Political Analysis Advance Access published November 22, 2006

doi:10.1093/pan/mpl009

UK OC OK?
Interpreting Optimal Classification Scores for
the U.K. House of Commons
Arthur Spirling
Department of Political Science, University of Rochester, NY 14627
e-mail: spln@mail.rochester.edu (corresponding author)

Iain McLean
Nuffield College, Oxford University, Oxford OX1 1NF, United Kingdom
e-mail: iain.mclean@nuffield.ox.ac.uk

Poole’s (2000, Non-parametric unfolding of binary choice data. Political Analysis 8:211–37)
nonparametric Optimal Classification procedure for binary data produces misleading rankorderings when applied to the modern House of Commons. With simulations and qualitative
evidence, we show that the problem arises from the government-versus-opposition natureof British (Westminster) parliamentary politics and the strategic voting that is entailed therein.
We suggest that political scientists think seriously about strategic voting in legislatures wheninterpreting results from such techniques.

1 Introduction

Party cohesion and whipping in the U.K. House of Commons suggests that the errors
across legislators and roll calls are not independent and identically distributed. As a result,parametric scaling techniques, which rely on this assumption, are inappropriate. In suchcircumstances, one possible solution is to use Poole’s (2000) Optimal Classification (OC)procedure (e.g., Rosenthal and Voeten 2004).
A sample of the rank ordering that the Poole (2000) OC procedure yields for the periodof the first Blair government (1997–2001) in the U.K. House of Commons is given in
Appendix A.1 If the technique has worked as expected, Appendix A ought to be an edited
list of Members of Parliament (MPs) from the most liberal parliamentarian in the Commons to the least liberal, from the least conservative to the most conservative. In terms ofparties, the ranking is as expected: the Labour party, which has socialist origins, occurs tothe ‘‘left’’ (lower) than the right-wing Conservative party and the placement of the Liberal
Democrats toward the center is quite plausible.

Authors’ note: Financial and technical support from The Star Lab is gratefully acknowledged. We are very
grateful to three anonymous referees for insightful comments on both content and structure. All errors andomissions remain ours and ours alone.
1
The full list is available on application from the authors. Appendix C gives some replication information thatreaders may find helpful.
Ó The Author 2006. Published by Oxford University Press on behalf of the Society for Political Methodology.
All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org

1

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Arthur Spirling and Iain McLean

Problematically, the last 30 scaled positions for Labour include MPs such as
Tam Dalyell (position 409), Robert Marshall-Andrews (411), Dennis Skinner (412),
Jeremy Corbyn (420), Diane Abbott (415), Tony Benn (417), Ken Livingstone (422),
and Bernie Grant (426). To be clear, OC classifies these MPs as some of the most rightwing of the Labour party. Ideologically then, they are the closest to the Conservatives. This
seems odd. Commentators—for example, Cowley (2002)—have not been slow to citesome or all of these individuals as Labour rebels, but not for the reason suggested by
the attendant analysis. Rather, these members are widely accepted as ideologically left
wing. Yet, here we observe them being placed right of their Prime Minister and, in fact,
the entire Cabinet.
Appendix B gives the iterations report from the OC rank order for 1997–2001. From thefirst iteration there are practically no classification errors (just 1% by the 10th iteration):the proportion of those correctly classified by the simple OC rearrangement of cut points
and then legislators is some 99.1%. By contrast, for the U.S. 107th Senate, the comparable
figure was 91.9%. Voting at Westminster seems ‘‘perfect’’ in one dimension.
This note argues that strategic, ‘‘government versus opposition,’’ voting at Westminster
leads to OC rank orderings that cannot be interpreted as ideological continua. We explain
our ‘‘possibility result’’ formally and informally in Section 2. In Section 3, we marshal
numerical, simulation evidence for our contention. In Section 4, we discuss some qualitative evidence and simulate a (we think) compelling counterfactual scenario based on
imputed sincere Conservative preferences that yield results consistent with our hypothesisthat strategic voting drives the misordering. In Section 5, we conclude and suggest future
avenues of research.
2 ‘‘Government versus Opposition’’ and OC

OC consists of two sequentially repeated algorithms: a cutting plane procedure and a legislative procedure. More formally, and drawing heavily on Poole (2000; 2005, 49–59), for
one dimension the OC procedure consists of four stages:
1. There are p legislators and s 5 1 dimensions of voting. The p  s 5 p  1 matrix
that contains the ideal points of the legislators is denoted x. First, generate starting
values for x, which will be iteratively improved (below). To do so, calculate the p p agreement score matrix where the ‘‘agreement score’’ between two members(voters, legislators) is the proportion of the divisions (roll calls) in which they
vote the same way. This agreement matrix is converted to a matrix of squared
distances, then double centered. Extracting the first eigenvector of thistransformed matrix gives the starting values, which in this case are a rankordering (Poole 2005, 49).
2. Fix the legislative rank ordering, use the Janice algorithm to find the optimal cutting
point ordering. For p legislators, on any particular roll call, there are a total of p þ 1
rank positions for a cut point, which will divide those who are predicted to vote‘‘aye’’ from those who are predicted to vote ‘‘no.’’ If the number of bills is n, thenthere are n total cut points. The cut points are picked such that they maximize thenumber of correct classifications. This means that, on any particular bill, the numberof misclassified legislators—i.e., those for whom the cutting line predicts they voted‘‘aye’’ but they actually voted ‘‘no’’ or the cutting line predicts they voted ‘‘no’’ butthey actually voted ‘‘aye’’—is minimized. When there are two or more cut points
that would maximize correct classification, the algorithm picks the one closer to thecenter of the legislator rank order (Poole 2005, 55). Notice that for two (or more)UK OC OK?

3

separate bills, there is no problem in having two (or more) cut points equal to one
another. We now have a joint ordering of legislators and cut points interspersed. As
an example, for p 5 5 members with ideal points x1 through x5, and n 5 4 bills, with
cut points b1 through b4, we might now have:

x2 , b2 , x1 5 x3 , b1 , x5 , b3 5 b4 , x4 :3. Holding the cutting point ordering fixed, use the Janice algorithm to find the optimal
legislator ordering. Because we have a (one-dimensional) joint ordering—fromstep 2—we have the polarity for each bill. That is, we are predicting one voting
side, ‘‘aye’’ or ‘‘no,’’ to be the ‘‘left’’ or ‘‘right’’ on any particular roll call. For
example, above we are predicting that legislators 2, 1 and 3 vote ‘‘left’’ on billnumber 1, whereas legislators 5 and 4 vote ‘‘right’’ on that roll call. Clearly, for nroll calls there are n þ 1 possible legislator positions. For any particular legislator,
the algorithm places him ‘‘left’’ or ‘‘right’’ relative to each roll call such that the
number of errors—in terms of his predicted ‘‘aye’’ or ‘‘no’’ votes on the bills—isminimized. This is done for all of the p legislators. When two or more rank positions
produce the same (maximum) correct classification, the algorithm picks the rank
position for the member that is closest to the median of the roll call cutting point
rank ordering (Poole 2005, 57).
4. Return to step 2 and repeat.
OC assumes that legislators’ preferences are single peaked and symmetric and the
choice space is Euclidean (Poole 2005, 46–48). Crucially, legislators are assumed to ‘‘vote
sincerely for the alternative that is closest to their ideal point’’ (Poole 2000, 212). The
resulting rank order is, in theory, that of the legislators’ ideal points. Conventionally,
analysts would interpret this ranking as an ideological spectrum.
The central problem is that not all MPs in the modern House of Commons votesincerely and proximally. Notice first that the governing party proposes almost all legislation voted upon at Westminster and controls the legislative agenda. Usually, the official
opposition will vote against a government bill in favor of the status quo, even when thestatus quo is further from their ideal point than the proposed policy. In this sense, Westminster systems are government versus opposition, and strategic voting by opposition MPs
simply to defeat the government, regardless of the issue, is common. By contrast, government party dissident MPs ‘‘rebel’’ when they vote their sincere preference against the
explicit wishes of the government and with—in terms of ‘‘aye’’ or ‘‘no’’—the opposition
parties. Rebelling is costly for dissidents because it can lead to punishment: these MPs will
be passed over for ministerial promotion and may be deselected for future elections (i.e.,the central party can decide not to allow them to compete for a seat). Hence, there is anobservational equivalence between the behaviors of rebel MPs from the governing party
and MPs from the opposition party that belie important differences in their true (sincere,ideological) preferences. Scaling techniques like OC will fail to distinguish between thesequite different motivations and place the two groups together in ranking terms.
More formally, suppose there are two types of parliaments demarcated by their legislators’ preferences. Actors in a type I parliament have preferences over policy x, which are
Euclidean with a quadratic loss function, represented as follows:ui ðxÞ 5 j x  xi j2 ;where, of course, xi is MP i’s ideal point.

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Arthur Spirling and Iain McLean

These actors vote sincerely and will be properly ranked by OC. By contrast, actors in
the type II parliament—of which type I is a special case—have single-peaked, symmetricpreferences over policy represented asui ðxÞ 5 j x  xi j2 þðI  ni Þ:Here, I is an indicator function taking the value 1 when the bill under consideration is
proposed by the government, and ni  0 if the MP is a member of the governing party andni  0 otherwise. So, ni represents the ‘‘strategic incentive’’ that MPs have to either support
or oppose the government regardless of their sincere preference over policy. In particular,
we expect that rebels with ni 5 0 vote sincerely. To elucidate our informal logic about why
OC will struggle to produce an ideological continuum in such cases, consider Example 1
and Example 2.
Example 1. Suppose there are three players, Far Left (FL), Left (L) and Right (R) with
ideal points satisfying xi 2 R1 ; in particular, xFL , xL , xR. Suppose there are n 5 2 bills,
with cut points bj 2 R1 ; j 2 f1, 2g, which relative to the status quo (SQ) and the ideal
points satisfy xFL , SQ , xL 5 b1 , b2 , xR and jb2  xL j . jSQ  xL j: Heuristically, we
could suppose b1 is proposed by the government (L), and b2 is not.
Then, when voting is of type I (sincere), OC will recover the correct rank ordering, xFL ,xL , xR.2
Explanation: Under sincere, type I, voting the matrix of votes will appear as

Bill

FL

L

R

1
2

0
0

1
0

1
1

where ‘‘1’’ is an ‘‘aye’’ vote and ‘‘0’’ is a ‘‘no’’ vote. Here OC will recover the correct
rank order, with no classification errors: no matter what the starting estimate of thelegislators’ order is, the cutting vector will be estimated as ðcI1 ; cI2 Þ; where cI1 2 ½xFL ; xL 
and cI2 2 ½xL ; xR : But then, only the correct order xFL , xL , xR can result from theprocedure.
Example 2. Ceteris paribus, consider a type II parliament in which nL 5 nFL 5 0 but nR
is sufficiently large (and negative) such that uR ðb1 Þ 5 jb1  xR j2 þ I  nR , uR ðSQÞeven though xFL , SQ , xL 5 b1 , b2 , xR : That is, R votes strategically in opposition
to the government on b1, even if the bill is an improvement for R relative to the status quo.
Then, OC will recover an incorrect rank ordering xL , xFL , xR.3

2

Notice that the ordering xFL , xL , xR is, in practice, equivalent in one dimension to xR , xL , xFL since thetechnique is ‘‘blind’’ in terms of which ‘‘end’’ is left or right. For simplicity, and with no loss of generality, weonly deal with the former case here.
3
We are assuming that Left proposes a bill at its own ideal point, though this is not necessary to make the example
work: all that is required is that SQ , xL , b1 , xR and that Right votes strategically for SQ.

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UK OC OK?

Explanation: Now, the voting matrix will appear as
Bill

FL

L

R

1
2

0
0

1
0

0
1

The cutting vector will be estimated as ðcII1 ; cII2 Þ; where cII1 2 ½xL ; xFL  and cII2 2 ½xFL ; xR ;
in which case L can be placed left of FL—reducing errors to zero—to give
Bill

L

FL

R

1
2

1
0

0
0

0
1

Once again, voting is perfect, but the conclusion that xL , xFL , xR is incorrect.
This is exactly what we saw when we applied OC to the U.K. House of Commons: farleft rebels appear between the moderate left government and the right opposition. In thenext section we test and extend our hypothesis with some simulations.
3 Experiments

We simulated a Westminster style parliament with 700 members organized in three groups
according to our examples above with ideal points relative to the status quo at zero: a Far
Left (100 members, ideal point at 4), a Left (300,2) and a Right (300, 2) group. Initially,
we assumed that 1000 policies (roll call votes) are proposed by the Left (in government)group and that they are distributed along the ideological spectrum, but clustered around thegovernment’s ideal point, as N ðl 5 2; r2 5 4Þ: Members behave as modeled above
with the indicator taking the value 1 for all policy proposals and ni varying as described
below. Members cast an ‘‘aye’’ vote if ui(x) . ui(SQ) and vote ‘‘no’’ otherwise. We
analyzed the resulting vote matrix with OC.
We claim that the opposition (Right) drives the result we observe because it votes
strategically. But the quantity of strategic voting can vary in two senses. First, we candirectly manipulate the magnitude of nR to capture the extent to which the Right is being
whipped across all the bills. We began by setting a large value of jnij for both Left andRight such that the former would always vote for the government’s proposals and the Right
would vote against. This placed the Far Left in the center of the OC ranking (position 301–400), exactly as expected. Next we held nL constant and allowed the Right’s degree ofstrategic voting to vary. Interestingly, we found a threshold effect: below a certain level ofnR voting was sufficiently sincere to ensure a ‘‘correct’’ ranking (with Far Left placed
positions 1–100); above the threshold, the Westminster result held, and the Far Left ismisplaced. So, once a (threshold) degree of strategic voting is introduced to the opposition
party, our claimed dynamic holds.
A second way in which strategic voting may vary pertains to the number of ‘‘free’’votes in the Commons. That is, we could assume that there is some proportion of bills
on which the party leaderships simply impose no order at all, but rather allow theirmembers to vote their conscience. On the other bills, nR is constant. Here, we supposed
again that the Left bloc always backs their own (government) policy, the Far Left
always votes sincerely, but that the Right votes strategically q percent of the time

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2

4

6

8

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Arthur Spirling and Iain McLean

2

4

6

8

10

Fig. 1 Effect of altering jnRj and jnFLj. Filled circles correspond to a correct OC ranking, and open

triangles correspond to incorrect OC ranking.

(i.e., on q percent of the roll calls). Interestingly, OC recovers the correct rank order until
q 5 60: i.e., the Right bloc is voting strategically well over half of the time. Hence, it seems
that part of the problem is the sheer number of strategic voting roll calls at Westminster.
Next, we allowed the Right and Far Left to vary in their response to government (Left)policy. In Fig. 1 we summarize these results. For some 75 combinations of nR and nFL wejudged the OC ranking to be correct if it returned nFL , nL , nR and incorrect otherwise.
The former classifications are denoted by filled points, whereas the incorrect classifications are open triangles. Notice that when jnij for the blocs is large—such that both groups
are voting strategically for all votes (nFL  9; nR  7)—the Far Left is placed incorrectly inthe middle of the rank order. We also found that once jnRj became sufficiently small (nR 3) such that not all voting was strategic, for even large values of jnFLj, so long as jnFLj 
jnRj, the correct rank ordering emerged. However, if jnFLj , jnRj, the Far Left group wasonce again placed to the right of the Left bloc. In general, this implies that when the incentive
to vote strategically—in absolute terms—is stronger for the opposition than the left-wing
rebels, the rebels will be misplaced. Notice that the few correct recoveries of the ordering forhigh levels of nFL (nFL  9) correspond to a counterfactual scenario where the Far Left hasa very high strategic incentive such that the Far Left essentially always votes for thegovernment. In this situation, the occasional deviation by Left members (due to an errorterm) will pull them toward the Right and the correct order may emerge.
Finally, we investigated an alternative governing circumstance where the Far Left wasable to propose its own policy (i.e., it was in government). In particular, policy was
distributed N ðl 5 4; r2 5 4Þ: We now allowed the Left group to vote sincerely on
all bills while employing a sufficiently high jnFLj, jnRj to ensure strategic voting on allbills by the extremes of the parliament. We found that the OC ranking was now correct: it
placed the Far Left , Left , Right in terms of rank ordering.

UK OC OK?

7

In short, the problem of the OC rank ordering for our simulated Westminster is exactly
a function of a moderate government (occasionally) proposing policy that a more radical
wing sincerely opposes and an opposition strategically opposes. In the next section wemove to some more qualitative evidence in favor of our claims.
4 Qualitative Evidence

The essence of the critique offered above is that, on any one division, either Labour rebels
voted against the government on matters of principle, whereas the Conservative opposition did so strategically, or vice versa. One way to show this is to consider some of thespecific bills over which the rebels dissented, and contrast their public statements—which
hopefully reveal their preferences—with those of the opposition. Cowley (2002, 22–93)
gives a thorough discussion of the issues that divided left-wingers from their more
conformist colleagues in the 1997–2001 parliament. In particular, three of the largest
rebellions (in terms of numbers of MPs) were on the Welfare Reform and Pensions Billof 1999 (74), the Transport Bill of the same year (65), and the Criminal Justice Bill of2000 (37) (Cowley 2002, 92). Briefly, and drawing on Cowley, we consider each inturn here.
The Welfare Reform and Pensions Bill dealt inter alia with reforms to the way that thestate paid incapacity benefit to the disabled. In particular, it proposed means tested benefits
and reduced payments for those who had made private provisions for health care4 or
pensions. Some 68 MPs signed an Early Day Motion,5 penned by Roger Berry (a Labour
backbencher), which called. . . upon Her Majesty’s Government to give more consideration to a more generous set of arrangements for those recipients of incapacity benefit who draw upon occupational pensions. [EDM 375,
1999]

Commensurate with this principled rhetoric, several MPs who would later rebel madeseemingly ideological statements in Commons’ debates on the subject. The Conservative
opposition is by both reputation and ideological commitment generally critical of broadbased state benefits funded by taxation. So, in response to Berry’s proposed amendment to
the government bill—an amendment that would drop means testing—we might therefore
expect the Conservatives to join Labour and overwhelmingly reject it precisely becausemeans testing disability benefit is presumably an improvement for the Conservatives
relative to the status quo. In practice, the Conservatives supported the amendment, andvoted with the rebels.6 This support included the then shadow (opposition) Secretary ofState for Social Security, Iain Duncan Smith. In this case, the Labour rebels appear to havevoted sincerely and the Conservatives strategically.
There is a similar story for the Transport Bill in which the privatization of the National
Air Traffic Control System was opposed by the rebels for ideological reasons, whereas
the Conservatives voted against the government and, contrary to their key industrial
policy of the 1980s and 1990s, strategically. Similarly the Conservatives backed the rebel
amendments that opposed the government on its proposals to reform the trial-by-jury
process: from the party that had prided itself for its toughness on crime and criminals,
this was surely a strategic act.
4

The United Kingdom has a ‘‘National Health Service’’ that funds medical services from general taxation, free atthe point of delivery.
A public statement by MPs that will not be debated in the legislature but that draws attention and support toa particular (policy) position.
6
Division 191, May 20, 1999.
5

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Arthur Spirling and Iain McLean

As a further check on our hypothesis, we conducted a counterfactual experiment. We
considered the five largest rebellions of the years 1997–2001 in terms of the expected(but counterfactual) Conservative preference on each of the votes. We supposed that,instead of abstaining or voting with the rebels, all the Conservative MPs voted with thegovernment on the following bills in their various stages, whenever 10 or more Labour
rebels voted against the government (actual number of roll calls pertaining to this bill):the Welfare Reform and Pensions Bill (10), the Transport Bill (8), the Social Security
Bill (3), the Child Support, Pensions and Social Security Bill (3), the Criminal Justice(Terrorism and Conspiracy) Bill (4), and the Criminal Justice (Mode of Trial) Bill (5).7
We removed the original division votes for these bills from the roll call matrix andreplaced them with the counterfactual ones. Now, the first dozen or so MPs in the rankorder produced by OC—from left to right—include Jeremy Corbyn (position 2), Robert
Marshall-Andrews (6), Tony Benn (7), Tam Dalyell (8), Dennis Skinner (9), Ken
Livingstone (11), Bernie Grant (12), and Diane Abbott (13). That is, when these few
votes are removed and the Conservatives are entered with their imputed sincere—rather
than strategic—preferences, OC correctly recovers the left-wing Labour rebels thatwere misplaced in the ways described in Section 1.
5 Discussion

Rosenthal and Voeten (2004, 620) argue that OC ‘‘is preferable to parametric methods forstudying many legislatures . . . because the nature of party discipline, near-perfect spatial
voting, and parliamentary institutions that provides [sic] incentives for strategic behavior
lead to severe violations of the error assumptions underlying parametric methods.’’ Theyshow that OC works well in analyzing spatial voting in the National Assembly of theFrench Fourth Republic (1946–1958), which featured not only perfect spatial voting but
differential party discipline—rigid in some parties and ‘‘more freewheeling’’ (Rosenthal
and Voeten 2004, 361) in others. They suggest that the method will work for otherlegislatures, citing inter alia Schonhardt-Bailey’s (2003) analysis of roll calls relating to
Repeal of the Corn Laws in the U.K. Parliament of 1841–1847. They conclude that nonparametric methods should in future be used for legislatures with stronger party systems
than the U.S. Congress, with strategic voting and with ‘‘both-ends-against-the-middle
voting.’’ They show that their method works for the legislature they study. We have shownthat it does not work for the modern House of Commons, and this is due to the sheer
preponderance of government-versus-opposition strategic voting; emphatically, this is not‘‘both ends-against-the-middle’’: the opposition votes strategically to defeat the government, the rebels vote sincerely.
As an aside, we note that the dynamic and problem we discuss has plagued techniquesclosely related to OC, like Guttman scaling (Poole 2005, 19, 45). For example, Aydelotte’s(1967, 1970, 1972) massive studies of the 1841–1847 parliament generated 21 Guttman
scales, one of them (the Miles motions scale) puzzlingly failing to integrate with the main
(big scale) dimensional measure, although Miles’s motions were about sugar duty, an issue
that fitted along the main dimension of the day. The reason is that Miles’s motions weredeliberately crafted in order to induce strategic voting and embarrass the government(Gash 1972, 447).
As a result of our experiments in Section 3, we can be a little more specific about when
OC will return a correct rank ordering: (1) when strategic voting is infrequent (occurring
7

In fact, the fifth largest rebellion occurred on the Freedom of Information Bill, but it is less obvious what theConservative preference on this issue was.

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UK OC OK?

on less than half of all votes, in terms of the opposition’s incentives); (2) when strategic
voting is not symmetric (i.e., when the opposition does not vote strategically, even if thegovernment loyalists do); (3) when rebels are less extreme than the government; (4) when
the incentive to vote strategically is stronger for rebels than it is for the opposition; and (5)when some legislation is not proposed (or, rather, whipped) by the government. We suspectthat condition (1) is generally satisfied in the Rosenthal and Voeten (2004) case.
With these caveats in mind, OC could well be helpful to researchers who were specifically interested in party discipline as a feature of legislatures. One option may be tocompare the same individuals’ ranks—like our rebels above—over time, since actors’
movements up and down the rankings could be either a product of ideological changeor, more likely, a product of their varying responses to the whip.
A claimed strength of OC—as opposed to the parametric approaches proposed by
Poole and Rosenthal (1997) and Clinton, Jackman, and Rivers (2004)—is that it does notrely on distributional assumptions about errors in voting. A consequence is that thetechnique is not model-based and hence does not permit probability statements overquantities of interest (e.g., we cannot know if we are more certain about MP A’s or MP
B’s position in the rank order). Moreover, missing data—abstentions in this case—are
essentially ignored in the fitting procedure (Poole 2005, 83). A model-based techniquewith a systematic treatment of missingness, which does not rely on parametric error
assumptions, would be an improvement. A different tack might be to ‘‘cluster’’ MPs
who vote similarly into qualitatively different groups. More particularly, we would liketo make probability statements over both the number of clusters and their membership (interms of MPs). This is a concern at Westminster precisely because different members
attend roll calls in varying proportions: the fact that missingness is not constant acrosslegislators should influence our measures. We suspect that a Bayesian clustering approach that has these features is both feasible and helpful, especially in combination
with OC. For example, we could perform a cluster analysis in which MPs are probabilistically grouped around certain issue areas according to their votes in particular rollcalls. Comparing the clusters with the OC rank order should elucidate patterns of rebellion—in terms of issues and MPs—that would otherwise be hidden. A Bayesian algorithm that solicits expert opinion—perhaps informed in part by OC—to generate priors
would be ideal. We leave this for future work.

Appendix A: Rank-Ordered Sample of MPs from ‘‘Left’’ to ‘‘Right’’ 1997–2001
Position
1
2
3
4
5
6
81
211
409
411

Name

PartyaScore

Radice, Giles
Galbraith, Sam
Davies, Ron
Turner, NeilGibson, Ian
Iddon, Brian
Blair, Tony
Prescott, John
Dalyell, Tam
Marshall-Andrews, Robert

LabourLabourLabourLabourLabourLabourLabourLabourLabourLabour

1
2
3
3
5
9
80
208
409
411
Continued

10Arthur Spirling and Iain McLean
Appendix A: (continued)

Name

PartyaScore

Skinner, Dennis
Abbott, Diane
Benn, Tony
Corbyn, Jeremy
Livingstone, Ken
Hume, John
Grant, Bernie
McGrady, Eddie
Mallon, Seamus
Jones, Ieuan Wyn
Bell, Martin Tat
Salmond, Alex
Ashdown, Paddy
Kennedy, Charles
Woodward, Shaun
Trimble, David
Heath, Edward
Hague, William
Widdecombe Ann
McCartney, RobertRoss, William
Paisley, Ian

LabourLabourLabourLabourIndependentb
SDLP
Labour
SDLP
SDLP
Plaid Cymru
Independent
SDLP
LD
LD
Labourb
UUP
Conservative
Conservative
Conservative
UKUP
UUP
DUP

412
415
417
420
422
425
426
428
429
431
432
435
458
458
490
492
508
605
634
667
667
667

Position
412
415
417
420
422
425
426
428
429
431
432
435
458
459
490
492
509
606
634
666
667
668

Note. Rank order based on 1279 roll calls. Note that MPs are classified according to their party affiliation at theend of the parliament, before the general election of 2001. Thus, Ken Livingstone is classed as an Independent
after being expelled from Labour in April 2001.
a
DUP, Democratic Unionist Party; LD, Liberal Democrat; SDLP, Social Democratic and Labour Party; UKUP,
United Kingdom Unionist Party; UUP, Ulster Unionist Party.
b
Livingstone began the parliament as a labour member but was subsequently expelled from the party.

Appendix B: Goodness-of-Fit Statistics for OC Analysis of 1997–2001 Parliament
Iteration
1
2
3
4
5
6
7
8
9
10

A

B

C

D

E

F

Roll calls
Legislators
Roll calls
Legislators
Roll calls
Legislators
Roll calls
Legislators
Roll calls
Legislators

1
1
1
1
1
1
1
1
1
1

5895
4896
4575
4449
4409
4381
4362
4350
4346
4341

515,966
515,966
515,966
515,966
515,966
515,966
515,966
515,966
515,966
515,966

0.011430.00949
0.00887
0.008620.00855
0.00849
0.008450.008430.008420.008410.98857
0.99051
0.99113
0.99138
0.99145
0.99151
0.99155
0.99157
0.99158
0.99159

Note. In the table, the columns are demarcated by letters. To wit, column A gives the subject of movement in theiteration, column B gives the number of dimensions of the analysis, column C gives the number of classification
errors, column D gives the number of choices, column E gives the error proportion, and column F gives thecorrect classification proportion after the respective iteration of the OC procedure is complete.

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UK OC OK?

Appendix C: Some Replication Information

The Poole (2000) technique is distributed as both a Microsoft Windows (with Intel processor) executable file and a Fortran program (which is compatible with Lahey compilers).
We assume most users will be using the Windows version.
Users should first download PERFL.EXE from http://voteview.com/Optimal_Classification.htm. Then, they should obtain the data for the parliament (1997–2001)
either from the current authors or from http://www2.warwick.ac.uk/fac/sci/statistics/
staff/academic/firth/software/tapir/ were it is held in a (zipped) comma delimited form
(further description of the data can be found in Firth and Spirling [forthcoming]). If thelatter, the data need to be recoded such that a ‘‘yes’’ vote is coded ‘‘1,’’ a ‘‘no’’ vote is coded‘‘6’’ and a missing value is coded ‘‘9.’’ The data need to be in a flat file format (like ASCII),
which looks something like the following:
AbbottDianeLab
AdamsIrenePaiLab
AingerNickLab
AinsworthPeterESCon
AinsworthRobertCovLab
AlexanderDouglasLab
AllanRichardSheLD
AllenGrahamNotLab
AmessDavidCon
AncramMichaelCon...
...

6661611166616161191. . .
9661699999999999999. . .
6661611166616161111. . .
1196166699999616699. . .
6661611166616161111. . .
9999999999999999999. . .
9611699161669999999. . .
6661611166616161111. . .
1196166699999619996. . .
1196166699999619999. . .

On the left are the names of the MPs (in alphabetical order) with a party indicator (LD,Lab, Con) etc. simply added at the end. On the right are the voting records for each bill.
The control card file, PERFSTRT.DAT should look as follows:
9701matrixformat.txt
NON-PARAMETRIC MULTIDIMENSIONAL UNFOLDING OF 9701 COMMONS
1 1279 20 34 39 18 10 0.005(34A1,3900I1) (I5,1X,34A1,2I5,50F8.3)
where 9701matrixformat.txt is saved to the same (working) directory as PERFL.EXE andPERFSTRT.
We use exactly the same defaults that Poole suggests on his Web site, except that the
number 1279 in the third row of PERFSTRT.DAT refers to the number of votes in our data,
39 refers to a (presumed) left member from our data set (Tony Benn). The classification
procedure was complete after approximately 1 min and 20 s on a 3.5 GHz PC.
References
Aydelotte, W. O. 1967. The country gentlemen and the Repeal of the Corn Laws. English Historical Review
82:47–60.
———. 1970. Study 521 (codebook): British House of Commons 1841–1847. Iowa City, IA: Regional Social
Science Data Archive of Iowa.
———. 1972. The disintegration of the Conservative party in the 1840s: A study of political attitudes. In The
dimensions of quantitative research in history, ed. W. O. Aydelotte, A. G. Bogue, and R. W. Fogel, 319–46.
Princeton, NJ: Princeton University Press.

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Arthur Spirling and Iain McLean

Clinton, Joshua, Simon Jackman, and Douglas Rivers. 2004. The statistical analysis of roll call data. American
Political Science Review 98:355–70.
Cowley, Philip. 2002. Revolts and rebellions: Parliamentary voting under Blair. London: Politico’s Publishing.
Firth, David, and Arthur Spirling. Forthcoming. Tapir and the public whip: Resources for Westminster voting.
The Political Methodologist.
Gash, N. 1972. Sir Robert Peel. London: Longman.
Poole, Keith T. 2000. Non-parametric unfolding of binary choice data. Political Analysis 8:211–37.
———. 2005. Spatial models of parliamentary voting. New York: Cambridge University Press.
Poole, Keith T., and Howard Rosenthal. 1997. Congress: A political-economic history of roll call voting. New
York: Oxford University Press.
Rosenthal, Howard, and Erik Voeten. 2004. Analyzing roll calls with perfect spatial voting: France 1946–1958.
American Journal of Political Science 48:620–32.
Schonhardt-Bailey, C. 2003. Ideology, party and interests in the British parliament of 1841–1847. British
Journal of Political Science 33:581–605.