British
Members of Parliament and their Constituents. Lexington: University of
Kentucky Press.
Paltzelt, W. 2000. What Can an Individual MP Do in German Parliamentary Politics. In The Uneasy Relationship Between Parliamentary Members and Leaders. London: Frank Cass.
Park, Jong Hee. 2006. “Modeling Structural Changes: Bayesian Estimationof Multiple Changepoint Models and State Space Models.” Prepared forAmerican Political Science Association Meeting August, 2006, Philadelphia.
Pattie, Charles, Edward Fieldhouse and R. J. Johnson. 1994. “The Price ofConscience: The Electoral Correlates and Consequences of Free Votes andRebellions in the British House of Commons, 19897–92.” British Journalof Political Science 24:359–80.

Section 5.0

132

Pattie, Charles J., Ronald J. Johnston and Edward A. Fieldhouse. 1995.
“Winning the Local Vote: The Effectiveness of Constituency Campaign
Spending in Great Britain, 1983-1992.” American Political Science Review
89(4):969–983.
Poole, Keith and Howard Rosenthal. 1997. Congress: A Political Economic
History of Roll Call Voting. New York: Oxford University Press.
R Development Core Team. 2006. R: A Language and Environment for Statistical Computing. Vienna, Austria: R Foundation for Statistical Computing. ISBN 3-900051-07-0.
URL: http://www.R-project.org
Riker, William. 1962. The Theory of Political Coalitions. New Haven: Yale
University Press.
Riker, William. 1964. “Some Ambiguities in the Notion of Power.” American
Political Science Review 58(2):341–349.
Riker, William. 1982. Liberalism Against Populism. San Francisco: W. H.
Freeman.
Riker, William. 1986. The Art of Political Manipulation. New Haven: Yale
University Press.
Ripley, Brian D. 1996. Pattern Recognition and Neural Networks. Cambridge: Cambridge University Press.
Rohde, David W. 1979. “Risk-Bearing and Progressive Ambition: The CaseSection 5.0

133

of Members of the United States House of Representatives.” American
Journal of Political Science 23(1):1–26.
Rohde, David W. 1991. Parties and Leaders in the Postreform House.
Chicago: University of Chicago Press.
Ruger, Theodore W., Pauline T. Kim, Andrew D. Martin and Kevin M.
Quinn. 2004. “Competing Approaches to Predicting Supreme Court Decision Making.” Perspectives on Politics Symposium 2.
Salter, Lee. 2004. “Parliament and The Parliamentarians: The Worrying
Case of the City of London (Ward Elections) Bill.” Political Quarterly
75:155–167.
Searing, Donald. 1994. Westminster’s World: Understanding Political Roles.
Cambridge, MA: Harvard University Press.
Shapley, L.S. and Martin Shubik. 1954. “A Method for Evaluating the Distribution of Power in a Committee System.” American Political Science
Review 48:787–92.
Shepsle, Kenneth. 1979. “Institutional arrangements and equilibrium in
multidimensional voting models.” American Journal of Political Science
23:27–60.
Shepsle, Kenneth and Barry Weingast. 1987. “The institutional foundationsof committee power.” American Political Science Review 81:85–104.
Spirling, Arthur and Iain McLean. 2007. “UK OC OK? Interpreting Opti-

Section 5.0

134

mal Classification Scores for the United Kingdom House of Commons.”
Political Analysis 15(1).
Springall, A. 1973. “Response surface fitting using a generalization of the
Bradley-Terry paired comparisons model.” Applied Statistics 22:59–68.
Stam, Allan C. and D. Scott Bennett. 2006. “Predicting the Length of the2003 U.S.-Iraq War.” Foreign Policy Analysis 2(2):101–116.
Stigler, S. 1994. “Citation Patterns in the Journals of Statistics and Probability.” Statistical Science 9:94–108.
Stuart-Fox, Devi M., David Firth, Adnan Moussalli and Martin J. Whiting.
2006. “Multiple Signals in Chameleon Contests: Designing and Analysing
Animal Contests as a Tournament.” Animal Behaviour 71:1263–1271.
The Economist. 2006. “Indoor rainforests: Rejecting Eden.” Print Edition
Jul 13.
Tsebelis, George. 2002. Veto Players: How Political Institutions Work.
Princeton, N.J.: Princeton University Press.
Tversky, Amos and Daniel Kahneman. 1981. “The Framing of Decisions
and the Psychology of Choice.” Science 211:453–458.
Venables, William and Brian Ripley. 2002. Modern Applied Statistics with
S. New York, New York: Springer.
Wawro, Gregory. 2000. Legislative Entrepreneurship in the US House ofRepresentatives. Ann Arbor: University of Michigan Press.

Section 5.0

135Western, Bruce and Meredith Kleykamp. 2004. “A Bayesian Change Point
Model for Historical Time Series Analysis.” Political Analysis 12:354–374.
Winston Churchill, Sir. 1954. “Duties of a Member of Parliament.” Parliamentary Affairs 8.