Dyadic Representation in a Westminster System

In Westminster systems characterised by cohesive national parties, is there any room for meaningful dyadic representation, whereby the ideological outlook and legislative behaviour of individual Members of Parliament reflects the political preferences of their constituents? Research on this question has until now been impeded by difficulties in measuring constituency-level opinion and individual MP preferences. In this paper, we focus on Britain and use multilevel regression and post-stratification to generate constituency level measures of opinion on economic issues, the European Union and same sex marriage. We find that constituency opinion on these issues is associated with MP preference variation within parties, as measured based on un-whipped legislative behaviour. Our findings thus suggest that there is a basic constituency-MP representation bond which operates in Britain in addition to the representation bond formed between voters and parties.


Introduction
For countries that elect their legislators using single-member districts, one potentially important form of substantive representation (Pitkin, 1967, 222-224) is the degree to which the policy preferences of legislators reflect the policy preferences of their constituentsa form of representation that has become known as dyadic representation (Weissberg, 1978). 1 In the United States, this phrase has become associated with a rich vein of literature which takes as its inspiration the work by Miller and Stokes (1963), and which has, over the decades, become increasingly sophisticated in an effort to identify the causal pathways through which such an association might arise (Hill and Hurley, 1999), and to deal with important objections challenging the identification of statistical measures of association with substantive representation (Achen, 1977;Masket and Noel, 2012;Hug and Martin, 2011).
Outside of the United States, with some rare exceptions (Converse and Pierce, 1986), the study of dyadic representation has withered on the vine (Powell Jr, 2004). In Westminster systems, where single-member districts at least imply some dyadic link between a legislator and their constituents, research has instead tended to focus on democratic representation via "responsible national parties", whereby cohesive political parties compete for government on national policy platforms (Miller and Stokes, 1963, 45). In Britain for example, major studies have analysed the links between national party platforms (e.g. Heath et al., 2001), national government policy agendas (Jennings and John, 2009) or national government spending (Soroka and Wlezien, 2005) on the one hand, and the preferences of the national electorate on the other. This paper asks whether there is any room for dyadic representation in Westminster systems, or whether 'constituency influence' in such party-centric systems is fully exhausted by the constituency's choice of a legislator from party X rather than party Y?
Research on this question has until now been severely impeded by a lack of appropriate 1 In countries with multimember constituencies, substantive representation is not dyadic, but involves a one-to-many linkage between a constituency and its several representatives (Golder and Stramski, 2010) empirical measures. First, it is expensive to obtain precise estimates of constituency opinion through mass surveys. Although the per-respondent cost of opinion surveys has decreased over time, sampling even a small number of respondents in each constituency quickly yields total sample sizes in the hundreds of thousands.
Second, it is also difficult to measure individual legislators' preferences. Response rates to elite surveys are low, and work based on responses to such surveys has had to resort to aggressive multiple imputation to deal with missing responses (Kam, 2001(Kam, , 2009. Strong party discipline also means that any differences of opinion between members of the same party are either reconciled in private settings (Cowley, 2002, 183;Norton, 1999), or, if they are made visible in legislative votes, are only made visible in ways incompatible with many of the models of sincere voting upon which many scaling techniques rely (Spirling and McLean, 2007).
Despite these challenges, we argue that it is possible to identify dyadic representation in a Westminster system, over and above the extent of dyadic representation that would be observed if constituency influence operated solely through choice of MP party. We study the British case and use methods of small area estimation to derive new estimates of constituency opinion both on a general left-right economic scale and on specific issues (same-sex marriage and the European Union). We then show how these measures of constituency opinion are associated with MP preferences, measured either via 'free votes' where party whipping is minimal, or by using early day motion signatures as an "unobtrusive measure" (Franklin and Tappin, 1977) of MP preferences (Kellermann, 2012).
Together with other recent research, our findings point toward a previously underappreciated representation mechanism in Westminster systems. Kam et al. (2010) have recently provided evidence that the ideological preferences of backbench MPs in the House of Commons significantly constrain policy-relevant choices made by party leaders, the actors conventionally assumed to dominate the policy-making process in Britain.
They speculate that this influence of rank-and-file MPs on party leaders could mean that the constituents who choose MPs have more influence in policy-making than previously thought. Of course, this only holds if MPs' preferences reflect those of their constituents.
Our findings suggests that they do, to a nontrivial extent.
We proceed as follows. In section 2, we discuss the extant literature on representation in Westminster systems, and give reasons why, on the face of it, we would be unlikely to find evidence for dyadic representation. In section 3, we provide estimates of constituency opinion on a general left-right economic scale, and on the specific issues of same-sex marriage and the European Union. In section 4, we provide estimates of MPs' leftright position, and discuss observed un-whipped votes on same-sex marriage and the European Union. The bulk of our analysis comes in section 5, where we show that the association between MPs' positions and those of their constituencies are greater than would be expected if constituency influence operated solely via the choice of MP party.
We conclude (in section 7) by discussing the practical relevance of our findings.

Literature review
More than fifty years after Miller and Stokes' original study, the literature on dyadic representation generally has investigated the mechanisms which underpin any link between constituency preferences and legislators' actions -the 'basic bond', as Converse and Pierce (1986) later put it. These studies suggest that dyadic representation is greater where representatives must face re-election (Tien, 2001), where re-election is imperilled by greater electoral marginality (Griffin, 2006), and where initial selection is more open (Gerber and Morton, 1998). Studies also suggest that representatives must correctly perceive their constituency's preferences, and whilst there is evidence that they do so poorly (Broockman and Skovron, 2013), there is also evidence that legislators do respond to the provision of information about constituency preferences (Butler et al., 2011). Some research has used information about constituency preferences from referenda to assess the degree of dyadic representation (Masket and Noel, 2012;Hug and Martin, 2011)which has the advantage of placing legislators and citizens on a common scale, but is less reliable the more referenda serve as second-order tests of ruling party support.
When we read this literature in light of what has been written on candidate selection, parliamentary behaviour, and electoral outcomes in the UK, we are forced to conclude that dyadic representation here is unlikely. First, for dyadic representation to exist, there must be variation in the policy preferences of MPs from the same party. Yet even absent possible sanctions, when MPs might be expected to express their sincerely held preferences, MPs from the same party generally display high levels of voting unity (Norton, 2003;Cowley and Stuart, 2010). Second, selection or sanctioning mechanisms apt to produce dyadic representation are weak. In the initial selection by local constituency parties of prospective parliamentary candidates, candidates' political views are only the fourth most important quality, after the candidate's vote-winning ability, their public speaking ability, and their enthusiasm (Norris and Lovenduski, 1995, 139). After initial selection, local constituency parties are unlikely to de-select candidates on the basis of political differences: "if [an MP] is rejected, his exit is more likely to be caused by scandal, drink, unusual indolence, or some other personal disability, than by political differences with his local party" (Gilmour 1971, 262, as quoted in Norton 1978. Electorally, "the prevailing view of political scientists is therefore that individual MP accountability in Britain is weak at best" (Vivyan and Wagner, 2012, 236). Thus, if dyadic representation exists, it operates in unpropitious terrain.
Perhaps because of the difficulties that dyadic representation would seem to face in the UK specifically and Westminster systems more generally, there has been little research on this topic. What research there is relies universally on proxies for constituency opinion, which both obscures the difference between interests and preferences, and elides many other unobserved constituency characteristics. For example, Hibbing and Marsh (1987) and Baughman (2004) both use the religious composition of constituencies -specifically, the percentage of Roman Catholics -to explain MPs' free votes on abortion and homosexuality. In a similar vein, Soroka et al. (2009) use the presence of a military base together with constituency-level unemployment to explain the volume of MPs' questions concerning defence and taxes and welfare respectively.
The lack of good measures of constituency opinion has limited research on dyadic representation -but this literature is also limited because there is little variation in parliamentary outcomes to explain. Levels of legislative cohesion in parliamentary systems in general are high compared to the United States, and levels of party unity in Westminster systems are higher still (Carey, 2007). The strong pressure exerted by party whips means that votes do not reveal differences in ideology, but rather differences in levels of government support (Spirling and McLean, 2007;Spirling and Quinn, 2010). Consequently, research into dyadic representation in Westminster systems must solve these twin problems. We tackle the problem of identifying unconstrained opportunities for MPs to reveal their preferences in section 4, but first we deal with the problem of estimating constituency opinion.

Constituency opinion
Investigating dyadic representation is difficult because it requires measures of constituency opinion, and because until recently such measures have been prohibitively expensive. If opinion in a given area can only be elicited through a survey of a moderately large representative sample of the population of that area, then for most parliamentary systems measuring opinion in all legislative districts would simply be too expensive to carry out, even supposing it were feasible. Fortunately, opinion within small areas can be estimated using information from large national samples together with auxiliary information about constituencies.
Researchers have used four main sources of information to provide small area estimates of public opinion. First, researchers have used 'global smoothing' -that is, they have modelled individual responses to survey questions administered nation-wide as a function of a global intercept, plus a constituency-specific intercept drawn from a distribution with mean zero and estimated variance. Constituency-specific estimates of opinion can be produced by combining the global intercept with the respective constituency-specific intercept. Second, researchers have used constituency level predictors -that is, they have modelled individual responses to survey questions as a function of a global intercept, plus a constituency-specific intercept which is modelled as a function of other constituency-level predictors (Buttice and Highton, 2013). As before, constituencyspecific estimates of opinion can be produced by combining the global intercept with the respective constituency-specific intercept. Third, researchers have used individuallevel predictors and post-stratification -that is, they have modelled individual responses to survey questions as a function of a global intercept and individual covariates (Park et al., 2004;Lax and Phillips, 2009;Warshaw and Rodden, 2012). Constituency-specific estimates of opinion can be produced by 'post-stratifying' -by generating predicted responses for covariate patterns which are then weighted by their weight in the constituency population. These post-stratification weights are typically derived from Census data. Fourth, researchers have used geographic information on constituencies -that is, they have modelled individual responses to survey questions as a function of a global intercept, plus constituency-specific intercepts which are drawn from a conditionally autoregressive distribution, such that 'closer' constituencies have more similar intercepts (Selb and Munzert, 2011). Once again, constituency-specific estimates of opinion can be produced by combining the global intercept with the respective constituency-specific intercept.
All of these different sources of information can be fruitfully combined, and in related work we show that their combination results in the best possible estimates of constituency opinion in Britain (Hanretty et al., 2014). The estimates of constituency opinion used here are thus based on post-stratified predictions from multilevel regression models including individual and constituency-level predictors together with spatially correlated random effects. 2 Table 1 sets out the different individual-and constituency-level predictors used.
2 All data preparation and post-stratification is performed in R (R Core Team, 2012). We estimate all multilevel regression models via Bayesian MCMC simulation using WinBUGS (Lunn et al., 2000), with the GeoBUGS add-on for any models including local smoothing (Thomas et al., 2004). For each model, we run three separate chains of length 50,000 iterations each, the first 10,000 of which are discarded as Three comments on this table are worth bearing in mind. First, not all individual level predictors are used in all studies. Specifically, study 3, on same-sex marriage, does not use some individual level predictors, because these were not included in the survey data we use to measure opinion on same-sex marriage.
Second, although all of the individual level predictors necessarily have a corresponding constituency-level average derived from the Census, it is not the case that every constituency-level Census-derived variable has an individual-level analogue.
Third, although there is Census information on the marginal distributions of all of the variables shown in Table 1, these marginal distributions may be very slightly different to the margins derived from the post-stratification weights. Post-stratification in the UK is slightly more involved than post-stratification in the United States, in that the full joint distribution of post-stratification variables is not available at the level of the Westminster parliamentary constituency. To create a joint distribution at the constituency level, we used information from the Census Sample of Anonymized Records to create a nationallevel joint distribution, which was then 'raked' to the known constituency-level marginal distributions by a process of iterative proportional fitting. For details, see Appendix A.

Opinions
Having discussed the method we use to generate estimates of constituency opinion, we now turn to the specific opinions modelled in each of our three studies. burnin. We thin the resulting chain by a factor of 10, leaving a total of 1,200 draws from the posterior for inference. Across the CIPS and AVRS surveys, we identified nine economic policy-related items with up to five response options (respondents were generally asked whether they strongly approved, approved, neither approved nor disapproved, disapproved, or strongly disapproved of a policy proposal). The nine policy items are detailed in Table 2.
Overall, we observe data on 10,821 individuals who responded to both the CIPS postelection wave and the AVRS post-referendum wave. Based on their answers to the nine economic policy-related items in Table 2   The Government's cuts in public expenditure are essential for the long-term health of the UK economy 1 = 'Disagree strongly', 2 = 'Disagree', 3 = 'Neither agree nor disagree', 4 = 'Agree', 5 = 'Strongly agree'

AVRS tuitionfees
The Coalition Government is withdrawing all financial support to universities for teaching their students, with the exception of science subjects. University managers think this will require them to raise students tuition fees from £3,250 up to as much as £9,000. Do you approve or disapprove of this policy? Which of the following statements comes closest to your view? 1 = 'Good public services can only be provided by the government', 2 = 'The government should do less to provide publicly funded services and do more to encourage people to provide services for themselves.' AVRS for same-sex marriage. Don't knows were excluded from the analysis.

Outputs
The results of the small area estimation of public opinion are shown in Figure 1. Generally, all three maps show an urban rural-divide, clearly shown by the lighter areas in the smaller city centre constituencies (lighter areas correspond to more left-wing positions, lower EU disapproval, and greater support for same-sex marriage

Legislator behaviour
Dyadic representation involves the study of at least six linkages (Miller and Stokes, 1963).
Of these six, one linkage is particularly important. That is the linkage between constituency opinion and legislators' legislative behaviour. Converse and Pierce (1986, 563) refer to this as the 'basic representation bond'. If the association between constituency opinion and legislative behaviour is near zero, 'we are justified in imagining that no popular representation is occurring' (Converse and Pierce, 1986, 505). Further research might investigate whether the lack of representation is due to a legislature of perfect Burkeans or a legislature of uninformed delegates, but the strength of this basic representation bond must first be established. Thus, research into dyadic representation in the United States first assessed the strength of this basic bond, before moving on to address other contributory links.
We therefore focus on investigating the association between constituency opinion and legislative behaviour in Britain. In doing so, however, we must carefully specify the kind of legislative behaviour we are interested in. Most roll-call votes in Britain are subject to strong party discipline. Any relationship between constituency opinion and measures of behaviour derived from (most) roll-call votes would therefore not reveal a basic representation bond, but rather a bond which is an artefact of a more fundamental linkage between the distribution of partisan support in each constituency and the responsiveness of political parties to the opinions of their supporters. We cannot therefore proceed by scaling recorded votes in the Commons and relating these to measures of constituency opinion, for this would misunderstand the nature of (most) recorded legislative voting at Westminster.
Our strategy, therefore, is to focus on instances where party discipline is not present.
In this section, we discuss three measures of legislative behaviour, drawn from a pattern of signatures to Early Day Motions, a free (unwhipped) vote on the European Union, and a free vote on same-sex marriage. We argue that in each case we can consider MPs' behaviour to be free of party discipline -explicitly, in the case of free votes; implicitly, in the case of Early Day Motions. As a result, we are able to investigate the basic representation bond between constituencies and legislators in situations where the preferences of individual legislators are observed.

Left-right economic positions
We measure MPs' position on an underlying left-right economic dimension based on their observed behaviour toward a subset of Early Day Motions (EDMs) relating to economic issues. EDMs are "formal motions submitted for debate in the House of Commons...
[which] allow MPs to draw attention to an event or cause". 4 Although any member of the House may sponsor an EDM, and any member co-sign another member's proposal, in practice it is mainly backbench MPs -those who hold neither government office nor office in the Opposition shadow cabinet -who do so. Because vanishingly few EDMs result in a debate, EDMs have limited consequences for policy or the use of legislative time.
The limited consequences of EDMs make them "unobtrusive" measures of backbench opinion, free of party pressure (Franklin and Tappin, 1977). In a recent article, Kellermann (2012)  proposal location relative to the status quo location. He innovates by assuming that each MP has a signing cost, c, such that MPs with higher signing costs will be less likely to sign an EDM irrespective of its location. By introducing this signing cost, EDM ideal point models account for the fact that the lack of a signature may either mean that the MP disagrees with the policy represented by the EDM, or that they were disinclined to sign for non-policy related reasons (they generally prefer to sign fewer EDMs; they are less gregarious, and so on).
We adopt Kellermann's general approach to estimating MP ideal points based on EDMs, but introduce two important adjustments to the model. First, whereas Kellerman's article involves separate estimation of the EDM policy proposal and status quo location by way of constraining proposal positions to be tightly related to the ideal point of the (named) proposer, in this article we use a slightly simpler model in which each EDM is characterized by a discrimination and difficulty parameter only. Our specification is thus more similar to the standard two-parameter item-response models commonly applied to roll-call votes (Clinton et al., 2004), but with an additional legislator-specific parameter capturing signing costs.
Second, to stabilise ideal point estimates for those who sign relatively few motions, we model MP ideal points as draws from a common party distribution. This modeling assumption is consistent with a reasonable prior belief that MPs from the same party are likely to have more similar preferences than MPs from different parties. The partial pooling of ideal points for MPs within the same party should also make it harder to detect within-party dyadic representation.
Formally, we see a signature from legislator i on motion j if and only if latent utility z ij > 0, where that latent utility is given by the equation where β is the item-discrimination parameter, and α the item difficulty parameter, and c i the signing cost faced by each legislator. Our priors are as follows: α ∼ N (0, 2); β ∼ N (0, 2); c ∼ N (0, 1); θ ∼ N (µ party , σ party ).
Our EDM data comes from the 2010-12 Parliamentary session. We began by excluding prayers for the reconsideration of secondary legislation, and early day motions that were geographically specific. 5 This left us with 2513 EDMs and 480 legislators who signed at least one of these EDMs. Next, because we are interested in measuring MP preferences specifically along an economic left-right dimension, we defined a list of key terms relating to this dimension and dropped from our sample any EDM that does not contain at least one these terms. 6 This leaves us with 902 motions for estimation. We estimate the model via MCMC in JAGS (Plummer, 2003). After a 6000-iteration burnin period, we ran and stored an additional 5000 draws from the posterior distribution.

The European Union
On the 15th May 2013, the House of Commons voted on an amendment to its response to the Queen's Speech (which is to say, its response to the government's legislative agenda).
The amendment would have expressed the House's respectful 'regret that an EU referendum bill was not included in the Gracious Speech'. The amendment was moved by Conservative Eurosceptic John Baron MP. Exceptionally, 7 the Conservative party had allowed its MPs a form of free vote on the amendment -whilst ministers would be obliged to abstain, backbenchers were free to vote as they wished. Ordinarily, this would make it difficult to discern abstentions from absences: although members may explicitly signal abstention by walking through both the 'aye' and 'no' division doors, this practice is not required of members. Fortunately, however, the division on the EU referendum amendment was immediately preceded by voting on the opposition response to the Queen's Speech, for which many Conservative MPs, and many ministers, were present. For nonpayroll MPs, we have therefore assumed that those who did not vote in favour of the amendment were against it.
Although support for a referendum on an issue is not normally equivalent to support for a particular outcome in that referendum, we assume that Conservative backbenchers who supported the referendum did so because they were Euroskeptic, and wished to move towards exit or reduce the powers of the EU over British affairs. This assumption would not hold across parties -the Liberal Democrats, for example, are in favour of a referendum on European Union membership, but are the most pro-European of the main parties. Nevertheless, we believe this assumption will be readily granted by those familiar with opinion within the Conservative party.

Same-sex marriage
On the 5th February 2013, the House of Commons voted on the second reading of the Marriage (Same Sex Couples) Bill. The Bill had been introduced in the Commons a month earlier, at its first reading, but as is customary the first reading involved no debate and no recorded vote. The second reading was therefore the first opportunity for Members of Parliament to debate the principles behind the Bill.
Because the Bill touched on issues of conscience, the main political parties chose to make the vote a free vote -that is, one without any party whip (House of Commons Li-

Analysis
Having discussed the three different outcomes/measures we analyse across our three studies, we now move on to the analysis of these three cases. For each study, we report the results of relatively sparse ordinary least squares or logistic regression specifications, and discuss the association between constituency opinion and outcomes even when controlling for party.   Based on Table 3, there does appear to be a meaningful association between constituency opinion and MP preferences concerning left-right economic issues. The co-efficient on constituency opinion is positive and significant when included as the only predictor of MP ideal point (model 1). Once MP party is controlled for (model 3), the estimated coefficient drops substantially in terms of magnitude but retains significance.

Left-right economic dimension
The coefficient estimates in the party-specific regressions (models 4,5 and 6) are also fairly stable and significant for the two larger parties, suggesting that the average association between constituency ideal point and MP opinion is not driven by the behaviour of MPs from one particular party. In other words, even when we study the primary dimension of party competition in a party-dominated system, dyadic representation nevertheless does appear to obtain.
To ease interpretation of the strength of the dyadic link in this case, Figure    The magnitude of the dyadic link is strong in this case. Based on Model 2, Figure 3 plots the predicted probability of a Tory MP supporting an EU membership referendum as a function of constituency EU disapproval. The graph shows a relatively steep fitted regression curve, with constituency opinion having a substantial effect on MP votes. For example, moving from the average level of disapproval in constituencies held by Conservative backbenchers present that day (51.6% disapproval) to a high level of disapproval (equal to the average plus one standard deviation, or 58.4% disapproval), results in a change in the predicted probability of an MP supporting an EU membership referendum of 10.6%. This a sizable effect, and one that is substantively more significant than that found for the study of MPs' left-right economic preferences.   The regression results indicate that, on the issue of same sex marriage, MPs are responsive to constituency opinion. In the models run on the pooled set of MPs, the coefficient on constituency support for same sex marriage is positive and significant whether or not party is controlled for (model 1 and 3). The estimated coefficient is also relatively stable when estimated separately in each of the party subsamples, although it only retains significance for the Conservative MPs.

Same-sex marriage
The substantive effects of constituency opinion here are similar to the substantive effects seen in our discussion of vote for a referendum on the European Union membership. Figure 4 plots the predicted probabilities deriving from a model which includes both party and constituency opinion (model 3). The fitted regression slope is steepest for Conservative MPs, for whom a change from average constituency support for same sex marriage (58.3% in support) to high support (63.5%) results in a change in the predicted probability of supporting the measure of approximately 10%. In contrast, the regression slopes for Labour and Lib Dem MPs are more shallow because they had a greater propensity to vote in favour of same sex marriage. Yet even for a Labour MP, a similar change in constituency support for same sex marriage from 58.3% to 63.5% results in a 3% increase in the predicted probability of voting for same sex marriage.
Thus, on this policy issue which is not strongly related to the primary dimensions of party competition, we find evidence of substantial dyadic representation.

Mechanisms for dyadic representation
The previous section found evidence for a basic representational bond between MPs and their constituents in Britain. We found evidence of a relatively strong bond on two issues -the European Union and same sex marriage -that are generally considered to be only weakly correlated with the main left-right dimension of party competition in Britain, and evidence of a weaker (but still operational) bond on that main dimension of party competition. What mechanisms might explain why this bond exists?
There are two broad families of mechanism which might explain an observed correlation between constituency preferences and legislative behaviour even after controlling for party. The first family of mechanisms refers to selection. Here, the observed correlation is due to the initial selection of a legislator who happens to share the constituency's preferences. Different means of selection, including lower barriers to entry and a broader selectorate, improve the chances that a faithful agent will be found (Gerber and Morton, 1998). Unfortunately, whilst there has been experimentation regarded the types of pool of potential candidates (Cutts et al., 2008;McIlveen, 2009 may therefore either suggestion that selection is not fundamental to explaining the basic representation bond, or that MPs' opinions drift in a similar fashion to those of their constituents, or that we lack the statistical power necessary to identify such interaction effects. Alternately, if selectorates who opted for more local candidates were more likely to share the preferences of their constituency, we might see an interaction between candi-date 'localness' and constituency opinion -but again, after operationalizing localness as a simple additive index (+1 if the candidate was born in the area, educated in the region at secondary school level, educated in the region at tertiary level, or worked in the region prior to becoming an MP), we find no significant link. 9 A second broad family of mechanisms refers to sanctioning. Here, the observed correlation is due to the legislator's desire to ensure re-election, which leads her to suppress their own preferences, and vote according to the preferences of her constituency. Since desire for re-election is usually assumed, and assumed to be constant, the most natural way of proceeding is to examine whether legislators with more slender majorities, who face a serious risk of not being re-elected, work harder to mirror their constituency's preferences.
Again, however, we see no statistically significant interaction between marginality and constituency opinion. 10 It might be possible to test whether MPs who have announced their intention to stand down are less good at representing constituency opinion -but this would require data closer to the election, when decisions regarding candidacy have already been made.
We are therefore limited in the conclusions we can draw concerning the mechanisms which underpin the basic representational bond present in the House of Commons.

Conclusion
This article began with the question as to whether, in a Westminster system such as  In this appendix we describe how we used the SARS together with the univariate statistics to estimate the joint distribution of our variables at WPC level, and how we checked these estimates against the available bivariate cross-tabulations.
We began with the SARS data, and created a six-dimensional matrix (2 genders × 9 age categories × 7 education categories × 2 marital statuses × 2 housing statuses × 4 social grades × two sectors of the economy (private and public)). Due to the changes in the education systems of England, Wales and Scotland over time, information on the educational attainment of over 75s was not included. We therefore estimated, using those respondents in the 65-74 age group only, a multinomial model of educational attainment using all of the remaining variables in our matrix as predictors. We used the predicted probabilities of attainment in each category to create estimated counts for each cell.
We then created as many copies of this six-dimensional matrix as there were WPCs (632). Call each of these the target matrix. For each constituency, and for each variable, we multiplied the entries in the target matrix by the proportion to which they were under-represented compared to the known marginal distribution provided by the Census Dissemination Unit. Thus, for Aberdeen North, the proportion of women in the population according to univariate census statistics (51.6%) is slightly lower than the proportion of women in the SARS (51.8%); and so all cells in the target matrix involving women were multiplied by 0.995, and all cells in the target matrix involving men were multiplied by 1.005. We finished this iterative 'raking' process when the mean absolute logged difference in these proportions was less than 0.0001. The result was an estimate of the joint distribution of variables in each constituency based on the known national joint distribution of variables as adjusted for the over-/under-representation of certain groups in each constituency.
In order to verify that these raked estimates were reliable, we compared our estimates to the limited bivariate cross-tabulations made available at WPC level by the Census Dissemination Unit. Here, we use tables CAS033 (Occupation by age) and CAS113 (Occupation by educational attainment). We converted these counts to notional weights by dividing by the grand sum. We can assess the congruence between our estimates and the actual Census joint distribution by calculating the absolute difference in the weight for each cell, and averaging across constituencies. The mean absolute difference for CAS033 was 1.28%; the mean absolute difference for CAS113 was 0.24%.

B Generating economic left-right scores for BES respondents
We generate economic left-right scores for BES respondents by estimating an ordinal item response theory (IRT) model based on their answers to the nine economic policy-related items in Table 2. Such models have been used elsewhere in the political science literature to measure, for example, levels of democracy across countries (Treier and Jackman, 2008).
Formally, let x ij be individuals i's chosen response category k on ordinal item j, where the number of response categories, K j , can vary across items. Our model of x ij is where Φ is the normal cumulative distribution function, γ j is the discrimination parameter for item j, τ jk is the threshold parameter for category k on item j, and θ i is individual i's latent score on an economic left-right ideological dimension.
We estimate the ordinal IRT model via MCMC using the R function MCMCordfactanal . To avoid memory usage problems (which arise due to the large number of respondents for whom we store θ i parameters), we stored every 10th draw of 1000 samples from the posterior distribution, following a lengthy 5000 iteration burnin period.