Identifying Intra-Party Voting Blocs in the
UK House of Commons∗
Arthur Spirling†

Kevin Quinn‡

June 29, 2009

Abstract
Legislative voting records are an important source of information about legislator preferences, intra-party cohesiveness, and the divisiveness of various policy issues.
Standard methods of analyzing a legislative voting record tend to have serious drawbacks when applied to legislatures, such as the UK House of Commons, that feature
highly disciplined parties, strategic voting, and large amounts of missing data. We
present a method (based on a Dirichlet process mixture model) for analyzing suchvoting records that does not suﬀer from these same problems. Our method is modelbased and thus allows one to make probability statements about quantities of interest.
It allows one to estimate the number of voting blocs within a party or any other groupof MPs. Finally, it can be used as both a predictive model and an exploratory model.
We illustrate these points through an application of the method to the voting recordsof Labour Party MPs in the 1997-2001 session of the UK House of Commons.

∗This work has beneﬁted from helpful comments from panel participants at the 2005 Annual Meeting of
the American Political Science Association, the 2005 Political Methodology Summer Meeting, and the 2005
Joint Statistical Meetings as well as seminar participants at Stanford University and Washington University.
Quinn’s research is supported by National Science Foundation grants SES 03-50613 and BCS 05-27513. Two
referees and an Associate Editor provided very thorough comments that improved the content and structureof our paper. We are indebted to the Editor for his helpful advice and assistance.
†
Department of Government and The Institute for Quantitative Social Science, Harvard University.
aspirling@gov.harvard.edu‡
School of Law, University of California, Berkeley. kquinn@law.berkeley.edu

11Introduction
Scholars of legislative politics frequently rely on legislative voting records to make in-ferences about the policy preferences of legislators (Poole and Rosenthal, 1985, 1991, 1997;
Heckman and Snyder, 1997; Clinton et al., 2004), the types of political issues that drive
political conﬂict (Poole and Rosenthal, 1997; Cowley and Garry, 1998), the cohesivenessof parties (Hix, 2002; Rosenthal and Voeten, 2004; Desposato, 2003) and the existence of
intra-party factions (Cowley, 2002; Rosenthal and Voeten, 2004) among other things. In
general, the methods used by political scientists to analyze such voting data are best applied
to voting records from legislatures, such as the US Senate and House of Representatives,that feature relatively weak parties composed of fairly autonomous legislators (Spirling and
McLean, 2007). The reason for this is that the usual models rely on a number of structural assumptions that are typically not even approximately met in parliamentary systems
with highly disciplined parties organized around the dichotomy between government andopposition. In what follows, we present a nonparametric model that does perform well (forboth exploratory data analysis and predictive inference) when applied to voting data froma parliament with extremely disciplined parties.
We apply this model to parliamentary votes from the UK House of Commons during theﬁrst Blair government (1997-2001), which has been of speciﬁc interest to political scientists
for several reasons—not least the fact that it represented the ﬁrst change in party controlof British politics for over 18 years. Moreover, as the ﬁrst ‘New’ Labour government it was
seemingly an uneasy alliance: on the one hand was a leadership that had actively abandoned
the tenants of socialist policy-making and that had received a landslide mandate to rule. On
the other was a historically and openly recalcitrant tranche of ‘Old’ Labour legislators,
dismissive of the modernizing project in its entirety. There was thus much speculation that
explosive divisions and factions would soon emerge to enervate the newly elected Prime

2

Minister.
Our primary object of interest is the identiﬁcation and interpretation of blocs of MPs
who have similar expected voting proﬁles. While much has been written on intra-party
factions in the UK (Cowley, 2002; Shaw, 1988; Berrington and Hague, 1998; Spirling and
McLean, 2007) most of this work relies on relatively crude methods of data analysis. By
taking a more sophisticated model-based approach we hope to sharpen existing insights into
intra-party divisions within the UK Labour Party. In addition, we hope to provide a set oftools that can be usefully applied to parliamentary voting more generally.
This paper is organized as follows. In the next section we brieﬂy discuss voting in the
UK House of Commons. In Section 3 we discuss previous approaches and their shortcomings
when applied to UK roll call data. In Section 4 we describe our nonparametric model.
Section 5 presents results from our analysis of the 1997-2001 UK data, and comments on
how this new approach might contribute to recent substantive debates in political science.

2

Divisions in the UK House of Commons
The majoritarian nature of the British electoral system ensures that the Prime Minister

is the leader of the largest party by vote share, and will hold a majority of seats in Parliament(Adonis, 1990, p. 21–25). The executive—the cabinet, headed by the Prime Minister—isfused with the legislature in that it essentially controls the business of the House of Commons.
This business refers to the proposing and passing of legislation, and also to the timetablingof the debate on these matters. Formal (and informal) rules of parliament enable inﬂuenceby the non-governmental parties throughout the parliamentary session; these are essentiallylimited to the opportunity to debate and counter-propose legislation.
The largest parliamentary party not in government forms the “Oﬃcial Opposition.” They
are joined on the opposition benches by all other (smaller) parties which are also outside of
the government. Though technically incorrect, we use the term “opposition” as a catch-all3

for the non-government parties here. As its moniker suggests, the opposition’s de facto role
is to oppose the government’s legislation. Since it normally lacks a uniﬁed political agenda(perhaps other than to defeat the government), the opposition’s constituent parts may give
dissimilar, even conﬂicting, reasons for their decision to vote (typically) contrarily to thegovernment’s agenda.
Congruent with this adversarial legislative principle, a member of parliament (MP) relies
on party patronage for career advancement, and their election at the constituency level isalmost solely a product of their party label (and that party’s current fortunes) rather thantheir personal appeal to voters (Jennings, 1969). Almost all voters base their localized ballot
box decision on the party labels of those competing: constituent service as a foundation of(re)election—in the US sense of pork-barreling localized beneﬁts—is absent.
By and large then, roll calls in the United Kingdom parliament amount to either supporting or opposing the government’s proposals. The parties are highly cohesive in voting:the great majority (approximately 99 percent) of divisions are whipped, insofar as the respective party leaderships state a party line which MPs are expected (and have incentives)to toe. Rebeling—in the sense of voting against the oﬃcial party line—scuppers promotion
prospects and leads to demotion where applicable. If rebels are particularly reckless, thewhip may be withdrawn (see Silk, 1987, p. 46-48). This latter punishment is the equivalentof expulsion from the parliamentary party, and usually prohibits the opportunity to run forthat party at the next (and subsequent) general election(s). Contrast this situation with
the US Congress where Representatives and Senators from diﬀerent parties form shifting
coalitions from bill to bill.
Given this logic, it should be clear that a government party MP rebels when she votes
against the explicit wishes of the government, and with—in terms of the similarity of the“Aye” or “No” division choice—the opposition parties. In particular, notice that these
rebels need not agree substantively with any of the opposition parties’ positions on the bill:4

for example, the government party rebels may feel some government bill does not allocate
suﬃcient funds to public spending (“not enough!”), whilst others (particularly amongst the
opposition) hope to defeat the bill on the converse basis that the proposal is proﬂigate (“toomuch!”). Note that this logic is clearly inconsistent with the assumption of sincere policybased voting that is at the heart of standard statistical models (Poole and Rosenthal, 1985,
1991, 1997; Heckman and Snyder, 1997; Clinton et al., 2004) of legislative voting. We now
clarify this point before developing a diﬀerent modeling strategy.

3Previous Literature and Approaches
Early analysis of roll calls includes the foundational work of Rice (1928) who suggested astraightforward and well-known index, here denoted r, which attempts to capture the unityof a party on any particular vote. That is,
r = 100|p − (1 − p)|where p is the proportion of the party voting ‘aye’ on the roll call. When scholarly interest
centers on aggregate party voting, the index is very helpful: it allows us, for example, tocompare the Labour party over the course of the parliament (mean r = 96.99, std dev=
11.65) to the main Conservative opposition (mean r = 96.19, std dev=14.54). However, it
tells us little about the number or membership of intra-party blocs (we will use ‘groups’
interchangeably in what follows) in the House of Commons—which is the focus here. This
critique applies equally to related metrics that consider the number of divisions on whichsome (arbitrary) proportion of the party votes similarly (see, e.g., Lowell, 1901).

3.1

Scaling and Projecting

Contemporary analysis of roll calls typically proceeds via an item-response approachsimilar to that implemented in the education testing literature as the one, two or three5

parameter item response theory model (see Rasch, 1961; Birnbaum, 1968; Lord, 1980). In
this setup, ‘test-takers’ are the legislators and the ‘items’ are the bills to be voted on:
rather than ‘ability’, we seek the representatives’ ‘ideal points’ which are located in somemultidimensional space. For political scientists, this modeling approach has a particularly
tidy behaviorial justiﬁcation, in that it can be seen as an empirical implication of the spatial
theory of voting (Downs, 1957; Poole, 2005). A standard version of this setup has a legislator
with ideal point xi ∈ R considering a choice between the ‘aye’ position ζj and ‘no’ (or ‘statusquo’) position ψj for the jth bill. If legislators have quadratic utility functions over thepolicy space, the relevant comparison is between the utility garnered from the proposal,
Ui (ζj ) = −||xi − ζj ||2 + ηij versus the utility from the status quo, Ui (ψj ) = −||xi − ψj ||2 + νij
where || · || is the Euclidean norm and η and ν are error terms. The observed data is the rollcall matrix Y with a typical element yij being zero (if the ith legislator votes to retain thestatus quo) or one (if she votes for the new proposal). With distributional assumptions on
the stochastic disturbances, estimation may be via (some version of) maximum likelihood(e.g. Poole and Rosenthal, 1997) or by way of Markov chain Monte Carlo techniques (e.g.
Martin and Quinn, 2002; Clinton et al., 2004).
Notice that, typically, no a priori restrictions are placed on the bills or members includedin the analysis and that the researcher does not use any bill-speciﬁc (‘this vote was about
farming subsidies’) or legislator-speciﬁc knowledge (‘this Senator is in the Republican party’)to obtain estimates of the parameters of interest. In the context of Westminster politics,
such scaling procedures will naturally place the government loyalists and the opposition atalternate ends of the ideological space since they have diametrically opposed records: theopposition votes non-sincerely and attempts to defeat the government at any opportunity.
Meanwhile the rebels, who vote ‘with’ the opposition some positive proportion of the time,
will be placed somewhere in the ‘middle’ (Spirling and McLean, 2007). No straightforward
post-estimation rotation or stretching of that space can resolve the diﬃculty. Table 1 sum6

marizes this problem, and reports the relative positions of ﬁve members whose comparative
ideological positions and ‘types’ are well known in the Westminster politics literature (see,e.g, Cowley, 2002). To represent the loyalists, we report results for Giles Radice who wasan early reformer of the Labour party known for his fealty to the Blair Government understudy, and John Prescott, a former leftist who was deputy leader of the Government during
this period. Jeremy Corbyn and Dennis Skinner are, respectively, the most and the tenthmost ‘rebellious’ of the 1997-2001 Labour MPs, in terms of defying their party whip. The
last member for consideration is William Hague, leader of the Conservative party and of the
opposition, and no doubt to the right ideologically of the House of Commons as a whole. The
table reports the estimated parliamentarian positions from three popular routines common
in political science: a non-parametric cutting procedure known as ‘Optimal Classiﬁcation’(Poole, 2000), a scaling model known as ‘NOMINATE’ (Poole and Rosenthal, 1997) and a
two-parameter probit model estimated via MCMC with diﬀuse priors (Clinton et al., 2004).
The data consist of the votes of every Labour and Conservative MP on every division. The
results clearly clash with our strong substantive priors; we see the left-wing rebels to the rightof the loyalists, and closer to the Conservative opposition than the Government apparatchiks.

There are, of course, simpler alternatives to those suggested above, and MacRae (1970)
discusses several. The researcher could, for example, obtain the Euclidean (or other) distance
between rows of the roll call matrix Y, and then apply, say, principal component analysis to
the resulting dissimilarities. A practical concern here is how to deal with missing observations
in Y , but, no matter how that is solved, the problem noted above reemerges. Consider thepartition of the distance matrix that includes just the rows dealing with our example MPs, as
displayed in Table 2. Again, we see that Hague, the opposition leader, is ‘closer’ to Corbyn(the left-wing Labour rebel) than he is to Prescott (the government loyalist). Unsurprisingly,
neither principal components analysis nor factor analysis does much better.
7

ideological space(groups)expected order
estimated rank
[Optimal Classiﬁcation]
estimated position[NOMINATE]
estimated position[Bayesian 2P probit]

Left
RebelsCenterGovt Loyalists
Prescott
RadiceRight
Opposition
Hague

CorbynSkinner

Radice [8.5]

Prescott [304.0]

Skinner [399.0]

Corbyn [419.0]

Hague [535.5]

Radice [-0.90]

Prescott [-0.85]

Skinner [-0.60]

Corbyn [-0.56]

Hague [0.90]

Radice [-0.14 ]Prescott [-0.14]

Skinner [-0.13]

Corbyn [-0.12]

Hague [0.15]

Table 1: Estimation of various MPs’ spatial locations with standard routines. At the top of the table,in the ﬁrst row, we give the expected positions/ordering from left to right: in reality, Corbyn and Skinner
are the most left-wing, Prescott and Radice and somewhere in the middle while Hague is to the rightof all the other members. The second row [in brackets] gives the estimated rank order of the members inquestion, via ‘Optimal Classiﬁcation’. The third and fourth rows give the estimated ideal points [in brackets]from two popular routines common in political science. Notice that non-sincere voting by the oppositionmeans that ‘Rebels’ from the governing party are placed ‘in the middle’ when we estimate their location
with standard statistical models: to the right of the Government and to the left of the opposition. For
example, substantively we know that Radice should have an ideal point closer to Hague, than Corbyn has
to Hague—yet we see the opposite in rows 2, 3 and 4.

CorbynSkinner
Prescott
Radice
Hague

Corbyn
0.00
5.63
10.75
10.01
33.74

Skinner
5.63
0.00
8.83
8.20
34.17

Prescott
10.75
8.83
0.00
3.73
34.35

Radice
10.01
8.20
3.73
0.00
34.54

Hague
33.74
34.17
34.35
34.54
0.00

Table 2: Distance matrix (partition of whole matrix) for MPs in running example. Notice that Corbyn is‘closer’ to Hague than Prescott is to Hague. This does not accord with our priors about ideological position.

8

3.2

Clustering

Explicitly searching for groups within parties is a sensible alternative to ‘scaling’. Part of
the appeal stems from the fact that we need not assume independence among observations
when interpreting the clusters. Rather than asserting that individuals have latent traits (andthat their errors are independent of one another) cluster approaches are congruent with aconglomeration of members who may be actively inﬂuencing one another to vote certainways.
The methodological options are many. Of the partition approaches, K-means (and its
derivatives) is perhaps best known (MacQueen, 1967; Hartigan, 1975). Standard drawbacks
include the fact that missingness is not handled by the routine and the number of clusters
must be a priori speciﬁed (much as the number of dimensions must be decided for an item
response approach). This latter point means that searching for an ‘optimal’ choice of K
is not generally possible. Instead, one can conceive of the data as the result of a mixture
distribution, the ‘optimal’ number of components of which may be estimated (Fraley andRaftery, 2002). Typically though, these techniques assume that the mixture is composed ofmultivariate normals, which is an odd modeling choice when the voting responses in question
are binary. This criticism similarly applies to model-based hierarchical clustering algorithms.
In any case though, investigating the substantive nature of the clusters is problematic. This is
primarily because we do not have immediate access to the criteria—in terms of the divisions—around which the clusters form. Thus, we cannot know from the estimation itself whether
a cluster corresponds to, say, ‘pro-life members’ or ‘anti-death penalty liberals’ or ‘antitax libertarians’ etc. Hartigan (2000) considers a ‘partition model’ wherein each bloc oflegislators votes similarly to one another on some set of bills; this approach allows for possible
cross-party voting that would seem incompatible with projecting the roll matrix to one or two
dimensions. Though estimated via Markov chain Monte Carlo, Hartigan’s method does not

9facilitate explicit comparison of models via a posterior over the number of blocs in the data,
which might have a philosophical appeal from a substantive political science stand point.
Moreover, the approach is reasonably computationally intensive: for 100 senators, and 101
votes, a billion partition pairs must be checked. In our whole data set (i.e. Labour andmain opposition members), there are 591 legislators, and 1278 bills—suggesting a somewhat
larger estimation problem.
All told, studying intra-party blocs is suitably approached as a clustering problem.
Desiderata include a model-based method that allows for a binomial data-generating process.
We would like to make uncertainty statements over cluster membership and know on what
basis the blocs are divided. Moreover, we would prefer an approach that is able to deal withmissing observations in a reasonable manner.

4

A Nonparametric Model for Divisions Data
Before describing the model’s formal components, it is important to be clear about thephilosophical task at hand. We wish to provide a sensible summary of the data that has
internal validity—i.e. we wish to uncover patterns in the roll calls that are helpful to substantive researchers. We are less concerned about the external validity of our estimates;
otherwise put, we are not attempting to provide a general empirical picture of Westminster
politics for all times and situations.
Let i = 1, . . . , I index MPs and j = 1, . . . , J index divisions. Our goal is to model the
I ×J matrix of observed votes by the I MPs on the J divisions. We let Y denote this matrix,
yi denote the vector of votes speciﬁc to MP i, and yij the observed vote of MP i on division
j. By convention, we code yij = 1 if MP i voted “Aye” on division j, yij = 0 if MP i voted“No” on division j, and yij is coded as missing if a formal vote was not recorded for MP i on
division j. All data analyzed below are from Firth and Spirling (2005), who have written apackage for the R statistical language and environment—called tapiR—that downloads roll10

call records and formats them in a helpful way for analysts.

4.1

The Likelihood

Given the binary nature of the observed vote matrix, a natural choice for the likelihoodof MP i’s vector of observed votes yi is:J∏yL(yi |θ i ) =θijij (1 − θij )1−yij

(1)

j=1

where 0 ≤ θij ≤ 1 gives the probability that MP i votes “Aye” on division j for j = 1, . . . , J.
We assume that missing values of yij do not enter into the product above. Assuming thevotes of MPs i and i′ are independent given θ i and θ i′ for all i and i′ we can write thelikelihood of the entire observed vote matrix as:
L(Y|θ) =I ∏J∏yθijij (1 − θij )1−yij(2)i=1 j=1

As the reader can easily see, the likelihood has as many free parameters as there are observed
data points and is thus primarily useful as a starting point for a hierarchical model rather
than a ﬁnal probability model in its own right. The next subsection details the prior usedin our model and shows how this prior greatly reduces the eﬀective number of parameters
to be estimated.

4.2

The Prior

Our modeling strategy borrows heavily from recent work on Bayesian nonparametrics(Escobar and West, 1995, 1998; Neal, 2000; Dahl, 2003; see also Ferguson, 1973; Blackwell
and MacQueen, 1973; and Antoniak, 1974). In particular, we assume that each θ i is a priori
drawn from a distribution G:[θ i |G] ∼ G.
Our model can be considered nonparametric in that we do not specify the parametric formof G. Instead, we assume that G is generated by a Dirichlet process with parameters α and11

λ which we write as:[G|α, λ] ∼ DP(αG0 (·|λ)).
Here G0 is the centering distribution and represents, in a certain sense, one’s best guess
as to the shape of G. The α > 0 is a concentration parameter that determines how close
realizations of G are to the centering distribution G0 . As α gets larger, realizations of G
tend to more closely resemble G0 . Finally, λ represents a vector of hyperparameters that
determine the shape of G0 . For the work in this paper we assume that G0 is the distribution
with density}J {∏Γ(λ1j + λ0j ) λ1j −1
λ0j −1g0 (θ i |λ) =θ(1 − θij ).
Γ(λ1j )Γ(λ0j ) ij
j=1

In words, G0 is the product of J beta distributions.
One property of the Dirichlet process that is of use in our application is that realizationsof G will be discrete with probability one (Ferguson, 1983). This property of the Dirichlet
process is useful in our application because it allows us to view our model as a countably
inﬁnite mixture model and to perform inference not only about which MPs are likely tocluster together in voting blocs (i.e., have the same value of θ) but also about the number ofdistinct voting blocs. In what follows, we let K denote the number of discrete support pointsof G. We note that the value of the concentration parameter α induces a prior distribution
over K– as α gets larger more mass is assigned to larger values of K.
To complete the model, prior distributions for α and λ need to be chosen. While α
could be ﬁxed at a user-speciﬁed value we prefer to give it a proper prior distribution andestimate it. In what follows we assume that α follows a gamma distribution with shape a0
and inverse scale b0 . As noted above our prior beliefs about α imply prior beliefs about the
number K of clusters. Herein, we set a0 = 4 and b0 = 0.75. Via simulation it was found thatwhen α is equal to its prior 5th percentile (1.82) 10 clusters contain 95% of 400 observations.
When α is set equal to its prior median (4.90) 20 clusters contain 95% of 400 observations.

12Finally, when α is set equal to its prior 95th percentile 33 clusters will contain 95% of 400
observations. These numbers seem reasonable to us given what we know about the amountof party discipline in the British Labour Party during this time period.
We complete the prior by assuming λ0j = λ1j = 0.1 for all j = 1, . . . , J. This is consistent
with a prior belief that the expected probability of a randomly chosen MP voting “aye” ona randomly chosen division j (θij ) is the same as the expected probability of that MP voting“no” on that division (1 − θij ) and that these probabilities are not close to 0.5. Speciﬁcally,
our assumption implies that under the centering distribution Pr(θij > 0.95) = Pr(θij ≤0.05) = 0.378. This prior decision is consistent with our goal of ﬁnding voting blocs thatare relatively homogenous in terms of observed votes. Allowing for more prior mass near 0.5
would allow for more within-bloc heterogeneity which we explicitly want to avoid.
It is important to be clear about the nature and stringency of the independence assumptions—
across votes and across MPs—being made in our model. As per Equation (1), we requireconditional independence of MP i’s voting decisions given MP i’s vector of vote probabilities(θ i ). Since θ i has as many elements as there are voting decisions, and we have chosen to set
the prior so that most of the elements of θ i are very close to either 0 or 1, this independence
assumption is relatively innocuous. Relatedly, we assume that yi is independent of yi′ given
θ i and θ i′ (see Equation 2). While this assumption is unlikely to be correct, we don’t see
this as particularly problematic if our goal is to summarize an existing vote matrix. Notethat if θ i = θ i′ MPs i and i′ are in the same cluster, thus a very strong form of dependence isactually allowed in our setup. The conditional independence assumptions we make would be
more worrisome if we hoped to use our model to examine counterfactuals of the sort, “howwould MP i vote if MPs i′ and i′′ both vote ‘aye’ ?”. We are not interested in such questions
here.

13

5

Results
Our primary focus is on identifying intra-party voting blocs in the British Labour Party

during the ﬁrst Blair government (1997-2001) along with the divisions that separated thesemajor groupings of MPs. In what follows, we analyze the Labour MPs behavior without
reference to the behavior of MPs from rival parties. With two exceptions, no Labour MP
has a voting record that even remotely resembles the voting record of any Conservative MP.
The exceptions are Shaun Woodward and Peter Temple-Morris who switched parties during
the 1997-2001 session of Parliament.

5.1

Labour Party Voting Blocs 1997-2001

After dropping unanimous votes and MPs who never voted (along with the party-switches
Shaun Woodward and Peter Temple-Morris) we have I = 424 Labour MPs and J = 198
non-unanimous (within the Labour MPs) divisions during the 1997-2001 Parliament. In
Figure 1 we summarize the data. The thin grey line in the main body of the plot records the
proportion of the party voting in the minority for any given bill in the data set (which arearranged chronologically on the x-axis). Notice that this proportion has reasonable varianceover time, although its moving average—described by the broken loess line—is relatively
low. The thick black line gives the cumulative proportion of members who have voted withthe minority of their party as each bill occurs. Note that, of 424 members, almost every
single one has deviated from the majority view at least once by the time the parliamentends. Finally, the x-axis itself is the mean proportion of members voting diﬀerently to themajority over all (1279) bills in the parliament. This is very close to zero, demonstrating
the generally strong party discipline in the Commons. All told, it is not immediately clear
whether there are multiple distinct subgroups of Labour MPs who tend to vote similarly.
Our modeling goal is to determine this.
The priors used to generate the results discussed below are that α ∼ Gamma(4, 0.75)
14Figure 1: Voting Summary for Labour MPs 1997-2001. Thin grey line is proportion of MPs
voting in minority on any given vote (broken line is loess moving average of this proportion).
Thick black line is cumulative proportion of MPs voting in minority over time. The interceptof the x-axis with the y-axis is the mean proportion (essentially zero) of MPs voting withthe minority of their party over the entire universe of bills for the period—which includes
some 1279 divisions.
and λ0j = λ1j = 0.1 for j = 1, . . . , J. As noted above, the prior for α was chosen based on
our prior beliefs about the number of groups and that fact that we believe that there will
be very few occasions when it is sensible to think the probability of an MP voting in either
direction is close to 0.5.
The model was ﬁtted to the Labour data using Markov chain Monte Carlo (MCMC).
Details of the MCMC algorithm employed are provided in Appendix A. The chain was run
for 510,000 iterations and the ﬁrst 10,000 iterations were discarded as burn-in. Because ofmemory constraints every 100th draw after burn-in was stored for a total of 5000 stored
draws.

15

Pr(K = k|Y)

k = 10 k = 11 k = 12 k = 13 k = 14
0.0478 0.4402 0.4418 0.0684 0.0018

Table 3: Posterior Distribution of Number of Clusters (Labour 1997-2001).
Figure 2 shows the marginal posterior density of α. As can be seen here, there is information in the data about the likely value of α. In particular, the data suggest that α istoward the lower end of the range we deemed a priori likely.

Figure 2: Marginal Posterior Density of α in ﬁt to Labour 1997-2001 Data. The dark line isa kernel density estimate of the marginal posterior and the light line is the Gamma(4, 0.75)
prior density.
The α parameter is really of interest primarily because of its eﬀect on the number ofclusters (voting blocs) that are supported by the data. Looking directly at the posterior
distribution over the number of clusters K is a more intuitive way to get some sense of theextent of clustering. This distribution is presented in Table 3.
As can be seen from Table 3, there is strong evidence that there are either 11 or 12
distinct voting blocs within the Labour party during the ﬁrst Blair government. The posterior
16

probability of their being either 11 or 12 blocs is 0.882.
While the number of voting blocs is of some interest we are primarily concerned with thesize and membership of each of the blocs. Because the number of clusters is not constantand the cluster labels are completely arbitrary (and change over the course of the MCMC
sampling) it is not meaningful to look at the number and identities of MPs in a cluster witha particular label. Instead, we focus on the probability that any two Labour MPs are in
the same cluster for all pairs of Labour MPs; i.e., Pr(θ i = θ i′ ), i = 1, . . . , I, i′ = 1, . . . , I.
These probabilities do not depend on the cluster labels or the number of clusters and arethus meaningful quantities. Taken together, these probabilities deﬁne an I × I matrix P.
It is worth emphasizing that P contains qualitatively diﬀerent information than thatusually examined by scholars of Westminster voting. In particular, previous work focusses
almost exclusively on voting in the Commons in terms of ‘rebellion’ by backbenchers. In
those accounts, behavior is binary: either MPs obey the whip, or they do not. Exemplars
in this vein include comprehensive tomes by Norton (1975; 1980) and detailed accounts
by Cowley (2002; 2005) where the goal is to describe particular episodes of dissent, those
involved and the eﬀect on policy making. In this undertaking though, notice that we are
not constrained by previously deﬁned categorization of either MPs (‘rebellious’, ‘loyalist’etc) nor divisions (‘controversial’, ‘whipped’ etc). Indeed, several of our clusters below arise
from bills that few scholars would necessarily know a priori were useful for categorization ofactors. The result is thus a more nuanced picture of behavior and structure in the (governing)
Labour party. Some scholars, e.g. Dunleavy (1993), have looked at intra-party dimensions of
conﬂict beyond a ‘left’ versus ‘right’ or ‘leadership’ versus ‘backbenchers’ dichotomy thoughsuch accounts do not often use data to test hypotheses per se. Thus our approach andﬁndings provide a new testing ground for such accounts.
Since P is too large to summarize directly, we sort the matrix to reveal the underlying
groups. We do this as follows. First, we create a dissimilarity matrix D based on Euclidean
17

distance between the columns of P (we experimented with several metrics, and all give
approximately similar results). Seriation with a minimized Hamiltonian path is then used tosort the rows and columns of P. This creates a two-dimensional representation of the MPs’
expected voting proﬁles in which MPs with similar voting proﬁles are located adjacent toeach other (see Hahsler et al., 2008, for details). The results are plotted in Figure 3, and thenames refer to individuals we discuss below. Darker (square) areas are groups that are tightly
bound together in terms of their cluster membership. Notice that the plot is symmetric, butthat there is no substantive sense in which we have a continuum of groups from, say, ‘left’to ‘right’ in the party; this logic applies similarly to our use of nominal numerical labels forthe blocs in what follows.
5.1.1

Core Loyalists

The ﬁrst bloc are the core Labour government loyalists who consistently support the
government on almost all divisions. It is very likely to contain the Prime Minister Tony
Blair, the Chancellor Gordon Brown and Foreign Secretary Jack Straw. Indeed, with justthree exceptions, every other member of the Cabinet that served between 1997 and 2001
inhabits this group. Intriguingly, of these three ministerial deviants, two were ﬁred in 1998
after just a year of service to the Prime Minister. This group also includes the majority ofthe members joining the Commons for the ﬁrst time in 1997. Bloc 11 is made up of similarly
loyal MPs such as Giles Radice, an early reformer in the ‘New Labour’ mould, along withDavid Blunkett, the Prime Minister’s ﬁrst choice for Secretary of State for Education. The
primary diﬀerence between this group and the core loyalists is over the choice of Speaker.
In the House of Commons, this is a non-partisan position, in which the governing party
often has a preferred candidate but whose election it does not whip. In this particular case,these MPs were less supportive of the purely loyalist choice of Michael Martin (the eventual
winner). All told, the loyalists constitute about sixty percent of all Labour members.

18

5.1.2

Leftists

Bloc 9 are the ‘hardcore’ rebels in the parliamentary party, who took a general disliking
to the government’s policy plans. This group includes ‘usual suspects’ like Diane Abbott,
Tony Benn, Bernie Grant and Jeremy Corbyn. All of these members are part of the left-wing‘Socialist Campaign Group’ that criticizes New Labour relentlessly from the backbenches.
They disapproved of government attempts to, inter alia, cut beneﬁts to lone parents anddisabled people, to privatize the national air control system, and to reform trial-by-jury
procedures. Other groups in the data are similar to this leftish caucus, but are exorcized byparticular subsets of issues: the welfare socialists of Bloc 4 (which includes former coal miner
Dennis Skinner) were keen to avoid changes to the beneﬁt system; Lawrence Cunliﬀe (whoforms Group 2) was unimpressed with plans to cut funding for university students; Bloc 3,
which includes the ﬁred cabinet minister David Clark, wanted the Freedom of Information
Act (2000) to go much further.
5.1.3

Mavericks

Several members, and several groups, are not best described as either loyal or rebellious.
Instead, they take unusual lines on certain (typically free) votes, that suggest they are
ideologically diﬀerent to the bulk of their colleagues. For example, members of Blocs 1(which includes sometime minister Tony Banks) and 10 generally felt that the City of London
Ward Election bill—which dealt with possible democratization of an ancient arrangement
for municipal governance in the capital—should go further in giving citizens voting rights.
By contrast, Blocs 6 and 8 were concerned that legislation dealing with ﬁrearms would
inappropriately punish law-abiding sporting shooters. Intriguingly, Bloc 6, which includes
Kate Hoey (now the chair of a major countryside interest group), was unusually keen on
fox hunting, a position associated with rural and aristocratic conservatives. For a party
that stresses equal rights and opportunities, it is odd that members such as Denzil Davies
19(forming Bloc 7) and those in Bloc 5 would be sceptical of government-backed plans to
reduce the age of homosexual consent from 18 to 16 (thus bringing it on par with that ofheterosexual consent). Nonetheless, these individuals made their views known in the voting
lobbies of the Commons.

Banks, Tony
Cunliffe, Lawrence
Skinner, Dennis

Hoey, Kate
Corbyn, Jeremy
Blunkett, David
Blair, Tony

Figure 3: Seriation Representation of Expected Voting Groups (Labour MPs 1997-2001).
Loyalists are bottom right dark square. MPs in bloc 1 are in the upper left corner (TonyBanks). MPs in bloc 12 are in the lower right corner (Tony Blair). Numbering of the blocs
proceeds down the main diagonal from 1 to 12.

5.1.4

Judging the Extent of Rebellious Behavior

To gain some additional insight into the nature and degree of rebellious voting behavior
in the Labour party during this time period we calculate an average voting proﬁle for each of20

the voting blocs. We let ȳk denote the average voting proﬁle for bloc k. The jth element of∑ȳk is simply taken to be the sample average ȳk,j = I −1 i∈Bk yi,j , where Bk denotes the kth
voting block as derived from the seriation of P above. With these average voting proﬁles in
hand we can make a number of comparisons between groups to examine the extent of theirdivergence in voting behavior. Our measure of voting similarity between bloc k and bloc k ′
is
s

i,i′

=1−J

−1

J
∑

I[|ȳk,j − ȳk′ ,j | > 0.5]

j=1which is 1 minus the fraction of absolute diﬀerences in average votes that are greater than
0.5. A value of 1 indicates that blocs k and k ′ have identical voting proﬁles, while a value of
0 indicates that all elements of the voting proﬁles diﬀer by more than 0.5.

Figure 4: Degree of Similarity to Labour Loyalists
and Socialist Campaign Group Rebels.
∑J−1
The y-axis in the left panel depicts 1 − J
j=1 I[|ȳ12,j − ȳk,j | > 0.5] and the y-axis in the∑J−1right panel depicts 1 − J
j=1 I[|ȳ9,j − ȳk,j | > 0.5]. Note that that even after excluding
Bloc 8 (which only consists of two MPs) that similarity to the Labour Loyalists (Bloc 12) is
not monotonically related to similarity to the Socialist Campaign Group (Bloc 9). This isconsistent with there being multiple types of “rebellious” voting in the House of Commons.
Note that the horizontal location of each point has been shifted purely for display reasons.
Figure 4 presents comparisons of all blocs to the Labour loyalist group (group 12) andall blocs to Bloc 9 (the Socialist Campaign Group rebels). Here we see that even the blocs
21

most similar to the Labour loyalists diﬀer substantially from the loyalists on about 5% ofvotes. On the other hand, four of the eleven non-loyalists blocs diﬀer substantially from theloyalists on between 20 and 50% of the votes. It is also the case that blocs that appear to beroughly equally similar to the loyalist bloc (say blocs 3 and 5) have very diﬀerent similarities
to the Socialist Campaign Group bloc. This highlights the point that the groups are being
formed not just on the basis of their similarity to the Labour loyalists but on their overallsimilarity to other voting groups. Finally, note that ranking blocs by their similarity to bloc
12 does not produce the inverse similarity ranking of those same blocs to group 9. Thissuggests that the nature of voting within the Labour party cannot be accurately captured
by a single dimension measuring loyalty to the government.
5.1.5

Diﬀerence vs Dissent, 1992–2005

Our approach here is a complement to, rather than a substitute for, earlier work thatconsiders ‘dissent’ as the key behavior of interest (e.g. Garner and Letki, 2005; Kam, 2001).
We can build on accounts such as Benedetto and Hix (2007), for example, who argue thatrebellion is most likely for backbenchers who are ‘rejected’ for promotion to higher oﬃce, or‘ejected’ from the front benches, having been ﬁred for some reason or other. While the P
matrix of bloc probabilities will certainly take the instances of rebellion into account, it will
also be conditioned on instances of ‘diﬀerence’ in less whipped votes. Moreover, the P matrix
can be calculated for diﬀerent subsets of the rolls calls—which allows a time component to
be introduced to the analysis. To see how this might work, consider Figure 5 whereineach subplot shows the diﬀerence between ﬁve MPs and the median MP’s closeness to theloyalist bloc for the Labour party in any given year. Nick Ainger, a long serving member
from the core loyalist group provides the baseline for the loyalist comparison. Here we haveextended the analysis, mutandis mutatis, to 1992–2005 which covers the period before Blairbecame leader of the Labour party and just before he stepped down (and have included party

22

switchers). The plots may be interpreted straightforwardly: when the lines rise, the MP is
becoming more likely a part of the loyalist cluster; when they fall, she is more likely to bepart of a diﬀerent (non-loyalist) cluster. The broken lines represent election dates. The ﬁrst
row is Tony Banks, a veteran left-winger who is, in fact, remarkable similar to the median
MP in terms of his probability of being within the loyalist cluster over time. This is despite
his promotion and then ﬁring as Sports Minister in 1999. By contrast, Jeremy Corbyn, inthe second plot, is very average in his behavior until just after the 1997 landslide election.
He then moves in a more rebellious direction than the median Labour MP, before starting tovote with the government again just before the 2001 election. By the time of the Iraq war, in
2003, he is has seemingly abandoned the loyalists for good. In the third row, Kate Hoey is anunusual case: a loyalist and latterly a minister until 2001, she is then ﬁred and moves froma zenith of loyalism to a grouping entirely separate from them. The loyalists do not seem tolose the Vauxhall MP for good, however, and she returns to the fold brieﬂy in 2002. As noted
above, Hoey is not necessarily in the same camp as Corbyn ideologically: for example, atleast part of her distance from the average Labour member is due to her outspoken support
in the Commons for fox hunting. A less nuanced story emerges for Glenda Jackson (fourthrow), who entered parliament in 1992 and was gradually promoted to government roles withmore responsibility. Perhaps unsurprisingly, she is no more or less loyalist than the median
MP during this time. Upon leaving front bench politics in 2000 (in an eﬀort to run for
Mayor of London) she remained relatively loyal, but then moved far from the median justafter the 2001 election and towards the left-wing of the Labour party. The last subplot isthat of Shaun Woodward, a loyal Conservative MP (and thus a member of the opposition)
who switched parties in 1999 and instantly became loyal to his new masters in the Labour
party.
These plots are hardly conclusive, but they do begin to illustrate the extra depth researchers can obtain by modeling voting records in terms of probabilistic clustering. Rather
23

Figure 5: Probability proﬁle, in terms of ‘loyalist’ cluster membership, for diﬀerent ‘types’ of
MPs over time in the House of Commons. Broken lines are election dates: ‘a’ denotes theperiod in parliament before the election in a given year and ‘b’ the period after.
than trying to laboriously code every division as whipped or unwhipped, and then to ‘countup’ the instances of deviant behavior to be used as a dependent (or independent) variable,
our approach allows analysts to directly and unavoidably compare and contrast MPs with
their colleagues. This facilitates a more helpful relative positioning and classiﬁcation labelthat has some of the strengths of scaling without the misleading inferences that arise with‘oﬀ-the-shelf’ methods. Moreover, unlike the foregoing literature on Westminster politics,
we can straightforwardly obtain the relevant divisions that ‘probably’ contribute to the proﬁles in the plot, without resorting to arranging every member on a crude ‘rebel’/‘loyalist’
continuum.

24

5.2

Model Fit

To get some sense as to how our model ﬁts the data we employ a posterior predictive
check (Gelman et al., 1996), that is similar in spirit to those discussed by Gelman (2004)
and Buja (2004). Speciﬁcally, we generate 19 new roll-call matrices from the appropriate
posterior predictive distribution. We then display image plots of these matrices in Figure 6
along with the observed roll call matrix. The observed roll call matrix is put in a randomly
chosen position. If it is the case that the model does a poor job of capturing observed
patterns in the data then the observed roll call matrix should be easily spotted in the 5 × 4“lineup” in Figure 6. We submit that the observed data are not easily detected and thus
this check provides no evidence of poor model ﬁt.

6Discussion
The modeling strategy discussed here has much to recommend it as a purely exploratory

method. It is model-based and thus allows for statements of uncertainty about all quantities
of interest. Further, model-based approaches do not suﬀer from the need to make essentiallyad hoc choices about a distance metric and/or how to handle missing data. However, unlike
standard model-based clustering methods (Banﬁeld and Raftery, 1993) we do not ﬁx thenumber of clusters a priori. Instead, we estimate the number of clusters and allow theuncertainty about this number to propagate naturally to the ﬁrst-level model parameters ofmost direct interest (the vote probabilities).
From a practical perspective, our method works well on real data from the UK House ofCommons. It allowed us to ﬁnd meaningful groupings of MPs within the Labour Party. Thesevoting blocs make substantive sense and accord well with more in-depth qualitative analyzesof the House of Commons during this period (Cowley, 2002). Similarly, we demonstrated
how our approach can be used to identify key divisions and conﬂictual issues. It is worth

25

Figure 6: Posterior Predictive Replications Along with Observed Data. The rows have beenorganized by group membership and the columns have been sorted ﬁrst by observed majority“No” vs. majority “Aye” and then by the number of non-missing observed votes within eachof these two groupings. Dark pixels represent “No” votes, light pixels “Aye” votes, and white
pixels missing values. The observed data are in fourth row from top and second column fromleft.
noting that this was accomplished with nothing more than the observed vote matrices. For
this reason, our method may be of some use as a tool for more qualitative researchers
whose goal is a detailed examination of key pieces of legislation and key factions within theparliamentary parties. Rather than sifting through the entirety of a parliamentary voting

26

record, researchers can use our approach to identify key votes and groupings of MPs thatare worthy of more detailed analysis.

27

A

The MCMC Algorithm
We begin by introducing some additional notation. Let ϕ1 , . . . , ϕK denote the uniquevalues of θ 1 , . . . , θ I (the support points of G). Let ci ∈ {1, . . . , K} denote the cluster
membership of MP i, i = 1, . . . , I. Speciﬁcally, ci = k ⇐⇒ θ i = ϕk .
One scan of the MCMC sampling scheme used to ﬁt the models discussed in this paper
is the following:
1. (a) Draw [c|Y, λ, α]or(b) Draw [ci |Y, c−i , λ, α] for i = 1, . . . , I
2. Draw [ϕk |Y, c, λ, α] for k = 1, . . . , K
3. Draw [λj |Y, ϕ, c, α] for j = 1, . . . , J
4. Draw [α|Y, ϕ, c, λ].
Step 1a) above is accomplished using the merge-split sampler of Dahl (2003) while step1b) uses algorithm 3 of Neal (2000). Every 3rd scan attempted a merge or split while theother scans used Neal’s algorithm 3 to sample c. It should be noted that the conjugacyof the beta centering distribution to the Bernoulli sampling density makes this step quite
straightforward. All that is required is the ability to evaluate a beta-binomial density andthe willingness to take care of some rather tedious bookkeeping.
Given Y, c, λ, and α, ϕkj follows a Beta(n1kj + λ1j , n0kj + λ0j ) distribution where n1kj
denotes the number of “Aye” votes on division j by MPs i = 1, . . . , I for which ci = k andn0kj denotes the number of “No” votes on division j by MPs i = 1, . . . , I for which ci = k.
Realizing that ϕ1 , . . . , ϕK are an iid sample from G0 (·|λ) (Escobar and West, 1998, p.

2812) we can write the full conditional in step 3) as:p(λj )K∏

g0 (ϕkj |λj )k=1

where p(λj ) is the (possibly degenerate) prior density for λj . We use the univariate slice
sampling algorithm of Neal (2003) to sample from this full conditional.
Finally, given the gamma prior we adopt for α, it is possible to use the data augmentation
approach of Escobar and West (1995) (see also Escobar and West (1998)) to sample α. Thisis the approach used in this paper.

29

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