American Political Science Review

Vol. 105, No. 2

May 2011

doi:10.1017/S0003055411000050

Strategic Opposition and Government Cohesionin Westminster Democracies
TORUN DEWAN London School of Economics and Political Science
ARTHUR SPIRLING Harvard UniversityCohesive government-versus-opposition voting is a robust empirical regularity in Westminster
democracies. Using new data from the modern Scottish Parliament, we show that this pattern
cannot be explained by similarity of preferences within or between the government and opposition
ranks. We look at differences in the way that parties operate in Westminster and Holyrood, and use roll callrecords to show that the observed behavior is unlikely to be determined by preferences on any underlying
issue dimension. Using a simple variant of the agenda-setting model—in which members of parliament
can commit to their voting strategies—we show that the procedural rules for reaching collective decisionsin Westminster systems can explain this phenomenon: in the equilibrium, on some bills, members of
the opposition vote against the government irrespective of the proposal. Such strategic opposition canreinforce government cohesiveness and have a moderating effect on policy outcomes. We introduce newdata from the House of Lords, the Welsh Assembly, and the Northern Ireland Assembly to distinguishour claims from competing accounts of the data.

A

pproximately 40% of those inhabiting
democracies live in systems that have
Westminster-style features, inter alia a fusionof executive-legislative relations, strong normsof majoritarian government, and few checks andbalances on executive agenda-setting power (Lijphart
1999, 10–11).1 A central behavioral regularity observedin such systems is a pattern of “government-versusopposition” roll call voting, whereby government
proposals are supported by a cohesive governing
majority and opposed by a cohesive opposition
minority. Indeed, it is only during periods of minority
government or national emergency,2 when bills aresupported by heterogenous coalitions of legislators,
that this pattern is broken.
What can account for this behavioral regularity inthe pattern of legislative voting? An obvious answer is“whipping”: inducements and punishments are meted
out, ensuring attendance and enforcement of the party
line. As shown by Kam (2009), party leaders have attheir disposal a range of formal and informal measures
Torun Dewan is Professor of Political Science, Department ofGovernment, London School of Economics and Political Science,
Houghton Street, London, UK WC2A 2AE (t.dewan@lse.uk).
Arthur Spirling is Assistant Professor, Department of Government, Harvard University, 1737 Cambridge Street, Cambridge, MA
02138 (aspirling@gov.harvard.edu).
We gratefully acknowledge research advice and assistance fromAmir Karger. We thank Jim Alt, Scott Ashworth, Amy Catalinac,Andy Eggers, Indridi Indridason, Nolan McCartty, Bonnie Meguid,
Slava Mikhaylov, Paul Mitchell, and Howard Rosenthal; participantsat the annual meetings of both the APSA and the MPSA in 2010 andat the Political Institutions and Economic Policy workshop held at
Harvard University; and, finally, three anonymous referees for theircomments on an earlier draft. We thank Micael Castanheira, GaryCox, Jon Eguia, Simon Hix, Rafael Hortala-Vallve, Ken Shepsle, andDavid Myatt for helpful discussions
1 Our claim depends on the inclusion of India, a country whose
institutional heritage stems from Westminster, but that deviates fromthe classic model.
2 Ramsay MacDonald’s National Government in Britain is an example of this phenomenon.

that provide incentives to backbenchers to act cohesively. Yet, this offers an incomplete explanation for
the general pattern of cohesive government-versusopposition voting. The key elements of cohesion, on
one hand, and “government-versus-opposition” voting, on the other, are not synonymous. In principle,
opposition party leaders could enforce any voting strategy (including, for example, supporting rather than opposing the government on every bill). Thus, although
whipping may well militate party cohesion, the specificpattern of unified roll call voting requires a separate
explanation.
The historical case for the claim is similarly lacking: Cox (1992), for example, can find no evidence of
any official whipping before 1832; yet, contemporary
observers of parliament wrote of “government” and“opposition” forces and their behaviors well before thisdate (see Namier and Brooke 1964, 190–91). Indeed,even the claim that whipping uniquely begets roll callhomogeneity is suspect in the Westminster context. In
an authoritative study of the origins of party cohesion, Cox (1987, 25) writes that “cohesion increased
markedly within the category of whipped votes, starting in the late 1860s and 1870s. Thus, although it istrue that the percentage of votes whipped increasedin the 1870s, this does not in itself explain the trends
in cohesion.” In fact, the relative timing of the origins
these behaviors suggests that, if anything, the causal
process runs in the opposite direction, with whipping
perhaps introduced as an implicit structural innovationfor opposition parties in the face of a government majority with agenda power. Indeed, Cox (1982) provides
evidence that between 1832 and 1871, cohesion among
the opposition was on average higher for the opposition
Tories than the governing Whigs.
A more subtle explanation for government-versusopposition voting is that cohesion within governmentand opposition ranks, and polarization between thesegroups, are the result of a simple sorting process. Thatis, members of parliament (MPs) join parties that337

Opposition and Cohesion in Westminster Democracies

advocate the policies they prefer and thus naturallyfind themselves agreeing and opposing the same sets ofpolicies when considered on the floor of the legislature.
Moreover, this pattern may be reinforced over time:
parties develop reputations for standing on particularpolicy issues; like-minded MPs are selected and standunder the party label; and socialization between MPs
on the backbenches, and in the lobbies and clubs eventually compounds the behavior. Put otherwise, “birdsof a feather flock together”: members of the governing and opposition parties vote cohesively primarily
because they share similar preferences.3
We present evidence that strongly suggests that voting patterns in Westminster-style democracies cannot
be explained by preference alignment alone. Using new
data from the Scottish Parliaments between 1999 and2003 and 2003 and 2007, we show that a pattern ofcohesive government-versus-opposition voting is apparent from the outset. This is hard to reconcile withwhat one would expect given stated preferences on theunderlying issues. To give an example, between 1992
and 1997, the Scottish National Party (SNP) voted differently than the Labour Party on just 4% of bills in
the House of Commons. This congruence is exactly
as one might expect from two center-left parties in
opposition. In contrast, just two years later in the first
Scottish Parliament, the Nationalists, now the main opposition party, were in disagreement with the Labour
Party 69% of the time. Moreover, our analysis of thedata shows that a single dimension can correctly predict
95% of the roll calls for Scotland. This dimension fits
a government-opposition divide with the Labour Party
and the Liberal Democrats at one end, the SNP and
Scottish Socialists at the other, and the Conservatives
in between. We show that this pattern cannot be explained by an underlying issue dimension.
We provide microfoundations for the emergence ofgovernment-versus-opposition voting in relating such
behavior to individual incentives that arise due tothe basic institutional infrastructure of Westminster
democracies. In particular, we investigate the possible
associations between voting patterns and the procedural rules for reaching collective decisions in such
systems: agenda-setting power is (usually) held by thegoverning majority in the Commons; a status quo policy
is replaced only if the government brings a proposal to
the floor that is majority preferred to it; and this decision cannot be overturned by a second chamber. We
adapt the basic toolkit of the spatial model: a set of MPs
with single peaked preferences on a set of policies eachin unidimensional policy space; members are sorted
into two main parties, one in government and one in
opposition; and on each policy, a member belonging to
the government is given agenda-setting power. To thissetup, we add that parties can commit to their voting
strategies: they can bind themselves, for example, by
invoking the party whip before the proposal is madeand votes are cast. This allows us to explore how different voting strategies affect policy proposals and hence
3 Krehbiel (1993) makes a related argument for the U.S. House ofRepresentatives (cf Rhode 1991).

338

May 2011

outcomes and payoffs: “sincere voting” occurs wheneach MP votes for a proposal as long as it does notleave her worse off than she would be if the status
quo remains in place, whereas “opposition voting” occurs when each member of the opposition always votes
against the government irrespective of the proposal.
We show that on some bills, “opposition voting” yields
higher opposition payoffs than sincere voting. On suchbills, the opposition binds itself to opposing any government proposal. The equilibrium involves a convex combination of “opposition” and “sincere” voting and fits
the stylized facts of government-opposition systems:(1) government and opposition tend to vote cohesively,(2) the opposition votes against the proposals put forward by the government, and (3) the opposition votes
against government proposals that leave them betteroff than they would be if the status quo remained inplace.
Our analysis provides a simple strategic rationale forgovernment-versus-opposition voting. By committing
to oppose the government, the opposition forces it into
proposals that appeal to a majority formed by its own(i.e., government) backbenchers. This can benefit the
opposition. A necessary condition is that parliament
is not completely polarized. Specifically, we requirethat on some bills, there is a degree of “overlap” inthe preferences of government and opposition MPs:on some policies, the members of the opposition party
have preferences closer to those of the agenda setter
than some members of government. This is a very weak
condition, almost certainly satisfied in all Westminster
systems, and we provide empirical evidence to demonstrate that it holds in practice. An implication of thisfinding is that the conditions that give rise to sincere andstrategic voting are not the same: sincere voting shouldbe (relatively) higher when government and opposition are completely polarized, strategic governmentopposition voting of the type that we analyze is higher
when there is a degree of convergence in underlying
preferences.
A main result stemming from our analysis is thatstrategic opposition and cohesive government voting
are two sides of the same coin: in equilibrium, cohesive
government-versus-opposition voting is mutually reinforcing; strategic opposition forces the government totake account of its own backbenchers, thus inducing
cohesion on the government backbenches. Our focus
on strategic interaction between government and opposition forces offers a different perspective to the predominant view that relates cohesion to internal party
factors (e.g., Cox and McCubbins 2005). Moreover, ouranalysis counters conventional wisdom that opposition
is marginal to policy outcomes in majoritarian democracies, described by Powell (2006):
opposition parties can use their legislative forum to raiseembarrassing questions in anticipation of the next election
and may occasionally find procedural levers of influence.
Nonetheless, no observer of usual policy-making processes
in Britain or France can doubt that the ability of minority
oppositions to shape policy in the interests of their constituents is usually extremely limited. (309)American Political Science Review

Furthermore, we show that, contrary to conventional
wisdom, cohesive government-versus-opposition voting can lead to greater moderation in policy outcomes.
In particular, when the opposition adopts a strategy ofoutright rejection, outcomes are closer on average tothe median MP position than those under sincere voting. Thus, although the institutions of “consociational”
democracy allow for greater inclusiveness (Lijphart1977), the importance of voting strategies deployed by
opposition parties in Westminster systems should not
be discounted. Even though it is generally acceptedthat opposition parties can exert pressure on minority
governments, our results suggest that they continue todo so when the government enjoys majority status.
This article is structured a follows: we justify our caseselection before discussing and presenting analysis on
our new data from the Scottish Parliament that confirms the robustness of government-versus-opposition
voting in Westminster systems. We then present a simple model and results confirming the relationship between strategic voting and the institutional structure ofWestminster. In the remainder of the article, we thenconsider alternative theories and extensions. Proofs
and other technical details are found in Appendices
A to E.

OUR CASE SELECTION
Although Westminster systems have features thatmake our analysis particularly pertinent—the relative
absence of checks and balances on executive powermeans that the opposition is limited to the use of its voting strategies in order to yield influence—governmentversus-opposition patterns are found elsewhere. There
are, however, practical reasons of data availability—
along with a desire to evaluate the relative, nuanced
claims of competing alternatives—to keep the analysis
more tightly focused. Although government-versusopposition voting is a pervasive feature in different
countries, it is possible that this empirical regularity
evolved independently in each country rather thanbeing related to a common set of institutions. Since
government-versus-opposition voting is observed indifferent places and at different points in time, its
emergence may be due to a common set of circumstances that can have an independent effect on thevoting patterns in these parliaments. Moreover, eventhough such voting patterns may plausibly be related to the institutional features of certain democracies, the question remains: which of these institutionalfeatures are important determinants of governmentversus-opposition voting? To analyze statements about
necessary conditions for behavior, we want cases that
present a particular pattern of variation on the “righthand side.” Specifically, and for various competing theories, we desire (at least) two cases that differ (only) on
the claimed variable of interest, holding other potential
confounders constant.
Data from the United Kingdom, the home of theWestminster system, provide just this. The Scottish
Parliament shares with the assemblies in Wales andVol. 105, No. 2

Northern Ireland both timing of its inception and acommon, inherited, political culture; thus, we can exploit institutional variation between these countries to
explore our hypothesis. To assess our main claim thata majoritarian executive is a requirement for the voting pattern in question, we can compare the Northern
Ireland Assembly—which abandons this practice—tothat of Scotland. To rule out (or rule in) alternative
hypothesis about other institutional factors that may
act as driving forces, we can compare and contrast
different cases. To assess the effect of legislative domain, we can contrast the Welsh case—which has nobudgetary powers—with that of Scotland. If we want todetermine whether the behavior in question is driven
by electoral considerations, then we can examine theHouse of Lords, where uniquely, membership is for life.
Finally, relative to Westminster, the devolved assemblies are particularly interesting because some MPs areelected directly by their constituents, whereas others
are elected from a party list. Thus, we can exploit thiswithin-country variation to assess the importance ofdifferent electoral incentives in driving opposition behavior. Performing such analysis provides interesting
insights that distinguish the particular institutional basis of government-versus-opposition voting from otherfactors. As we see, careful case selection allows us
to provide concrete evidence that supports our claimthat majoritarian control over agenda setting, rather
than other institutional factors, explains the patternof government-versus-opposition voting. We postpone
such comparative analysis until the section dealing withalternative theories and the plausibility of our assumptions. In the next section, we introduce our main data
for the Scottish case.

THE EMERGENCE OF
GOVERNMENT-VERSUS-OPPOSITIONIN SCOTLAND
Established in 1998, the Scottish Parliament is the devolved national, unicameral legislature of Scotland,
which has 129 elected members each elected for a fouryear term. Its ambit includes all Scottish matters not
specifically “reserved” to the United Kingdom Parliament; in practice, this means that members may legislate in areas such as education, agriculture, health,local government, and justice. Indeed, ministers in Edinburgh have the same executive powers in these particular policy arenas as their counterparts in London
enjoy for their portfolios. A comparison between the
behavior of its members with that of members of theWestminster Parliament is instructive. Although mostof the members of the newly elected parliament had
not previously served in Westminster, the parties they
represented were the same as those represented in
the House of Commons. This allows us to compare
party behavior in both legislatures at the same points
in time.
However, there are important institutional differences between the two parliaments that allow us
to draw conclusions about the likely cause of any

339

Opposition and Cohesion in Westminster Democracies

May 2011

Scot II

Scot I

01–05

97–01

92–97

FIGURE 1. Parties Relative to One Another in “Agreement” Terms, Specific Numbers Are Actual,
Absolute Disagreement Scores for Parties
Lab SNP

LD

Con

0

0.22

0.92

0.06

Lab

SNP LDCon

0

0.41 0.47

0.91

Lab

SNP LDCon

0

0.69 0.69

0.89

Lab LDGreenCon

SNP Soc

0 0.030.5

0.6

0.69 0.71

Lab LD

Green Con

SNP

Soc

0 0.030.55 0.56

0.61

0.71

Notice relative positions of Tories and Scottish Nationalists at Westminster (first three rows) and Scotland (last two rows), respectively.
Con, Conservatives; Green, Green Party; Lab, Labour Party; LD, Liberal Democrats; SNP, Scottish National Party; Soc, Socialist Party.

variation in the behavior we find. Unlike its counterpart in London, the Scottish Parliament was designed,
both architecturally and in terms of its institutional
make-up, to avoid the adversarial nature of politics inWestminster. The crafters of the constitutional reformthat brought to an end the period of history since 1707,
by which all Scottish affairs were dealt with by Westminster, envisaged a devolved assembly that would
work on more consensual lines. For example, the assembly itself was designed so that members of the Scottish Parliament (MSPs) sit in a semicircle rather thanon opposing benches.4 Perhaps more important, MSPs
are elected under a mixed member proportional system: 73 constituency members are elected under “firstpast the post,” whereas a further 56 are elected under
proportional representation from party lists in 8 regions. The first two governments comprised a coalition
between the Scottish Labour Party and the Scottish
Liberal Democrats.
Although the Scottish Parliament deviates fromthe classic model in important ways, many of thequintessential features of the Westminster democracy
are intact. The chamber is unicameral and, althoughprovisions are made for committee and individual
members to introduce bills, the lion’s share of parliamentary business involves the discussion and debate on
measures introduced by the executive (Mitchell 2000,
610–11). Thus, although the composition of parliament
and the rules by which members are elected differ fromthose found at Westminster, the key feature of Westminster democracy—namely, the fusion of executivelegislative relations with agenda-setting power being
given to the majority party—remains central to politics
at Holyrood. Similarities in the behavior of the parties
across these parliaments can then be related to thiscommon institutional feature. In fact, although avoiding the confrontational politics of Westminster-stylearrangements was the aim, a pattern of governmentversus-opposition was evident from the outset (seeMitchell 2000, 620). To show this, we begin by calculating the agreement between party A and party B as
the proportion of times the majority of each party votethe same way (“aye” or “no”), dropping all divisions
on which one or other of the parties had no members
voting.5 The “disagreement” between any two parties
is then calculated as one minus the agreement score.
Figure 1 shows the parties in the three Westminster Parliaments from 1992 to 2005, and the first two
Scottish Parliaments from 1999 to 2003 and from 2003
to 2007.6 Each line represents a parliament, and eachpoint a party in terms of its disagreement score relative to the Labour Party. Because, by definition, theLabour Party must agree with itself 100% of the time,
its disagreement is zero, and that party appears to the
far left. The party that disagrees with the Labour Party
most often in each parliament is assigned to the far
right of the line: in this way, the parliaments are easily
comparable in terms of relative differences between

4 “The choice of a semi-circular layout reflects the desire to encourage constructive working among the MSPs. This layout contrasts
with the seating arrangements of the Westminster Parliament, where
Government and Opposition parties face each other directly” (The
Scottish Parliament Public Information Service 2009, 2).

5 For the Scottish Parliament case, we code stated abstentions as
missing data; this avoids counting ambiguous cases as either firm
support or opposition.
6 At the time of writing, the third Scottish Parliament had not yet
completed its 4-year term.

340

American Political Science Review

TABLE 1.

Vol. 105, No. 2

Mean Rice Index Scores for Various Parties at Westminster and Holyrood

Labour Party
Conservative Party
Liberal Democrats
SNP
Socialist Party
Green Party

1992–1997

1997–2001

2001–2005

Scot I

Scot II

93.68
95.40
82.71
99.18
—
—

96.99
96.19
96.32
98.99
—
—

95.17
95.64
95.23
99.47
—
—

98.92
98.56
95.21
95.48
100.00a100.00

99.02
98.27
98.38
97.30
96.98
99.72

a Scottish Socialists consist of one member in the first Scottish Parliament and thus receive a 100% Rice index

score by definition. SNP, Scottish National Party.

the parties. The specific numbers listed in the graphic
are the actual, absolute, disagreement scores with theLabour Party. Thus, the Conservatives are the furthestfrom the Labour Party in the 1997–2001 Westminster
Parliament, disagreeing 91% of the time. A striking
feature of these data is the position of the SNP: broadlyaligned with the Labour Party in the 1992–1997 Westminster Parliament, when both are in opposition, but
strongly opposed to the Labour Party in Scotland.
The evidence suggests that despite their ideological
profiles, parties play different roles depending on theparliament in question. Specifically, the Tories appear
to be the most recalcitrant members at Westminster,whereas it is the Scottish Nationalists (along with the
Scottish Socialists, who do not have seats at Westminster) who are the more antagonistic at Holyrood. Theseobservations fit the notion that during this period the
SNP was the main opposition party who opposed measures introduced by the Labour Party-Liberal Democrat coalition. The analysis suggests that the structureof government-opposition voting can be related to theinstitutional similarities between the Scottish Parliament and the Westminster Parliament.
Of course, although it is well known that“government-versus-opposition” voting is dominant at
Westminster (Spirling and McLean 2007), it is plausible that roll call patterns at Holyrood are dictatedby other dynamics. In particular, voting might, in fact,reflect underlying policy divisions. Because we do not
observe exactly the same individuals voting in bothparliaments and, moreover, because the precise institutional rules differ between parliaments, we need toinvestigate other factors that may underpin these voting patterns. In addition, our claim that the SNP agrees
with the Labour Party in Westminster “x percent of
the time” assumes that the parties vote cohesively. It is
possible that some members are more or less alignedwith their counterparts in other parties.
First, then, we explore the level of intraparty cohesion. In Table 1, we report the “Rice index,” denoted r,which attempts to capture the unity of a party on any
particular vote (MacRae 1970; Rice 1928). That is, r =100|p − (1 − p)|, where p is the proportion of the party
voting “aye” on the roll call. As can be readily seen,
parties at both Westminster and Holyrood average amean Rice score of more than 95%. Bearing in mind
that this includes purported “free votes”, it seems safe

to assert that party cohesion is as prevalent and robustin the Scottish Parliament as in the House of Commons.
Indeed, with the exception of the Liberal Democrats at
Westminster in 1992–97, the median value of the Rice
index in every case is 100%.
Establishing that there is one predominant dimension to roll call voting and that dimension
is “government-versus-opposition” is slightly lessstraightforward. We proceed by rank ordering members via the nonparametric optimal classification (OC)routine (Poole 2000) and inspect the dimensions interms of both substantive interpretation and goodnessof-fit. In Table 2, we report the proportion of votes
correctly predicted from this procedure and the aggregate proportional reduction in error from the relevant dimension of model.7 As with all such techniques,
these numbers must (almost) always increase as themodel becomes more complex; the key is to select adimension number wherein an additional dimension is
not “worth” the extra parameter. In practice, we seethat a simple one-dimensional model predicts approximately 95% of the voting decisions correctly for boththe first and second Scottish Parliaments.8 Adding afurther dimension allows us an improvement of just
4%. As a comparison, the equivalent figure for theHouse of Commons (1997–2001) is 99% and for the
U.S. Senate (90th), a relatively low 84%. We thus
settle for the single-dimensional fit and offer a substantive interpretation of this dimension.
Table 3 reports the rank position (from 1 through134) of each party by using the party leader’s score asa proxy. In terms of Figure 1, the results are similar.
Once again, we see the Labour Party and the Liberal Democrats at one end of the continuum, and theTories and Greens somewhere between them and theScottish Nationalists and Scottish Socialists. Given that
7 In particular, we used the OC package (Poole et al. 2010) in R (RDevelopment Core Team 2009). We drop all roll call votes where lessthan 2.5% of the minority casts a vote, and we drop all legislators
who do not vote at least 20 times.
8 We also fitted a one-dimensional model to the third parliament(2007–2011), although we had only around 200 roll calls available atthe time of writing. Nonetheless, we obtained a rank order similar tothat shown previously. In terms of the relative positions of their leaderships: Labour > Liberal Democrats > Conservatives > Greens >Scottish Nationalists. Some 96% of roll calls are correctly predictedwith this model.

341

Opposition and Cohesion in Westminster Democracies

TABLE 2.

May 2011

Votes in Scottish Parliament Explained in One and More Dimensions

Scotland I
Scotland I
Scotland II
Scotland II

Dimensions

1

2

3

4

Percent correctly predicted
Aggregate reduction in error
Percent correctly predicted
Aggregate reduction in error

0.955
0.844
0.947
0.800

0.992
0.974
0.989
0.957

0.994
0.980
0.992
0.971

0.994
0.980
0.994
0.976

TABLE 3. Number of seats and Optimal Classification (OC) of
First and Second Scottish Parliaments

Scotland I
MSPs
OC Rank
Scotland II
MSPs
OC Rank

LabourParty

LiberalDemocrats

Conservative
Party

Green
Party

Socialist
Party

Scottish
National
Party

56
34

17
63.5

18
91

1
95

1
97

35
103

50
30.5

17
58.5

18
76.0

7
95.5

27
112

6
128

For each parliament, the first row shows the number of members of (the Scottish) Parliament by
party. The numbers in the second row are OC ranks of the leaders of the various parties. Bothparliaments have a total of 134 members. MSP, member of the Scottish Parliament.

the Labour Party—a traditional party of the tradeunions—and the Scottish Socialists occupy opposite
poles of the rank order with the right wing Conservatives between them, it is difficult to believe that we areobserving a left-to-right phenomenon. An alternative
is to regard this dimension as a Scottish independence
continuum, with the Scottish Nationalists—who are actively campaigning for full political autonomy9—at one
end and the Labour Party, which opposes such moves,at the other.10 The position of the Conservative Party
scuppers this interpretation: unionists by name and nature, they opposed the original creation of the Scottish
Parliament. We would thus expect them to appear at
one end of the independence spectrum, but here they
appear between the Labour Party and the Nationalists
on this dimension.
To summarize, our analysis suggests that parties
in Scotland are extremely cohesive in their voting
and, in terms of overall patterns of roll call behavior, “government-versus-opposition” is the order ofthe day. The pattern of government-versus-opposition
voting is very different than what we would expect
if MPs were voting along ideological lines, and thissuggests that this voting is strategic. Moreover, the factthat there is institutional variation between the Westminster and Holyrood parliaments implies that thisstrategic aspect is related to the common institutional
9 Indeed, at the time of writing, the Nationalists were actively campaigning for a referendum on independence.
10 The Greens are generally in favor of independence, and thus, theirpositions seem appropriate here. The Socialists are correctly placed
relative to the Labour Party, although it is difficult to believe thatthey are keener on autonomy than the SNP in the second parliament.

342

features of these parliaments. The key feature that links
them is that the government agenda is implemented by
the majority party, which operates without checks andbalances.

A MODEL OF WESTMINSTER DEMOCRACY
The data suggest that a pattern of cohesive
government-opposition voting is unlikely to arise due
to preference-based voting alone and that a significant
aspect of government-versus-opposition voting relates
to strategic considerations that arise given the institutional infrastructure of Westminster democracies. The
key institutional feature related to such voting patterns is the near monopoly of agenda-setting power enjoyed by the executive.11 To provide microfoundations,
we craft a simple “bare bones” model that captures
this core element of Westminster democracies, combined with strong party discipline, and show how these
ingredients relate to the voting strategies deployed bygovernment and opposition forces.
11 For Westminster, findings from Kam et al. (2010) suggest thatsincere member preferences overlap across parties and are not naturally one dimensional. Agenda-setting power emerges as a key
determinant of cohesiveness and stability in other systems, too. For
example, Jillson and Wilson (1994, 152–53) report that the Continental Congress was characterized by an “absence of stable coalitions”
because agenda control was not assigned to any particular person
or body. In such institutions, “any actor can bring forward an issue
that splits a previously winning coalition.” Similarly, Jenkins (2000,
815) compares the Federal and Confederate Congress, revealing thatwhen “the party in the majority (through the actions of its leaders)
controls the legislative agenda [it] . . . lends structure to Congressional voting, which in turn induces stability in individual-level votechoice.”American Political Science Review

Parliamentary Agenda and Party Structure. We begin with a parliamentary agenda that consists of a set of
J independent policies. We assume that the policy spacefor each j ∈ J is unidimensional. As already stated, themain institutional feature of Westminster democracyis that the government agenda is implemented by the
majority party. For most of our results, we concentrateon the case where the agenda setter on policy j is
the median of the governing party on that policy, but
the exact identity of the government representative
who holds the agenda-setting power is of no consequence to our results. We write the proposal of theagenda setter on the jth policy as ψj .12
We make a simple adaptation to the agenda-setting
model of Romer and Rosenthal (1978), which has beenused to analyze majority party control over the agenda
in congressional systems under different procedural
rules (Cox and McCubbins 2005). Analysis of thesemodels focuses on the unique subgame perfect Nashequilibrium in which, given a proposal made by theagenda-setter, all players vote sincerely. The game weanalyze is, in contrast, more suited to the Westminster
scenario, where the government majority has strong
agenda-setting powers; can block opposition amendments and curtail parliamentary debate via guillotine
measures and programming of government bills; and,critically, where parties can commit to their voting
strategies. As noted at the beginning of the article, empirical scholars of parliamentary settings have viewed
the ability of parties to discipline their members as a
distinguishing feature of such systems. Cox’s authoritative study, for example, shows that party discipline
emerged in the United Kingdom in the 19th century
in tandem with increasing control over the agenda
exerted by the governing majority. Our framework
allows us to explore the implications of this commitment ability alongside the agenda-setting powers of
the government. The critical aspect of our timing isthat we assume that MPs can choose whether to bindthemselves (e.g., invoke the party whip) to voting together before the proposal is made. This is, of course,
equivalent to opposition members casting their votes
before the government introduces its bill to the floor.
In short, we treat the party whip as a “bridge-burning”
device that is central to policy outcomes in Westminster
systems.13
To capture the basic party division in Westminster
democracy, we begin by assuming a set m of MPs who
12 Implicitly in what follows, we assume that the proposals are not“confidence matters”: that is, simply defeating the proposal does notadversely affect the agenda setter’s ability to introduce bills per se.
Harold Wilson, prime minister of a Labour minority government
in the 1970s, made it quite clear that, without a specific vote ofconfidence attached to a bill, “a snap division or even, perhaps insome cases, a more substantial one. . . would not necessarily mean,
and would not, indeed, immediately mean, any fundamental decision about the future of the Government or about a Dissolution”(Hansard 1974).
13 The term “whip” used here encompasses different, unmodeled
notions of how a party might bind its members to particular voting
instructions. Eguia (2008) discusses several relevant instances. In
one, a member contributes to a common pool for party funds thatshe forfeits if she reneges on her agreement to vote according toparty instructions. In another, costless punishments are implemented

Vol. 105, No. 2

belong to a governing party and a set n who belong to an
opposition party. We assume that the governing party
has a majority (i.e., m > n) and that parties are jointly
exhaustive and mutually exclusive: all members belong
either to the governing or to the opposition party, andno member belongs to both. We define a member as
belonging to a party when, on average, her views on
a particular policy coincide with those of an (average)
member of her party. Thus, parties are formed of likeminded individuals. More formally, we assume that oneach policy issue, the ideal points of members of thesame party are independent and identically distributed(iid) draws from a (possibly common and known) continuous distribution. For example, for some of our simulations later in this article, we treat the ideal point ofeach member of the governing party on the jth policy
as a draw from a normal distribution with the samemean and variance, and a member of the opposition
party has a draw from a normal distribution with adifferent mean and (possibly) different variance. This
assumption means that whereas ex ante backbenchers
are homogenous, ex post they are heterogenous withrespect to their ideal points on a particular policy. The
uncertainty in payoffs is itself not important—what
is important is that members can bind themselves tovoting with their party once preferences on the realline are revealed (but before the proposal is brought
forward).14 However, the variance in members’ ideal
points across policies captures an important elementof Westminster democracy, namely, that on some policies members of the opposition may find themselvesmore aligned with the government than with their fellow partisans. Somewhat surprisingly, and as we show,
this feature of Westminster life is a critical ingredient
toward cohesive government-opposition voting.
Voting Strategies. Given the parliamentary agenda,
a voting strategy is a vector of votes for the ith member where the jth element of the voting vector corresponds to a binary decision—either “aye” or “no”—on
a division over policy j. Some voting strategies are of
immediate interest. With “sincere” voting, member i,with “ideal point” xij on the real line that forms thepolicy space of policy j, compares her utility from theqjth status quo, which we write as xj , with the utility she receives from the jth proposed bill. Assuming that utility decreases monotonically in the distance
between a member’s ideal point and the alternatives,then the member votes for the proposal if and only ifq|ψj − xij | ≤ |xj − xij |, where the weak inequality implies the imposition, with no loss of generality, ofa tie-break rule whereby indifferent legislators backthe proposal over the status quo. Another interestingcase is where a member of the opposition votes “no”
irrespective of whether this critical inequality is satisfied. This suggests that a member of the oppositionby the party after the division of Parliament, which can affect thereelection prospects of the MP.
14 For some of our results (Propositions 1 and 2), the exact timingof commitment is irrelevant given our assumptions that ex ante MPs
have identical preferences.

343

Opposition and Cohesion in Westminster Democracies

FIGURE 2.

May 2011

Five-member Example

ψj

g1

g2

o1

SQ
g3

ψj

g1

g2

o2

SQ
o1

g3

o2

In both scenarios (rows), g2 is the (government) agenda setter. The first row shows the policy outcome (dashed line, ψj ) under opposition
voting. The second row shows the outcome (ψj ) under sincere voting. Opposition members, o1 , o2 , are better off in that the final billpassed is closer to their ideal points, when strategically opposing.

strategically opposes a proposal that, in the event thatit receives majority support, would provide her with apayoff higher than that attained when the status quo
remains in place. The question we ask is: under which
circumstances will MPs bind themselves to voting together? In the case of the opposition, such binding
commitments can take a very stark form: they commit
to voting against any proposal the government brings
to the floor. We refer to such voting as “opposition”
voting. Our main focus is on situations where MPs canbind themselves in the event where all members fromtheir party are better off by so doing. That is, theybind themselves to a vote on a particular bill when
the payoff to all members from doing so exceeds thatattained from following a different protocol. Since allmust agree to invoke the commitment device, a natural
focus is on the Pareto-dominant Nash equilibria of thesubgame that involves the agenda setter bringing a proposal to the floor before MPs cast their (final) votes.
Asymmetric Commitment versus Government
Agenda-setting Power. Our framework allows us to
explore the implications of party commitment
alongside the agenda-setting powers of the governing
party. We begin by establishing our main results for thecase where the opposition has greater ability to commit
to its voting strategies. In this sense, we think of commitment as a substitute mechanism that the opposition
has available when the government is granted agendasetting powers. As motivation for this example, wemight consider that the government, which maintains
a majority, must appeal to a broader coalition of votersthan the opposition, which, by definition, is smaller insize and thus more compact. This would be the case,for example, where, as in the UK, many districts are
partisan and won by landslides, whereas others are
more closely fought contests. When the majority party
has a relatively large share of MPs elected in closerun elections, they have less ability to discipline theirmembers. The opposition, in contrast, when reduced toits core, has greater control over the actions of its representatives. We capture this distinction in stark form344

by assuming that the opposition can commit to a voting
strategy, whereas the government backbenchers only
ever vote sincerely. This serves as a useful theoretical
exercise that helps us establish an interesting baseline
result that shows that the ability of the opposition tocommit to opposing government proposals can counteract the agenda-setting power of the government.
We illustrate this effect with a simple example in
Figure 2 that depicts a single policy agenda: j = 1, m =3, and n = 2. For this example, we order and label themembers of the government by their ideal points g1 <g2 < g3 , and do likewise for the opposition so that o1 <o2 . We assume that g2 is the government agenda setter. The dashed line indicates ψj , her optimal proposal
conditioned on different voting strategies deployed by
the opposition, and the status quo SQ. The top row
illustrates the optimal policy when the opposition opposes all government proposals, whereas the bottom
row indicates the optimal policy when the opposition
vote sincerely. Under an opposition voting strategy,
the proposal must make the (right) pivot with ideal
point g3 indifferent between her voting strategies. In
contrast, under sincere voting, the proposal must leave
the median member o1 indifferent between the statusquo and the proposed policy. It is clear by inspection of
Figure 2 that “opposition voting” leaves both opposition members better off than sincere voting. Moreover,given this opposition voting strategy, the government
members can do no better than vote sincerely. Thus,
although for these parameter values both strategies
would be Nash equilibria of the subgame in which thegovernment makes a proposal and MPs cast their votes,
here the opposition would choose to bind themselves
to voting against any government proposal.
There are two critical features of this example. First,
the status quo policy lies on the “opposition” side of
the agenda setter’s ideal point. In Figure 2, the agenda
setter belongs to a “left” governing party, and the status
quo is to the right of her ideal point. Clearly, when thestatus quo is to the left of the agenda setter’s ideal
point, then she can propose her own preferred policy
and thus receive the support of her own backbenchers

American Political Science Review

irrespective of the actions taken by the opposition. The
second feature is that there is overlap in the ideal pointsof the government and opposition members. In Figure
2, the ideal point of the rightmost member of the governing party is to the right of the leftmost member ofthe opposition. When this is not so, then again the votesof the opposition are irrelevant to the final outcome
because the agenda setter need only appeal to the government backbenchers. In Lemma 1 in Appendix A,
we show that this result generalizes to all such policies.
Here, we focus on the main intuition. On any given
bill, with a given status quo and government proposal,
an opposition member can find herself in one of two
situations: either (1) her vote is irrelevant to the final
outcome because, given the government proposal, amajority of government members vote “aye”; or (2) her
vote can influence the final outcome, and as a memberof the opposition bloc, she votes against the proposal.
The latter situation may arise when she finds herself
in agreement with the government proposal under sincere voting, whereas some members who belong to thegovernment majority are at odds with the proposed
policy. In this situation, the optimal policy proposal(under sincere voting) makes the member strictly indifferent between voting for or against the government. If,
in contrast, she strategically votes “no,” then the government must satisfy its recalcitrant government members. Such strategic opposition can induce a proposalthat is more favorable to all opposition members; thus,
if they could (and they can), then opposition members
would bind themselves to voting in this way.
This example provides an illustration of behavior consistent with the stylized fact of cohesive
government-versus-opposition behavior: the opposition votes cohesively; the government is cohesive; and,
although the government supports the agenda setter’s
motion, the opposition does not. Several other features
are interesting: the opposition votes against proposals
that leave them better off than the status quo; and, finally, there are policy consequences of the opposition’s
action—the outcome is closer to the median preferenceof parliament than it would be under sincere voting.
The more general insight is that strategic opposition
can induce a proposal that is more favorable to all
opposition members. In short, opposition voting counteracts the government’s agenda power.
In our discussion, we have focussed on the comparison between “opposition” and “sincere” voting on
a particular bill. As we have shown there are bills
on which, if the opposition were faced with a choice
between these options, they will bind themselves touse of the former. Of course, we must also consider
other voting strategies—it is possible that there is another option between outright opposition and sincerity
that yields a better outcome for all—and we do so in
Proposition 1 in Appendix A, where we state our result
more formally. There, we show that the equilibrium of
our voting game for the entire parliamentary agenda,
with asymmetric commitment, involves the opposition
adopting a strategy that is a convex combination of“opposition voting” on some bills and “sincere” voting
on others; in the former, the opposition binds its mem-Vol. 105, No. 2

bers to voting against any proposal; in the latter they
are free from party discipline. We also show (Proposition 2) that for some range of the parameter space,this equilibrium is robust to deviations by coalitions of
opposition members (technically, it is coalition proof).
Symmetric Commitment. Thus far, we have considered a situation where the opposition has greater commitment ability than the government. Although thegovernment can bring take-it-or-leave-it policies to thefloor, the opposition can then combine to counteract
the government’s agenda-setting power. As seen, theparty whip is a particularly powerful tool for the opposition to wield because it brings them policy concessions that, in the absence of such a commitment
device, they would be unable to attain. In light of this,
it is useful to consider a world where the government
has access to a similar commitment technology thatit can use to buttress its agenda-setting power. We
suppose that the government can also commit to its
voting strategies in the event where, doing so, they
make all members better off. The equilibrium of ourgame is robust to this adaptation. In short, regardlessof whether the opposition chooses to bind itself toopposing all government policies, all combinations ofproposals and government voting strategies must makeat least one member of the government worse off thanthey would be under under sincere voting. As a result,the government cannot bind itself to do other than votesincerely. We state this result formally in Proposition 3
in Appendix A. The intuition is, however, immediatefrom inspection of our example depicted in Figure 2.
There, recall that the opposition opposes all government proposals. Then the final outcome lies within the
Pareto set of government MPs ideal points. Thus, although commitment yields a Pareto improvement for
opposition members, it can yield no such improvement
for the government. Cohesive opposition voting underpinned by the development of stringent whipping
can then be viewed as a prudent strategy in response
to a government with agenda control that cannot best
respond by using similar strategies. A conjecture is thatsuch opposition strategies provide incentives for thegoverning executive to increase centralization of thelegislative initiative (see Cox 1987, ch. 6).
Other Forms of Commitment. We have yet to consider what happens when the government has commitment ability and the opposition has none, or when thegovernment can commit to other voting strategies that
do not yield Pareto improvements over those obtainedby sincere voting. As seen, the strength of opposition
voting hinges on the fact that, when the opposition
votes against all government proposals, the government must appeal to their recalcitrant backbenchers bymaking a policy concession to them. Suppose, however,that the government could obtain a “yes” vote fromsome such members on policy proposals that, if realized, leave these MPs worse off on that particularbill than they would be under sincere voting. For example, returning to Figure 2, suppose that the agenda
setter could obtain a policy closer to g2 . As shown by345

Opposition and Cohesion in Westminster Democracies

Huber (1996) and Diermeier and Feddersen (1998),
if the government can credibly invoke the threat ofa confidence vote procedure, under which they mightlose their agenda-setting power, then they can extract
policy concessions from their backbenchers.15 If, on agiven bill, the government has credible access to sucha procedure, then, in our setting, the opposition would
no longer be able to extract any gains through theuse of their voting strategies. They may well oppose(or perhaps not), but either way there are no policy
concessions to be had from so doing.
Opposition Voting in a Large Parliament. Our results show that a strategy involving outright opposition
on some bills can yield dividends to the opposition.
Here, we exploit a key element of our model—namely,
that, on average, members of the opposition are inagreement with each other; thus, the average gains
from use of their voting strategies should be similar.
We explore how the magnitude of this advantage varies
with different exogenous parameters: the distributionof ideal points, the size of the assembly, and the relative
size of the government.16 We proceed by making distributional assumptions on these key parameters andsimulating roll call behavior in large parliaments.
Overlap and Strategic Advantage. Our main results
confirm that the relationship between polarization andthe advantage of strategic voting is nonmonotonic. In
particular, if some members of the opposition are closer
to the government agenda setter than to members of
the government who would be decisive if the opposition vote strategically, then the incentives for strategic
voting are undermined. Why is strategic voting dominant only when polarization takes intermediate values?
The intuition is straightforward. If polarization is high,then the opposition is largely irrelevant to outcomes,
and members of the opposition are indifferent between
their voting strategies. If it is too low, then at least some
opposition members find themselves in relative agreement with the government agenda setter and prefer
to vote sincerely. We illustrate this result in Figure 3,
which simulates a large parliament where 301 members
belong to the governing party and a range belong tothe opposition. On each policy j, the ideal points of thegoverning party members are drawn from a normal
distribution with mean −1 and variance 2, whereas all
opposition members’ ideal points are drawn from anormal distribution with a mean that varies between 7
and 11 at regular intervals. A status quo is generated as
15 Huber develops the spatial model to show that the ability of thegovernment to declare any policy an issue of confidence means thatthe government may be able to pass bills with the support of their own
backbenchers, even though some government backbenchers prefer
the status quo. Diermeier and Feddersen use a bargaining model toshow that government cohesiveness is higher under a confidence voteprocedure than in its absence: when casting their votes, government
backbenchers take into account the future loss of income should thegovernment to which they belong lose its agenda-setting power.
16 Because the variable of interest is continuous and the parameters
are many, outside of particular examples (as in Figure 2), we cannot
report a simple typology of status quo positions and the corresponding strategy choices.

346

May 2011

a single draw from a uniform distribution with a given
maximum and minimum on the real line. For each meanvalue in the sequence, a total of twenty parliaments are
simulated, each consisting of 1,000 bills.
On the horizontal axis, we plot a measure of polarization that we term “overlap.” This is the proportionof opposition members whose ideal points are to theleft of the rightmost member of the government divided by the size of the parliament. When this measure equals zero, the set of ideal points of governmentand opposition members are disjoint. In contrast, if
overlap is 1, then, on average, there is no ideologicaldistinction between the views of members of government and opposition. The (smoothed) curves on thevertical axis depict the payoff differential to the mostmoderate (most “left wing”) member of the opposition between adopting a sincere voting strategy andan opposition one when the proposal is endogenous
to these voting strategies.17 When the curve lies above
zero, on average, the payoff of an opposition strategy
for the most moderate member of the nongoverning
party, and therefore all other members of the opposition, is higher than that of a sincere voting one. Eachcurve relates to a different size of opposition ranging
from 100 to 300. The shape of the curves depicting thepayoff differential follows the logic described previously: starting at zero overlap (complete polarization),the payoff differential is increasing, and it reaches amaximum at intermediate levels of polarization.
Strategic Voting and Policy Moderation. A related
question concerns the impact of different voting strategies on the policy outcomes of the parliament. Under
sincere voting, upon conclusion of the parliamentary
agenda, and on each policy, the outcome will lie in theset of points between the ideal point of the agenda
setter and the median member. Under strategic voting,all outcomes lie in the set of points bounded by theideal point of the agenda setter and the government
pivot. In both situations, the agenda setter exploits herrole to induce outcomes that are as close as possible
to her ideal point, and so the Condorcet outcome ischosen only in the rare case where the agenda setter
has the median preference. A corollary of our main
result is that if the opposition vote strategically, thenoutcomes can be closer to the outcome that would prevail under sincere voting. To illustrate, we simulated alarge parliament as previously shown. We recorded, forevery bill, the distance between the ideal point of themedian legislator and the outcome under opposition
voting minus the distance that emerges under sincere
voting. We then took means. When this (mean) difference is negative, opposition voting yields outcomescloser to the median legislator than sincere voting does.
Conversely, when this difference is positive, the outcome from opposition voting must be further fromthe median legislator (and thus the distance further)than that under sincere voting. Figure 4 displays our results for different opposition sizes and demonstrates a
17 Note that the absolute magnitude of the utility gains is irrelevant;here, we only need to consider the relative payoffs of different actions.

American Political Science Review

Simulation Results, Assuming Government of Fixed Size (301 Members)
100
150
200
250
280
290
296
298
300

1.0

300 MPs

298 MPs

296 MPs

0.5

Utility Adv from Oppn Voting

1.5

FIGURE 3.

Vol. 105, No. 2

290 MPs
280 MPs

0.0

250 MPs

0.00

0.02

0.04

0.06

0.08

0.10

0.12

Overlap

Curves show utility gain of opposition/strategic voting (over sincere voting) for most moderate member (most “left wing”) of opposition
party, for various numbers of opposition MPs and overlaps. The line labeled “300 MPs” refers to an opposition of size 300. Below 0 on
the y axis, there are negative consequences of strategic voting: in these scenarios, the most moderate opposition member is better off
using sincere voting. MP, member of parliament.

nonmonotonic relationship: the welfare improvement
due to “opposition” voting initially increases with polarization, before decreasing as “sincere voting” becomes beneficial.
Related Notions of Opposition. We end this section
by briefly discussing how our results relate to otherapproaches to cohesion. An observational implicationof our findings is that individually rational MPs castin the role of opposition should vote as a bloc. In our
account, they do so because, by cohesively opposing thegovernment, they counteract its agenda-setting power.
Our noncooperative and policy-based approach provides an alternative to that found in the cooperative
literature. Straffin (1997) adapts the Shapley index toshow that a minority can increase their voting power
through bloc voting. However, if the majority best
responds (by also voting as a bloc), then the minority would exert more power (in the Shapley-Shubik
sense) if there was no bloc voting. Of course, there areother theoretical reasons for bloc voting: Cox (1987,66), argues that whipped votes were popular precisely
because they provided MPs with a strong cue.
Discussion. Although cohesion has previously been
understood as arising due to internal party pressures,
we have shown that the distinct pattern of governmentversus-opposition voting is due to strategic interac-tion between the backbenches. Opposition parties canuse their votes to counteract the agenda-setting power
enjoyed by the government. In particular, when thegovernment has the power to make take-it-or-leave-it
proposals to the floor of of the House, the opposition
can extract policy concessions by adopting a stance ofoutright rejection of any government proposal. Such
opposition, in turn, reinforces government cohesion.
A surprising corollary to this result is that policy outcomes can be closer to the median preference of theparliament under strategic rather than sincere voting.
The ability of the agenda setter to move outcomesaway from those that would be implemented under
the Condorcet procedure (in a unidimensional policy
space) is mitigated by opposition strategies. Our analysis suggests that Westminster-type systems may not
be as unrepresentative, or the role of opposition party
members as marginal, as previously believed.

ALTERNATIVE THEORIES AND
PLAUSIBILITY OF OUR ASSUMPTIONS
Thus far, we have shown that the basic pattern ofgovernment-opposition voting is consistent with what
we would expect to find when the opposition adopts
optimal voting strategies in Westminster democracies. New data from the Scottish Parliament and our347

Opposition and Cohesion in Westminster Democracies

Simulation Results, Assuming Government of Fixed Size (301 Members)

2.0
1.0

1.5

100
150
200
250
280
290
296
298
300

0.0

0.5

Sincere voting moderates−0.5

Effect of Sincere Voting on Policy Moderation

2.5

FIGURE 4.

May 2011

Opposition voting moderates

0.2

0.4

0.6

0.8

Overlap
Curves show moderation effect for various numbers of opposition MPs and overlaps. Below 0 on the y axis, curves imply that “opposition”
voting has a moderating effect; above zero, curves imply that “sincere” voting has a moderating effect. MP, member of parliament.

Analyzing Our Assumptions. Our results rely on two
main assumptions: the ability of the opposition to credibly commit to their voting strategies, which we have already discussed; and the monopoly over agenda-setting
power enjoyed by the government. Our key results
depend on a further condition: namely, the existenceof overlap in the ideal points of MPs.

autonomy of committees during parliamentary passage
of a bill, and the structure of the parliamentary phaseof budgeting. Among three countries deemed to havehigh agenda-setting powers is the United Kingdom,
the paradigm case of the Westminster system (the others are France and Greece).18 In Westminster systems,
we find relatively few checks on executive power, andso agenda setting is a particularly potent weapon for
the government. However, even in the absence of regional or other power centers from where they canwield influence, the opposition parties can still extract
concessions via the voting strategies they adopt in thelower chamber. In fact, our analysis offers a different
interpretation of one of the main findings in Doring(2001), namely, that countries that “rank highest in
government control of the agenda, obviously pass more
conflictual laws,” where the conflictual nature of a law
is determined by the proportion of “no” votes. Our
analysis suggests, instead, that opposition voting is adirect strategic response to the government’s agendasetting power, is not conditioned on the type of bills theAgenda-setting Control. Our analysis suggests thatthe opposition will adapt its voting strategies in theface of a government with powers to bring take-it-orleave-it offers to the floor. Doring (2001) uses measuresrelated to three indicators to assess the agenda-setting
power of European national governments: the extent
of the government’s prerogative over bills, the relative

18 Even those countries where our assumptions do not hold andwhere the government’s control over the agenda is relatively low,for example, the Netherlands, do place strong restrictions on amendments made to the government’s budget proposals (although Greece
does not). Our insights may then carry beyond Westminster, although, of course, the institutional structure in these countries ismore nuanced than the one we describe in our model.

theoretical analysis point to the conclusion that thepattern of government-opposition voting is related tothe basic institutional features of Westminster democracies and, in particular, to the agenda-setting powerof the majority party that forms the executive. In thissection, we check the robustness of our findings byanalyzing our underlying assumptions and by taking on
board alternative institutional accounts of our data. In
particular, we address the possibility that governmentversus-opposition voting arises due to (1) electoral
signaling, (2) incentives due to the electoral system,and (3) the different jurisdictions of the parliaments inquestion.

348

American Political Science Review

government proposes, and can lead to greater policy
moderation.
The Overlap Condition. A necessary condition forstrategic opposition voting is the existence of overlap in
the ideal points of government MPs and those of opposition members. This critical overlap condition is a very
weak requirement. Nevertheless, empirically identifying this effect is not straightforward. This is because
analysis of roll call votes conflates the ideal preferencesof MPs with the strategic incentives they face to votein particular ways. In particular, such votes reveal thepressures for conformity induced by the party whip.
That said, we can look at a series of ostensibly “unwhipped” votes—whose status was reported as such inofficial Commons documentation (see House of Commons Library 2008)—and estimate a one-dimensional
spatial model from them for all parties. We give details
in Appendix D, but our key finding is that for 1997–
2001 and then 2001–2005, approximately one third of
the opposition party’s MPs are located to the left ofthe most right-leaning government MP. Hence, to theextent that we can treat these roll calls as valid indicators of sincere latent ideological positions, overlapping
preferences are an empirical fact.
Alternative Theories. We consider three alternative
accounts of the government-versus-opposition patternin our data.
Electoral Signaling. We begin by dealing with a (webelieve) common view that cohesive governmentopposition allows voters to demarcate parties in policy
terms. That is, parties adopt such strategies to signal tothe electorate that there is, in fact, “clear blue water”
between government and opposition on the issues ofthe day. That is, although the opposition might prefera particular government to the status quo, it still votes
against it to signal general opposition and “difference”
to the governing party.19 Although the clear blue water
hypothesis is, we believe, commonly accepted, it does
not provide a convincing account of our data. In elections to Westminster that took place in Scottish constituencies, the main two-party races—in both 1992 and1997—were between the SNP and the Labour Party.
The same is true of elections to the Scottish Parliament.
Thus, the clear blue water argument cannot plausibly
explain both the Westminster and Holyrood agreementscores observed in Figure 1.
A more compelling argument against the electoral
signaling account comes from analyzing data in assemblies that share the basic institutional features of ourmodel but where electoral incentives are absent. Members of the House of Lords are not elected and areappointed for life. As a result, they have no individualized electoral incentives to vote strategically because
they have nothing to gain from establishing a difference in policy position between their party and another.
Figure 5 displays the results of a one-dimensional OCof the roll call data for the House of Lords in 2001–2005.
19 The logic here is that, pace Downs (1957), there may be a cost to
ambiguity at election time (e.g., Shepsle 1972).

Vol. 105, No. 2

As seen, the Labour Party is generally to the “left” ofthe cross-benchers and Liberal Democrats, who are to
the “left” of the Conservatives. However, the identities of the ranked peers are instructive: Baroness
Amos and Lord Williams—both leaders of the House ofLords during the period—appear to the “left” of theirparty (actually, they share the same rank). Meanwhile,
Labour Party “rebels” such as Baroness Kennedy of
the Shaws (see Russell and Sciara 2007, 307), and Lord
Plant appear to the right of these government officeholders. Of course, this makes little sense from an
ideological perspective, yet is entirely in keeping withwhat we observe in the House of Commons (Spirlingand McLean 2007): the one-dimensional classification
is simply a rank order from most “progovernment” tomost “antigovernment” (note that Margaret Thatcher,former Tory prime minister and Lord Strathclyde, thehead of the opposition, appear far to the “right” on thisplot).20 The bottom line here is simple: with unified
agenda control, but in the absence of individualized
electoral incentives, voting takes a government-versusopposition form.21
The historical record is also more consistent with
our account. As early as 1766, contemporary parliamentarians such as Lord Rockingham were able toclassify their colleagues in the House into a “government” and “opposition,” along with an approximately
equal number of independents (Namier and Brooke
1964, 190–91). The opposition during the period was
not a unified force, but rather a series of personalized(Whig and Tory) factions lead by aristocratic notables.
Note that this is some 60 years before the first Reform Act of 1832, and thus there can be no notionthat the parties—such as they were—offered alternative programs to woo voters in the constituencies. Indeed, relatively few districts were competitive in any
sense: “rotten” boroughs—wherein the electorate wasutterly controlled by local landowners—were common
and typically elected two members to the legislature.
Even as late as 1820, more than one third of the 558 MPs
owed their positions to patronage rather than open
contest (Thorne 1986, 44). Thus, a pattern of roll call behavior consistent with a government-versus-opposition
divide substantially predates competitive elections andparties with well-defined and ideologically distinct appeals to voters.
Incentives Due to the Electoral System. As noted in
our previous discussion of the Scottish case, the Holyrood Parliament differs from Westminster in that some
Scottish Members of Parliament (SMPs) are electedunder list Proportional Representation (PR). The fact

20 Moreover, the fit is strong relative to, say, the U.S. Senate or House:some 97% of votes are correctly predicted with this one dimension.
21 An interesting feature of the Lords is that votes cast are unrelated to career concerns. Peers have typically retired from Cabinet
activities and cannot expect promotion (back) to the executive. Consequently, party whips have almost no power to discipline membersof the Lords and thus to compel government-versus-opposition voting. This suggests that the strategic aspects of government-versusopposition voting may exist, even in the absence of strong commitment mechanisms.

349

Opposition and Cohesion in Westminster Democracies

TABLE 4.

May 2011

Kolmogorov-Smirnov Test for Scotland
First Parliament

SNP
Conservative Party
Labour Party
Liberal Democrats

Second Parliament

SMD

List

p Value

SMD

Listp Value

8
1
55
12

28
19
3
5

0.28
0.20
0.50
0.84

8
3
47
13

19
17
4
5

0.66
0.26
0.89
0.37

Null hypothesis is that list and SMD assembly members’ estimated ideal points are drawn fromthe same distribution. A p > .05 implies that we fail to reject the null (i.e., list and SMD members
behave similarly). SMD, single member district; SNP, Scottish National Party.

OC for House of Lords

eryde
tch thcl
Tha StraLabourCrossbnch

Lib Dems

Conservative

FIGURE 5.

os
Am ms
lia
l
i
W

0

edy
nt
Pla Kenn

100

200

300

400

500

600

OC Rank Order
Note that government office holders appear to the “left” of the Labour Party, whereas rebels appear to the “right” of the same party. Thisis as expected for government-versus-opposition voting. OC, optimal classification.

that the list system appears to increase parliamentary
representation for certain groups (Brown 2000) mightprovide different incentives and lead one to expect differences in the voting behavior of MPs elected under
this system. It is then plausible that differences in the
behavior of elected Scottish representatives in Whitehall and Holyrood can be explained by differences inthe electoral system. As a fillip to our argument that
it is the institutional features common to both Westminster and Holyrood—namely, the control over theagenda that is enjoyed by a majoritarian executive—
we compare the voting records of those SMPs electedunder single member district (SMD) plurality, 73 in all,350

to that of the 56 members elected under list PR. In
fact, and as explained in Tables 4 and 5 in Appendix
B, we fail to reject the null hypothesis that the ideal
points of the members from these different samples
are drawn from the the same distribution; thus, there isno obvious difference between the behavior of list and
SMD legislators within the same party.
Differing Jurisdictions. A plausible hypothesis is thatpatterns in our data reflect the functional separation ofpolicy domains. For example, although Holyrood andWestminster are similar in the structure of the executive, the jurisdiction of the parliaments is markedly

American Political Science Review

TABLE 5.

Vol. 105, No. 2

Kolmogorov-Smirnov Test for WalesFirst AssemblyPC
Conservative Party
Labour Party
Liberal Democrats

Second Assembly

SMD

List

p Value

SMD

Listp Value

9
1
27
3

8
9
3
4

0.96
0.80
0.17
0.97

5
1
29
3

7
10
0
3

0.99
0.18
—
1.00

Null hypothesis is that list and SMD assembly members’ estimated ideal points are drawn fromthe same distribution. A p > .05 implies that we fail to reject the null (i.e., list and SMD members
behave similarly). PC, Plaid Cymru; SMD, single member district.

different. To explore whether policy domain or executive structure can best explain the pattern ofgovernment-versus-opposition voting, we look beyond
these parliaments to the assemblies of Wales andNorthern Ireland. These assemblies are very similar
in terms of their jurisdiction. They also share, to a large
extent, a common inherited political culture that may
have an independent effect of patterns of legislative
behavior. However, and as we describe later, these assemblies are very different with regard to the structureof the executive.
Initially, the powers of the Welsh Assembly were
simply those previously held by the Secretary of State
for Wales, and there was no separate executive. In 2006,
the new Government of Wales Act formally divided thelegislative and executive, with the latter drawn from theformer. But, even with the earlier arrangement, it was
the Cabinet—rather than the committees—that played
the key role in developing and introducing legislation
for consideration (Laffin and Thomas 2000).22 Hence,
the agenda-setting role we allude to in our model holds
for the executive in Wales.23
In contrast, the Northern Ireland Assembly, although similar in terms of policy domain to the Welsh
Assembly, was designed with “consociational” (in thesense of Lijphart 1977) principles in mind, and thelegislature has various features that make it very different to the House of Commons. In Northern Ireland, in contrast to Westminster, Scotland, and Wales,
agenda-setting power is not controlled by a majority.
The Cabinet is necessarily drawn from both unionist
and nationalist communities with specialized procedures for allocation of portfolios (see O’Leary, Grofman, and Elklit 2004). Following the 2007 election, theparties included in government were represented bymore than 90% of the members. Moreover, in Northern Ireland, the planned roll call agenda is subject to
22 In practice, the Welsh Assembly is not as fractious an environmentas Westminster in general. We see a large number of unanimous rollcalls in Wales in which all members consent to the motion, and theseare especially common when cross-chamber reports and recommendations are being voted on.
23 Wales (like Scotland) uses a mixed-member proportional representation system to elect its members. However, we find no evidence
that—contingent on party membership—the types of legislators differ
in their roll call voting behavior at division time. See Appendix B for
details.

special voting procedures that require “parallel consent” and “weighted voting” to account for preferenceson both sides of the constitutional divide (Wilford 2000,
581). This is combined with a strong (and diverse bycomposition) committee system and a mutual veto forsome matters. In short, in Northern Ireland, in the absence of majority control of the agenda, and with several checks and balances on executive power, we would
not expect strategic “opposition” voting at division
time.
Figure 6 presents the OC of Welsh roll call votes forthe first (1999–2003) and second (2003–2007) meetingsof the assembly.24 A single dimension correctly predicts
more than 97% of the votes in both periods. On thisdimension, Plaid Cymru, the Welsh nationalists, appear
to the “right” of the ruling Labour government. Thiscannot represent an ideological scaling because Plaid
Cymru are to the left of the Labour Party and the Liberal Democrats on socioeconomic issues, and furthestfrom the Conservatives on matters of constitutional reform. In fact, their placement is as we would expect according to government-versus-opposition voting, andthis is in keeping with qualitative accounts of recent
Welsh parliamentary history (McAllister 2000). A further justification for our claim is given by examining
the specific position of John Marek, a left wing Labour
rebel who was deselected by his party after criticizing
its policies as being unduly conservative. Notice that
Marek moves “right” in the OC plots: a relocation thatmakes sense only if we regard the scaling as reflective of government-versus-opposition. That is, Marek’s
true ideological position is to the left of the Labour
Party; yet, his scaled position is to the right because
he now opposes its proposals. The Welsh case thus
confirms that strategic opposition voting emerges inlegislatures outside Westminster and Holyrood, given
the basic institutional apparatus of an executive able tocontrol the agenda (and some mild conditions imposedon preferences of members).
Figure 7 shows the data from the Northern Ireland
Assembly. The first subfigure refers to an OC of rollcalls during the period 1999–2002, after which the assembly was suspended. The second subfigure is then the
period from the 2007 elections through to June 2008.
24 See Appendix C for details on our data and operations.

351

Opposition and Cohesion in Westminster Democracies

FIGURE 6.

May 2011

Scaling of the Welsh Assemblies: Government-versus-opposition

LabourLabourPd Cymru

Pd Cymru

Lib Dems

Lib Dems

Cons'tive

Other

Cons'tive

John MarekJohn Marek

0

10

20

30

40

50

60

0

10

20

30

OC Rank Order

40

50

60

OC Rank Order(a) First Assembly(b) Second Assembly

Note position of John Marek: his left wing views cause him to leave the Labour party; yet, he is subsequently positioned to their right.
Parties are Labour, Plaid Cymru (Pd Cymru), Liberal Democrats (Lib Dems), Conservatives (Cons’tive), and Others.

FIGURE 7. Scaling of the Northern Irish Assemblies:
Government-versus-Opposition Pattern is Absent

DUP

UUP

UKUP

DUP

UUAP
SF
NIUP
Ind
UUP
IHC
PUP
Greens
Allce
Allce

SDLP

NIWC

SDLP

SF

PUP

0

20

40

60

80

100

0

20

40

60

80

100

OC Rank Order

OC Rank Order(a) 1999–2002: UUP and SDLP Dominate Executive(b) 2007–08: DUP and SF Dominate Executive

Full key for the many parties is found in Appendix C.

In the prior period, the Ulster Unionists (UUP) andthe nationalist Social Democratic and Labour Party(SDLP) were the largest two parties and earned thefirst and deputy first minister slots. In the next period,
the Democratic Unionist Party (DUP) and Sinn Féin

352(SF) took those roles. The other major parties werealso, by constitutional construction, included in the
Cabinet. If our analysis is correct, then we should nolonger expect (larger) parties to consider themselves
out of power at any particular time, and in the absenceAmerican Political Science Review

of “opposition,” we would expect parties to vote alongideological lines. Figure 7 demonstrates this pattern: inthe upper portion, the coalition of the UUP and SDLP
appears in the middle of the one-dimensional scaling(which correctly predicts 95% of the votes), whereas
the DUP and SF (who did not possess the top positions
at this time) disagree more often with the coalition
and, crucially, one another. In the second plot, we see
the same pattern with the requisite identities reversed:
now the DUP and SF form the center of the dimension(again, a single dimension predicts 95% of the votes
correctly). Thus, although the pattern we observe inthese figures reflects subtle differences in the make-upof the executive at different times, we do not observeanything equivalent to government-versus-opposition
voting.
In sum, the pattern of voting in the Welsh Assembly conforms to what we should expect given theunified control of the agenda by the governing majority. Removing this necessary condition for strategic opposition voting—that of unified agenda-setting
power for the executive—leads to the converse prediction: the scaling of roll calls should no longer reflect
a government-versus-opposition dynamic. Data fromthe Northern Ireland Assembly suggest the hypothesis
is correct: in the Northern Ireland Assembly, with its“shared” executive, the government-versus-opposition
pattern disappears. Thus, constitutional variation in
the new assemblies introduced under the New Labour
constitutional reforms can account for differences inthe voting patterns of these assemblies. The evidence
refutes the claim that government-versus-opposition
voting is related to differences in policy domain (orthat it arises as an “indigenous” aspect of politics in the
British Isles).

IMPLICATIONS WITHIN AND BEYOND
WESTMINSTER
Within parliamentary systems that provide strong
agenda-setting powers to the government, the abilityof the opposition to extract policy concessions via theirvoting strategies might vary according to the structureof the party system. We use the illustrative case ofa single-party majority government with single-party
opposition. Clearly, our findings extend directly to parliamentary situations where the government and/or
opposition contains multiple parties and, in particular,
to the case where the ideal points of government andopposition MPs lie, on average, at either side of a single
cut point (that may, for example, distinguish a left voting bloc from a right voting bloc). If these conditions
are not met, for example, where opposition parties canbe found either side of the governing party, then weshould still observe strategic opposition voting. Then,
whereas it would not be possible for each opposition
party to simultaneously extract policy concessions on
the same policy dimension, each party would extract
concessions on different bills. However, even in thiscase, if one party were the main party of opposition,and the status quo policies are, on average, closer toVol. 105, No. 2

the ideal points of their MPs than to those of the government, then a strategy of outright opposition to thegovernment will yield dividends to the minority.
Our focus has been on Westminster systems with
their fusion of executive and legislative powers and majoritarian control of the agenda combined with strong
party discipline. As shown by Hix and Noury (2008),
government-versus-opposition voting is most prominent in Westminster-style systems but also observed
elsewhere. It is possible then that our insights carryover to other parliamentary systems. Indeed, in many
non-Westminster parliamentary systems, agenda setting is controlled by a minimal winning coalition andstrong party discipline exists: thus, majoritarian control of the agenda should also give rise to strategic
opposition. However, in non-Westminster systems, therole played by opposition voting strategies may be
countered by other constitutional checks and balances;these issues remain ripe for further exploration.

CONCLUDING COMMENTS
Using new evidence from the first two Scottish Parliaments between the years 1999 and 2007, and comparing and contrasting it with evidence from theWestminster Parliament, we challenged the view thatcohesive government-versus-opposition voting patterns can be explained by similarity of preferences
within and between the government and opposition
ranks. By exploiting the institutional variation between Westminster and Holyrood, we showed thatgovernment-versus-opposition voting can plausibly belinked with the key institutional similarities of thesesystems, namely, the procedural rules for reachingcollective decisions in Westminster systems in which
agenda-setting power is given to the majority party.
Our formal analysis reveals that strategic oppositionis central toward explaining the cohesive nature anddistinct pattern of government-opposition voting. The
opposition can gain by adopting “just say no” strategies
that counteract the government’s control of the agenda.
Doing so reinforces the cohesion among government
backbenchers, and the end result can be greater policy
moderation. Our insights challenge conventional wisdom that the opposition is marginal to policy making
in Westminster democracies.25

APPENDIX A:FORMAL RESULTS AND PROOFS
To show our main results, we introduce some basic notational
definitions. Recall that, on each policy, the government members’ ideal points are iid draws from a (common and known)
distribution. With no loss of generality, we suppose that the
government is the “left” party. Now suppose that, on eachpolicy, we order each government member according to theirideal points on that policy from the leftmost to rightmost

25 Our study suggests that results in Hicks and Swank (1992) and
Mikhaylov (2007) showing general effects of opposition policy positions on policy outcomes may well hold true in the restricted sample
of majoritarian democracies.

353

Opposition and Cohesion in Westminster Democracies
government member. We define xj as the ideal point of¯
the leftmost member of the oppositionon the jth policy.
Adopting Krehbiel’s terminology, we define the government’s (right) pivot on policy j as the member with ideal pointx‡j such that there are exactly (m + n)/2 government memberswith ideal points less than (i.e., to the left of) x‡j .26 We defineψ‡j as the policy proposal that leaves this pivot strictly indifferent between voting “aye” or “no” when voting sincerely.
Finally, we define x†j as the preference of the median memberof parliament and ψ†j as the policy proposal that leaves herstrictly indifferent between her actions under sincere voting.
We write ψj as the proposal made by the agenda setter of the
majority party on the jth policy and refer to the status quo
position, which remains in place if the government proposalqdoes not achieve majority support, as xj .

Asymmetric Commitment. The main case we explore
involves asymmetric commitment. On any bill, the opposition
can bind itself to vote in a particular way if, by so doing, theirMPs can attain higher payoffs. We begin by showing that onsome bills opposition MPs will commit to using a voting protocol in which members do not vote sincerely. We do this byshowing that on these bills sincere voting is Pareto dominatedby “opposition” voting in which opposition MPs vote “no”
on all proposals. Our analysis focuses on the interim, after
ideal points have been realized but before the agenda setter
makes a proposal.
LEMMA 1. Suppose that the parliamentary agenda consistsof a single policy and that (1) xq > x† , (2) x ≤ x‡ , and (3)¯in which|x − ψ‡ | ≤ |x − ψ† |. There is a Nash equilibrium¯¯
the opposition members always vote “no” and government
members vote “aye,” and then the expected payoffs from thisstrategy to members of the opposition are higher than thoseobtained when all members vote sincerely.
Proof of Lemma 1. The key policy outcomes are ψ† and ψ‡ :the first occurs when all vote sincerely, and the second when
opposition members oppose all proposals. It is straightforward to show that if conditions (1) and (2) hold, then ψ‡ ≥ ψ† .
We need only show that the posited profile is an equilibrium
and that the opposition member with ideal point x receives a¯ all votehigher payoff from this equilibrium than one in which
sincerely. Under the posited profile, MPs from the governing
party vote “aye,” the opposition vote “no,” and the policy
outcome satisfies ψ‡ = |2x‡ − xq|. Since, by definition of ψ‡ ,the right pivot is indifferent between her actions she has
no incentive to deviate; all government members for whom
xi < x‡ strictly prefer the proposal to the status quo and haveno incentive to deviate either; fixing these voting strategies,
the bill then passes, all other MPs xi > x‡ are indifferent between their voting strategies, and thus none have an incentive
to deviate. So, we show that all government members voting“aye,” all opposition members voting “no,” and the agenda
setter proposing ψ‡ forms a Nash equilibrium. Suppose thatthe opposition instead vote sincerely, then the agenda settercan do no better than making the median MP indifferent between her voting strategies and thus ψ† = |2x† − xq|. Supposethat ψ† = ψ‡ that conditions (1), (2), and (3) hold, and that,
contrary to our claim, this equilibrium yields a higher payoff
to members of the opposition than obtained in equilibrium
when all opposition members vote “no” on all government

26 We can similarly define the government’s (left) pivot, but this is
not necessary for our purposes.

354

May 2011
proposals. In particular, it must then yield a higher payoff to the leftmost member of the opposition. But this canonly be the case if |x − ψ‡ | > |x − ψ† |, which contradicts the¯¯䊏premise.
We have shown that on some bills the opposition will not votesincerely. Moving further, we characterize the equilibrium forthe whole parliamentary agenda:
Proposition 1. For a parliamentary agenda J ∈ Rd , d ≥ 1, theequilibrium involves the opposition voting “no,” irrespectiveof the government proposal, on some bills and voting sincerely
on others. The equilibrium has the following form: for any j,q
if (1) xj > x‡j ; (2) xj ≤ x†j ; and (3) |xj − ψ‡j | ≤ |xj − ψ†j | then¯(a) all government¯ members vote sincerelyand¯ in favor of
the agenda setter’s proposal; (b) all opposition members voteagainst the government on each bill; and (c) the governmentq
proposal satisfies ψ‡j = |2x‡j − xj |; if (1), (2), or (3) do not hold,then the government proposal makes the median member,whether a member of the government or the opposition, inq
different between voting “aye” or “no;” thus, ψ†j = |2x†j − xj |,and all MPs vote sincerely.
Proof of Proposition 1. The strategy calls on opposition
members to vote sincerely unless the conditions in Lemma
1 are satisfied, in which case they oppose all government
policies. Recall that on each policy the members’ ideal points
are iid draws from a distribution with positive support. Thus,
for a given parliamentary agenda, there is a strictly positive probability that the agenda includes a policy such thatthe conditions in Lemma 1 are satisfied. On such policies,
the interim utility from opposing all policies exceeds thosefrom voting sincerely as shown previously. Starting from thesubgame where the agenda setter introduces her proposal,“opposition” voting Pareto dominates sincere voting. Since
we can therefore rule out sincere voting on these bills, the opposition will bind themselves (to a different voting protocol)
on such bills. We make a stronger claim that the opposition
will commit to the voting profile described. For this to be so,
it must be that such a strategy yields a Pareto improvement
over all other voting strategies in the subgame, starting withthe agenda setter’s proposal. In principle, this is a hard claim
to prove since we must check a very large number of different
strategies. We take a simpler route. A Pareto improvement
must involve an outcome that lies outside the Pareto set of
opposition members ideal points. We know that when conditions (1) and (2) hold, then ψ‡j ≥ ψ†j . Moreover, condition(3) |xj − ψ‡j | ≤ |xj − ψ†j | ⇒ xj > ψ†j . Since if ψ†j < xj < ψ‡j ,¯¯then ¯no outcome¯ can be Pareto
improving; our claim
canonly be false if, given some voting strategy deployed by the
opposition, a Pareto improvement exists and ψ‡j < xj . Then,for example, the outcome ψ‡j < ψj < xj would yield ¯a Pareto¯
improvement. Suppose that the opposition
could bind themselves to such a voting strategy that, given the agenda setter’s best response, yields this outcome. We leave this voting
strategy undefined but—since the best policy opposition
members can achieve by all opposing on that particularbill is ψ‡j —it might involve a combination of complicated
votes across different bills. However, ψj > ψ‡j implies thatthe agenda
setter is worse off when the final policy outcomeis ψj , and so she prefers outcome ψ‡j . Moreover, given ourassumption of sincere voting by government members, she
can always attain her payoff from introducing ψ‡j by bringing
this proposal to the floor, where it will pass with the supportof her own backbenchers. We conclude that, if there were avoting strategy that yields a Pareto improvement toAmerican Political Science Review
opposition members, then this cannot form part of a Nashequilibrium. The only voting strategy the opposition can commit to then is the one described, and in the equilibrium, they䊏will vote along these lines.
Note on Proposition 1. We have used the Pareto criterion
to select among the multiplicity. Perhaps a different selection
criterion is more appropriate? Bernheim, Peleg, and Whinston (1987) suggest that in selecting equilibria, the Pareto
criterion should be applied not to the set of all Nash equilibria, but instead to those equilibria that are coalition proof.
This entails that the equilibrium should be robust not only
to deviations by individual players (members), but also todeviations by (any) coalitions of players; and that these deviations should themselves be robust to further sub-deviations,which in turn should be robust to finer deviations. (A related
concept that does not rely on such a recursive structure isStrong Nash equilibrium.) The justification for using this particular refinement here is that we may have ruled out a voting
strategy that, although not better for all, could be better forsome members of the opposition party. Whereas previously
we allowed the opposition to invoke the party whip only on
bills where all opposition members could be made better off
when they voted “no,” here they can do so only when there
exists no faction, of whatever size, that could do better byfollowing a different voting strategy. In principle, once again,
this is hard to show: there are many voting strategies and(now) many different coalitions. Nevertheless, we can makeprogress by focussing on particular outcomes.
Proposition 2. Suppose that the opposition can invoke theparty whip on a bill to enforce a “no” vote only when there exists no faction of opposition members who would do better by
voting “aye” on that bill. For a parliamentary agenda J ∈ Rd ,d ≥ 1, the equilibrium involves the opposition voting “no,”irrespective of the government proposal, on some bills andsincerely on others. The equilibrium has the following form:q
for any j, if (1) xj > x‡j , (2) xj ≤ x†j , (3) |xj − ψ‡j | ≤ |xj − ψ†j |,¯¯¯‡and (4) xj > ψj then (a) all government members vote sin¯
cerely and in favor of the agenda setter’s proposal; (b) all
opposition members vote against the government on each bill;qand (c) the government proposal satisfies ψ‡j = |2x‡j − xj |; if(1), (2), (3), or (4) do not hold, then the government proposal makes the median member, whether a member of thegovernment or the opposition, in different between votingq“aye” or “no,” thus, ψ†j = |2x†j − xj |, and all MPs vote sincerely. If the opposition is more restricted in the use of theparty whip, then it will adopt “opposition” voting on fewerbills.
Proof. The proof follows the same steps as used in
Proposition 1. We first show that there are some bills on
which the opposition will not vote sincerely. If (1) and (2)hold, then ψ‡j > ψ†j . Now if ψ†j < xj < ψ‡j , then it is also the¯case that there is no coalition of opposition
members, of any
size, who receive a higher payoff in an equilibrium where
they vote sincerely rather than following the prescribed profile. To see why, note that the profile calls on all opposition
members to vote “no” on a bill if conditions (1) and (2) are
met and if the leftmost member of the opposition, with ideal
point xj , is at least indifferent between her actions. However,¯ is so, all members with ideal points x > x strictly
when thisijj¯
prefer to vote “no” also. It remains to show that thereis nostrategy other than the one described that is preferred by any
faction of opposition MPs. Since xj > ψ‡j , there exist policy¯
by a coalition ofoutcomes ψj > ψ‡ that would be preferred
opposition members. One such policy is ψj = xj . However,¯Vol. 105, No. 2
such outcomes can never be realized in equilibrium. Since
government members vote sincerely, the agenda setter canalways obtain her payoff from policy outcome ψ‡ by bringing
a proposal that leaves the government’s pivot indifferent between voting “aye” or “no.” Thus, all government members
vote sincerely, and so this proposal will pass. The final partof the proposition contrasts outcomes with those obtained in
Proposition 1. This follows because it is possible that conditions (1), (2), and (3), which are the same as those used in theprevious result, are met, but that there exists a coalition of
opposition members who by voting differently could attaina preferred outcome ψ‘j < ψ‡j if such a proposal were made;then the requisite proposal will be made by the agenda setter.
䊏Symmetric Commitment. We now suppose that both thegovernment and the opposition can bind themselves to avoting protocol on a bill if, by so doing, their MPs can attainhigher payoffs. In the absence of such a Pareto improving
strategy, we restrict them to voting sincerely.
Proposition 3. Suppose that both the government and the
opposition can invoke the use of the party whip when doing
so yields higher expected payoffs for their members, then thegovernment votes sincerely and the opposition uses the strategy
described in Proposition 1.
Proof of Proposition 3. Under the posited profile, on any
policy j, the outcome is either ψ†j or ψ‡j . The former occurs
when one of conditions, (1), (2), or (3), in Proposition 1 isleft unsatisfied, and so the strategy calls on the opposition tovote sincerely. Suppose that the government could commit
to its voting strategies and that there were some combinationof proposal and votes that yielded a policy outcome less thanψ†j . This must leave the median member worse off. Either
the median is a member of the government or there must
be a government member to the right of the median who isalso worse off. Any outcome involving ψ > ψ†j can never bepart of an equilibrium since the proposer prefers ψ† and thus
has a profitable deviation. The more difficult case is whenconditions (1), (2), and (3) hold; then the equilibrium policy
outcome is ψ‡j , which by definition makes the government“pivot” indifferent between her actions. Any policy outcome
ψ < ψ‡j must, by definition, make at least one member ofthe government worse off. Following the preceding logic,
no outcome ψj > ψ‡j can be part of an equilibrium. Thus,in equilibrium, the government votes sincerely because it
cannot bind itself to do otherwise, and the opposition best
responds by using the strategy described in Proposition 1. 䊏Note on Proposition 1. If the opposition has use of the party
whip, then the outcomes will correspond to those described in
Proposition 1 and our previous results continue to hold. The
argument is not watertight. We restrict the government tousing sincere voting in the absence of a Pareto improvement;
however, if this were not the case, then, although there would
still be an equilibrium in the form of that described previously,
it would not be unique.

APPENDIX B: BEHAVIORAL SIMILARITY OF
LIST AND SINGLE MEMBER DISTRICTMEMBERS IN SCOTLAND AND WALES
Writing the list members of the party p as pl and the SMD
members as ps , we proceeded as follows:355

Opposition and Cohesion in Westminster Democracies

TABLE 6. Overlap at Westminster:
1997–2001, 2001–2005
1997–2001 2001–2005
Overlap: govt/Conservatives
Overlap: govt/all oppn

0.12
0.33

0.14
0.39

Ideal points estimated via Bayesian IRT model.

1. We estimated a one-dimensional Bayesian IRT model(see Jackman 2008) on these data (10,000 iterations of
the sampler, 5,000 iterations as burn-in).
2. We extracted the ideal points for each party p, and compared the distribution of pl ’s ideal points and ps ’s ideal
points via a two sample Kolmogorov-Smirnov test inwhich the null hypothesis is that the sets of ideal points
for list and SMD members in p are drawn from the same
distribution.
Our results are as reported in Tables 4 and 5, where we also
report the numbers of legislators in each group and at eachtime in our sample. Note that, in every case given here, forevery parliament, the null hypothesis that pl and ps are drawn
from the same distribution cannot be rejected. That is, there
is no obvious difference between the behavior of list and
SMD legislators within the same party when it comes to rollcall voting.

APPENDIX C:OPTIMAL CLASSIFICATION OF THE WELSHAND NORTHERN IRISH ASSEMBLIESFor Wales, our reported OC of legislators was constructed in
the following way:
1. Our roll call matrix for the assemblies was constructed from the official reports of daily activity(“Records of Plenary Proceedings”) in the legislature
at www.assemblywales.org/bus-home/bus-chamber/buschamber-first-assembly.htm and www.assemblywales.org/
bus-home/bus-chamber/bus-chamber-second-assembly.
htm.
In particular, we used Perl in conjunction with regularexpressions to pull the votes from the pdf files andcompile them to a matrix with rows as (uniquely named)
legislators and columns as items on which they werevoting.
2. We fitted an OC in one dimension, in the sense of Poole(2000) using software from Poole et al. (2009) with standard defaults (a minimum of 20 votes for each legislator, with 2.5 set as minimum acceptable standard for“lopsided” votes).
For Northern Ireland, we filled a Freedom of Information(FOI) request and received the relevant matrix of roll callsfrom the FOI Officer at the Northern Ireland Assembly.
These cover the period July 1998–June 2008, although formuch of that time the assembly was suspended (2002–2007).
Our specification for the OC scaling was as reported for the
Welsh case.

356

May 2011
The full key for Figure 7 is as follows: Democratic Unionist Party (DUP), United Kingdom Unionist Party (UKUP),
Ulster Unionist Assembly Party (UUAP), Northern Ireland Unionist Party (NIUP), Ulster Unionist Party (UUP),
Popular Unionist Party (PUP), Alliance Party (Allce), Social Democratic Labour Party (SDLP), Northern Ireland
Women’s Coalition (NIWC), Sinn Fein (SF), Green Party inNorthern Ireland (Greens), Independent Health Coalition(IHC).

APPENDIX D:EMPIRICAL CONDITIONS: ANALYSIS OF
FREE VOTES AT WESTMINSTER
Our analysis requires that the status quo lie to the right of theagenda setter’s ideal points on some policies. Although from astatistical perspective, it is not generally possible to precisely
measure where the status quo for policies lies. Nonetheless, it
is reasonable that governments in Westminster systems will
predominantly move policy “down” the real line toward theirideal points. Certainly, this is true of the Scottish Parliament
where the Labour Party and the Liberal Democrats sought toreverse policies implemented during 18 years of Tory dominance at Westminster. In addition, we require “overlap.”
Although calculating the precise degree of overlap in MPs’
views in the House of Commons is difficult, almost all rollcalls are subject to reasonably strong “whipping,” meaning that “sincere” (latent) preferences are rarely recorded
at division time (Spirling and McLean 2007), and evenwhen votes are ostensibly “free,” mild party-based pressure
may still be applied (McLean, Russell, and Spirling 2003).
Nonetheless, we obtained a rough estimate by proceeding asfollows:
1. Using a report fromHouse of Commons Library (2008, 6),
we obtained a list of roll calls that “had been announced
as being a free vote for Labour, Conservative and Liberal
Democrat Members” for the first and second Blair parliaments: 1997–2001 (15 free votes) and then 2001–2005(65 free votes).
2. We matched these roll call names to voting data provided
by Firth and Spirling (2005).
3. We estimated a one-dimensional Bayesian IRT model(see Jackman 2008) on these data (25,000 iterations of
the sampler, 5,000 iterations as burn-in).
4. We then report the “overlap” between nongovernment
parties’ ideal points O and the governing Labour Party
G as the number of individuals in the opposition whose
estimated ideal points were smaller (to the “left of”) themost “right wing” government MP. We write the vector ofthese individuals’ ideal points as o and denote the numberof such individuals as |o|. Thus, our measure is|o ∈ O : o < max(G)|.
|o|Note that we assume free votes for the three main parties,
which comprise 95% of the seats in the Commons, are also
free votes for the minor parties.
In Table 6, we record the overlap between the governing partyand (1) the main, Conservative, opposition party; and (2) all
opposition parties. As seen, these proportions are around
one seventh and one third, respectively. We indicate themost “right wing” Labour MP in both periods is Kate Hoey,
who is well known as a supporter of fox hunting—an unusualAmerican Political Science Review

Vol. 105, No. 2

APPENDIX E: OPTIMAL CLASSIFICATION
OF THE HOUSE OF LORDS

FIGURE 8. House of Commons: Empirical
Overlap of Ideal Points
3.0

Our reported OC of legislators was constructed in the following way:

0.5

1.0

1.5

2.0

2.5

1. Our roll call matrix for the 2001–2005 parliament wasprovided by The Public Whip, www.publicwhip.org.uk.
2. We dropped bishops (who vote very rarely anyway) and
fitted an OC in one dimension, in the sense of Poole (2000)
using software from Poole et al. (2009) with standard
defaults (a minimum of 20 votes for each legislator, with
2.5 set as minimum acceptable standard for “lopsided”
votes).
3. In reporting, we dropped seven Lords not attached tothe main groups (including the cross-benchers): Lord
Beaumont of the Green Party, Lord Stoddart of Swindon(Independent Labour), and five others (Lords Dearing,
Fitt, Grenfell, McAlpine, and Young).
Kate Hoey−1

0

REFERENCES
1

2

Ideal Points

0.5

1.0

1.5

(a) 1997–2001

Kate Hoey

−1.5

−1.0

−0.5

0.0

0.5

1.0

1.5

2.0

Ideal Points(b) 2001–2005
Government MPs are distributed as the density that peaks to
the left with a solid line; opposition MPs are distributed as thedensity peaking to the right drawn with a broken line. MP, member of parliament.

position for a Labour MP, but common among Conservative
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course, with just 15 and then 65 roll calls to estimate thepositions of more than 650 MPs, we cannot claim any particular precision for our findings. Nonetheless, the notion that
there is overlap in at least one policy dimension—roughly
estimated—is apparent.

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