The Death of May’s Law: Intra- and Inter-Party Value Differences in Britain’s Labour and Conservative Parties

Party competition in Great Britain increasingly revolves around social or ‘cultural’ issues as much as it does around the economic issues that took centre stage when class was assumed to be dominant. We use data from surveys of members of parliament, party members and voters to explore how this shift has affected the internal coalitions of the Labour and Conservative Parties – and to provide a fresh test of ‘May’s Law’. We find a considerable disconnect between ‘neoliberal’ Conservative members of parliament and their more centrist voters on economic issues and similarly significant disagreement on cultural issues between socially liberal Labour members of parliament and their more authoritarian voters. We also find differences in both parties between parliamentarians and their grassroots members, albeit that these are much less pronounced. May’s Law, not for the first time, appears not to be borne out in reality.

systems -including the dominance of the Conservative and Labour parties in the UK (McKenzie, 1955) -were originally built, and towards what are often broadly termed 'cultural' or 'social' issues. Comparative discussion of the changing nature of party systems has tended to draw on cases where their fragmentation has led to new parties forming on this emerging cultural or values cleavage (De Vries and Hobolt, 2020), either through increasing support for radical right parties (Kriesi et al., 2006) or green and liberal parties (Alber, 2018). Alternatively, the focus has been on the decline of mainstream parties of either the centre right (Bale and Rovira Kaltwasser, 2021;Spoon and Klüver, 2019) or particularly the centre left (Benedetto et al., 2020). Meanwhile, in the UK it was long assumed that the 'thawing' of the country's traditional class-based structure of party competition would lead to the fragmentation of the two-party system (Curtice, 2010).
In fact, what occurred was more complicated. The Scottish National Party's seeming hegemony in Scotland, a decade of electoral volatility (Fieldhouse et al., 2019), and second-order elections that have seen both populist radical right and liberal parties prosper (Cutts et al., 2019) have certainly tested the British party system. Yet, the Conservative and Labour parties have survived intact as institutions without either's collapse or wholesale replacement, albeit with markedly different levels of recent electoral success. Rather than the decline of the UK's two-party system becoming inevitable, it has if anything reversed: in 2017, the two main parties took 82.4% of the UK vote, the largest since 1970; and even after a dip in 2019, the two-party vote share still stood at 75.7%, the largest combined Conservative-Labour total since 1992. This prompts a puzzle: what does the process of realignment do to the internal coalition of parties that survive a significant churn in their electoral support triggered by cultural issues?
Of course, any such realignment does not render economic differences and attitudes meaningless. To paraphrase Lipset and Rokkan's (1967) famous 'freezing hypothesis', as political parties have attempted to adapt to the new electoral context of the 2020s, they still hope, at least to some degree, to represent 'the cleavage structures of the 1920s' (see also Mair, 1998). Voters, and parties, adjust to the importance of cultural and social issues without necessarily abandoning their economic values (Surridge, 2020).
The job of navigating this conflict between the 'old' politics of class and the 'new' politics of social identity falls to those who make up political parties: members of parliament (MPs), party activists and party members. Indeed, it may fall on those who -in most instances -will have been attracted to a party for its ideological position on one dimension of political competition to redefine that party so that it can viably represent a position on a different political axis. This is perhaps particularly true within party systems like Britain's where the barriers to entry are higher, and where, therefore, 'old' rather than new challenger parties are more likely to do the supply side work of adjusting to changes in the demand side of party politics.
Understanding where the different sections of parties -elites, members and votersstand in relation to one another on ideological questions matters, both to voters and to those within political parties. It lets voters compare their social and economic views to those they vote for to represent them. We go beyond the rhetoric and policy positions of parties to understand the 'black box' of parties as ideological coalitions. In turn, this is obviously also of interest to party strategists -telling parties where they are most disconnected from voters, and which sections of their internal coalition are most likely to cause internal friction as these tensions are managed. And, of course, such data and insights are invaluable to those working to understand the nature of party political competition.
Using John May's (1973) 'special law of curvilinear disparity' as a heuristic, this article examines the distribution of views on both the liberal-authoritarian and left-right axes within the Conservative and Labour parties in the UK. It does so in order to understand the extent to which these parties align with their voters, and with the median voter, across both these dimensions. A greater understanding of the internal ideological dynamics of both partieswhich sections of their hierarchies occupy the most 'extreme' position on both the axes, and which specific issues drive these differences -can give us some clues about how electoral realignment might affect the internal coalitions that make up these parties in the future.
Our study begins by revisiting the core assumptions of May's law -including some of the less well-remembered aspects of his article that merit reconsideration. It then explains the choice of the British case, before setting out the data and questions used for analysis. After that, the article presents empirical evidence on the extent to which the British Conservative and Labour parties fit, or fail to fit, May's theory across fundamental social and economic values. Finally, it reflects on what the distribution of views within parties tells us about the process of realignment within British politics to date, as well as what this might mean for the dynamics of party competition in the future.

Revisiting May's Laws
Published nearly a half century ago in this journal, John May's (1973) article on the distribution of ideological preferences within political parties -and the 'special law of curvilinear disparity' -remains a much-used frame through which political parties are understood, so much so that it is 'more or less taken for granted' (Faucher, 2014: 5). It is a theory praised for its elegance and simplicity, and for the fact it accords with much of the common wisdom on political parties.
May theorised a tripartite structure which, as shown in Figure 1, split party organisations into the following three broad groups: party leaders (ranging from those in executive office to those representing the party); sub-leaders who operate as activists at a local party level or are members of parties; and non-leaders, or followers -the voters who back a party come election time. These categories were essentially arbitrary, but what was important was the principle: the 'special law of curvilinear disparity' rested upon assumptions about the nature of political incentives. Successful office-seeking, thought to be achieved by ideological congruence between a party and the median voter, brings with it material rewards that benefit those who sit higher up in a party's hierarchy. These rewards are supposedly not sought by sub-leaders, who are instead motivated by ideological concerns. As a result, voters usually take the most moderate line on issues, sub-elites prove the most ideologically extreme, whereas top elites are located somewhere in between -more ideologically motivated than mere voters but more determined to win power than a party's footsoldiers.
May's original article was lacking in any systematic evidence to support his special law -although he claimed it had an 'aura of verisimilitude', based on 'respectable testimony and some harder evidence' (May, 1973: 139). There have since been relatively few studies that have been able to draw upon data to directly test May's law, including an analysis of the British case now over two decades old (Herrera and Taylor, 1994;Kennedy et al., 2006;Narud and Skare, 1999;Norris, 1995;Widfeldt, 1999). In part, this is because of the difficult task of collecting reliable data across these various strata of party organisations. While voter surveys are widespread, reliable data on party elites has traditionally been especially difficult to access -dependent upon access and hindered by lower elite response rates compared to surveys of voters (Hoffmann-Lange, 2008). Survey research on party members often had to rely upon researchers gaining access to membership lists; the creation of large-scale internet panels has only recently allowed a viable alternative to emerge (Bale et al., 2019a: 2).
However, the comparative evidence from those studies that do exist suggests a weak or non-existent relationship between May's law and reality. Individual case studies have updated the theory: Pippa Norris' (1995) article on the Labour and Conservative parties incorporated a multi-dimensional issue space in to a theory that originally rested solely on a left-right cleavage; May's law was tested by adding a subjective national identity dimension to the left-right cleavage, in the context of Catalonia (Baras et al., 2015); an exploration of Dutch party politics focused on perceptions among top leaders and sub-leaders of the opinion structure within parties, and their relation to it (Van Holsteyn et al., 2017). Yet, all this literature argues that May's Law's Downsian view of the vote-maximising objectives of parliamentary parties is ultimately reductionist. Similarly, the basic assumption that party activists are more inspired by ideological purity has been tested and found wanting by work in areas such as membership recruitment, which point to a more diverse set of incentives to join and become active within political parties (Poletti et al., 2018;Seyd and Whiteley, 1992). Despite its ubiquity, then, the consensus in the (limited) literature is that May's law, while neat, is flawed as a theory of party organisation.
Yet, for all the critiques, less work has been done to build upon May's work, or to attempt to give alternative explanations for how ideological views within parties might be distributed. Kitschelt (1989) argued that the intra-party theory May posited may be empirically valid under certain conditions of party competition and suggested that, in multi-party systems, party activists are likely to be more 'extreme' when the social cleavage represented by a party is highly mobilised -for example, if immigration issues are highly contested, then the populist radical right is likely to attract more 'extreme' activists. This link between cleavage politics and organisational dynamics was theoretically useful. However, like others, Kitschelt did not have sufficient data to adequately test this innovation -or to suggest alternative models of ideological distribution.
Paradoxically, the best article to provide alternatives to the special law of curvilinear disparity is May's original article, which -largely forgotten now -also posited several alternative theories, some of which have echoes in later work in political psychology. These included the idea of leaders as deviant rightists, on the grounds that 'persons of relatively high social status . . . gravitate toward positions of leadership and bring with them relatively Rightist views'; as well as leaders as extremists, the idea that party leaders may hold stronger ideological views than those lower down the party food chain, as it is those politicians supplying ideological conflict that are most likely to benefit from it. Indeed, there is evidence from the political psychology literature, particularly but not exclusively from the US case, of the institutional incentives that partly drive affective polarisation and confrontation among elites (Jost et al., 2008;Layman et al., 2006).
Each of these alternative theories has some intuitive value that is worth revisiting using the contemporary British case. For example, there is theoretical plausibility in May's idea of leaders as extremists in the context of the dynamics of realignment: after all, if a party's voters are increasingly pulled together by social values on the 'new' axis of competition, as a group they might well have more disparate and heterogeneous economic values on the 'old' axis. However, the leaders of parties are likely to hold strongly ideologically defined and more homogeneous positions on the 'old' axis.
The idea of leaders as deviant liberals -that is, as a cohort they are more likely to hold a liberal position on the liberal-authoritarian axis than the median voter -might also have contemporary value. Two of the most commonly cited and well-established drivers of authoritarian attitudes are levels of education and a broad mistrust of global and national governance (Langsaether and Stubager, 2019;Norris and Inglehart, 2018). As an increasingly well-educated group that is an intrinsic part of that system of government, we might expect MPs to be more liberal than other strata (Runciman, 2016). Indeed, the evidence from political psychology suggests 'psychological sorting' leads to political elites holding some distinct characteristics: in the context of Britain, Israel, New Zealand and the United States, this has meant evidence of higher tolerance of those with opposing ideologies (Sullivan et al., 1993). There are also some obvious examples of this in British politics. For example, the strategy of leaders of both the Conservative and Labour parties has often been to decrease the salience of issues such as immigration in office or at least to fail to match rhetoric with policy action (Evans and Chzhen, 2013;Partos, 2019). A further example would be the UK's decision to leave the EU ('Brexit'), to which a majority of MPs in both the Labour and Conservative parties were opposed -a position strongly correlated with a liberal value position (Evans and Menon, 2017).

The British Case
The structural changes happening in most other comparable European democracies, outlined earlier, were amplified and accentuated in the UK by Brexit, an event and subsequent process that reinforced new political identities that were best understood through the lens of social or cultural values and which cut through existing party loyalties . As a result, a degree of realignment -or what has been called a 'tilting of the axis' (Jennings and Stoker, 2017) -has taken place in British politics. This realignment produced electoral outcomes in June 2017 and, even more so, in December 2019 that would have been difficult to imagine a decade ago (Cutts et al., 2020). Between 2015 and 2019 the Conservative Party lead over Labour among middle-class voters fell, at the same time as it turned a deficit among working class voters to a lead of over 20 percentage points relative to the Labour Party (Evans and Mellon, 2020). The 2019 election appeared to be the final nail in the coffin of the old link between class (or at least long-standing measurements of class) and voting.
This demographic realignment was caused by the links between voters' attitudes and their electoral choices changing, as electoral competition became as much about policy areas like immigration and liberal-authoritarian issues as it did about the politics of redistribution, economic justice and the free market (Fieldhouse et al., 2019). The content of party competition has been fragmented by debates around Brexit, the electoral geography altered by the debate over Scottish independence, and the dynamics of minor party competition redefined by the collapse of the Liberal Democrats and the rise of the United Kingdom Independence Party (UKIP) and the Brexit Party. Yet, in spite of this, in the Westminster parliament, the major parties continue to dominate: at the 2019 general election, the Conservative and Labour parties won 567 out of 650 seats; in 2010, this number was 564. So, while it may be the case that in other comparable Western European democracies measuring ideological voting blocs and the success of challenger parties at general elections can provide a way of understanding party system change, in the UK it is mainly the results of second-order and devolved elections, as well as opinion polling data, that have so far allowed us to see quite how under strain the party system really is (Awan-Scully, 2018). Another route to understand realignment, however, would be to look inside the major parties -at the evolution of the internal coalitions that make up the Conservatives and Labour.
The interaction between social values and economic circumstances is sometimes said to be an artificial distinction: economic structural inequality is thought to create the conditions where social values become increasingly important in determining voter choice (Bornschier, 2010;Evans and Tilley, 2017). Yet, this causal relationship could work in the opposite direction during a period of realignment. Parties may attract new support on the cultural dimension, and subsequently adapt their economic offer in response to their new electoral coalition's wider distribution on the left-right axis. Mainstream centre-right parties may shift their economic stance to the left to accommodate the fact they represent a greater number of economically 'left-behind' voters. Centre-left parties, attracting a greater number of liberal (and middle class) voters, may also adapt their economic offer in response. Certainly, this dynamic is widely perceived to have taken place under Theresa May and Boris Johnson's leadership of the Conservatives prior to the Coronavirus pandemic. Estimates from the Manifesto Project found the 2017 Conservative manifesto was the most left-wing since 1964 (Allen and Bara, 2019), while in his first speech as Prime Minister Boris Johnson claimed his economic focus would be on 'levelling up' across the country and reviving the fortunes of the UK's 'left-behind' towns and cities (Johnson, 2019). In the early months of 2020, the government's embrace of state intervention was 'causing alarm among Tory MPs (particularly in the more affluent parts of the country) and Tory activists (particularly on the Thatcherite right)' (The Economist, 2020).
The majoritarian nature of the UK's political system also poses a specific set of questions about how mainstream parties respond to changing social and economic structures. In a Westminster system where populist parties of any stripe find it more difficult to gain a strong electoral and institutional foothold due to higher barriers to sustained representation in the House of Commons, mainstream parties have additional strategic space to absorb voters with extreme policy positions on the liberal-authoritarian axis. However, if these voters are driven by stances on issues of national identity and social authoritarianism that are not shared by mainstream elites, this begs a question of sustainability: can these mainstream politicians keep a lid on populist insurgents in the long-term if as a group they hold broadly liberal positions? This is particularly pertinent if the 'cultural backlash thesis' (see Eatwell and Goodwin, 2018;Norris and Inglehart, 2018) holds: that is, if the key variable that explains populist politics is authoritarian sentiment, not economic circumstances.
Analysing the British case is also important as the relative power of party members has increasingly come to be seen as a factor driving changes in the nature of the British party system. Within the Conservative party, pressure from members and activists played a key role in encouraging the party's movement towards a referendum on EU membership, and the subsequent post-referendum movement towards a 'hard' Brexit (Bale et al., 2019a). This has led to MPs who opposed this direction describing 'extreme right wing' party members and 'entryists' as a significant driver of the direction of Conservative Party policy (BBC News, 2019). Within Labour, Jeremy Corbyn's leadership was defined by a conflict between a Parliamentary Labour Party who did not support the leader, and a party membership -and, more specifically, an energised activist base -who were supporters of the Corbyn project (Younge, 2017). Simultaneously, on the issue of Brexit, the party's bolstered membership pulled the Labour leadership towards an increasingly 'anti-Brexit' position (Bale et al., 2019b). The rise of Jeremy Corbyn as leader was eased in part by membership rule changes under Ed Miliband which allowed registered supporters to vote in Labour leadership contests. This was a rule change that had, paradoxically, long been seen as a way of empowering casual, more moderate supporters at the expense of more left-wing activists (Russell, 2016).
The perception of a relative increase in the influence of party memberships has led to normative calls from some political scientists and political historians for power over the choice of party leaders to return to MPs (Russell, 2020;Saunders, 2019). This rests in part on the assumption that party elites are more responsive to the views of the median voter than elites. Ideologically-driven members, the logic goes, exacerbate processes of polarisation. Certainly, the survey evidence suggested that on the issue of Brexit, party members pushed party strategies towards the extremes (Bale et al., 2019a: 65-70). Yet, if members are pushing parties further towards either social liberal or social authoritarian positions, they could in fact be working to ensure the UK's two-party system more effectively represents new cleavages in public opinion.

Data and Approach
This article draws on three separate data sources. The full descriptive data across each battery of questions for both parties is set out in the Supplementary Information attached to this article.
For voters, we use weighted waves of the longitudinal British Election Study Internet Panel. We draw on wave 6 (fieldwork post-2015 general election), wave 13 (post-2017 general election), wave 17 (fieldwork November 2019) for political values and wave 19 (which gives post-2019 election data from voters) for voter choices. This is a large online panel study. For example, when looking at data from 2019, the British Election Study (BES) panel contains a combined sample size of 23,315 of those who completed both waves 17 and 19 -creating a sample size of 8393 Conservative voters in the 2019 general election, and 6541 Labour voters. 1 For party members and activists, we use data from the Party Members Project, conducted in December 2019. 2 This survey was conducted by the research organisation YouGov as part of an ongoing project on party membership in the UK. These data allow for analysis of a representative sample of the Labour (n = 1365) and Conservative (n = 1279) memberships. In addition to testing the relationship between different strata within a party, large-scale internet panels allow us to explore the in-built assumption within May's Law that levels of campaigning activity correlate with higher levels of extremism among party activists. We use robust sub-samples of both memberships, segmented by their retrospective self-reported level of activity in the 2019 general election campaign, measured in the hours committed across the campaign: Conservative Party -0 hours (n = 737), 0-5 hours (n = 218), 6 hours or more (n = 297); Labour Party -0 hours (n = 541), 0-5 hours (n = 298) and 6 hours or more (n = 455). This allows for an approach that empirically expands on that of Norris (1995), who exclusively analysed members who attended selection meetings and was not able to distinguish and analyse members by their level of activism.
Finally, for MPs we use a representative survey of 88 MPs (drawn from a pool of 99 interviews with MPs across all parties, and following contact with 398 MPs): 49 Conservatives and 39 Labour MPs. These data comprised face-to-face interviews conducted in January and February 2020 by the research organisation Ipsos Mori. The data weight responses by seniority of MPs (ministerial and backbench), region, gender and whether they were recently elected in the 2019 general election. Previous analyses in the British context have only been able to capture parliamentary candidates, rather than MPs (Norris, 1995). 3 To draw cross-sample comparisons, we utilised two batteries of questions, designed and used by the British Election Study over repeated elections, measuring underlying social and economic values. Created by Evans et al. (1996), these value measures use five survey questions to capture the traditional 'left-right' dimension -concerned with economic justice, the distribution of resources and economic power -and a further five to measure a 'liberal-authoritarian' dimension concerned with testing issues such as national identity, criminal justice and adherence to authority. The individual questions are listed in Table 1 along with an explanation of the Likert-type rating scale utilised.
In his original article, May noted that to test the law properly required posing 'a battery of questions simultaneously to at least six cohorts' (May, 1973: 142; one of the reasons he lacked systematic data for his article and why formal tests of it have been so rare). Our data cover six cohorts, although the surveys are not exactly simultaneous. Data from voters were gathered a month before data from party members; data from MPs were gathered in the subsequent two months. However, since these questions are designed to tap into stable long-term values, which by definition should not change much in the short term, and given that the time gap here is still relatively small, we see this as a limited matter. Something with the potential to shift long-term attitudes might be the COVID pandemic (discussed further below), but almost all of the data were collected while COVID was either unknown or, for most people in the UK, a minor overseas issue. 4 The value of any insight that these findings provide is of course dependent upon the continued reliability and relevance of the two batteries of questions as a measurement of intrinsic economic and social values. Like all survey questions and measurements of attitudes that pertain to fundamental values questions, there is the risk of social desirability bias -although in this case, the same problem would apply to all of the other studies drawing on these questions. It is also possible that batteries of questions devised decades ago no longer capture the key divisions in British politics. While a full discussion of the merits or otherwise of these questions is beyond this article, we are confident that they are still of value. For one thing, the findings clearly show that the measures still have the ability to detect intra-and inter-party divides. We tested each scale for internal reliability and construct validity Responses from Conservatives all had weaker reliability on social than on economic questions, while patterns for the Labour Party showed high reliability across all three datasets. Moreover, the individual-level positions on these values questions should play a role in shaping attitudes to more policy specific questions. Again using the BES, we were also able to test individual-level correlations between these questions and more recently designed policy-specific questions among the public (not an analysis that we could conduct for our elite or member samples). We tested the relationship between the economic values battery and a set of questions designed to test attitudes to austerity and support for the idea that cuts to public spending, the National Health Service (NHS) and local services, and the role of private companies in running public services have 'gone too far'. We were also able to measure the relationship between the social values battery and questions against the question of whether attempts to give equal opportunities to women, ethnic minorities and gay and lesbians have 'gone too far'. The results are detailed in the Supplementary Information. In both cases, we find that the economic and social values questions are significantly, although not all strongly, correlated with attitudes to policy-specific questions; they have, in other words, a level of correlation with these contemporary issues that one might expect given their purpose -to tap into attitudes that form part of a voter's judgements about issues, while not being wholly determinative. Overall, therefore, these questions, across both batteries, remain a valid and robust tool to explaining social and cultural values.
In the 'Analysis' section to follow, this article will first test the applicability of May's Law of Curvilinear disparity -mapping our data on the social and economic values of MPs, party members (divided by their campaigning activity) and voters. We then explore the role of education in these results, testing whether the graduate make-up of MPs explains these differences. Then we provide some longitudinal context, exploring the Economic values • Government should redistribute income from those who are better off to those who are less well off; • Big business takes advantage of ordinary people; • Ordinary working people do not get their fair share of the nation's wealth; • There is one law for the rich and one for the poor; • Management will always try to get the better of employees if it gets the chance. Social values • Young people do not have enough respect for traditional British values; • For some crimes, the death penalty is the most appropriate sentence; • Schools should teach children to obey authority; • Censorship of films and magazines is necessary to uphold moral standards; • People who break the law should be given stiffer sentences. For each question, respondents answered on a five-point scale -from which we created a Likert scale. The scale ranges from -2 (for left or socially liberal views) to +2 (for right or socially authoritarian views) -for example, if every respondent in each category strongly agreed with each (left-wing) statement, the group would be scored as -2; if all respondents disagreed with each statement, they would be scored as +2. If every respondent in each category strongly disagreed with each (socially authoritarian) statement, the group would be scored as -2; if all respondents strongly agreed with each statement, they would be scored as +2. extent to which these intra party values divides are a product of political realignment over the last three electoral cycles before discussing the implications of these findings. Figure 2 shows the aggregate data for each of the five measurements of economic values. We break the data into five groups: at the top are MPs; there are then three separate categories of members, depending on how active they were in the 2019 election; last -but not least -we give the score for those who voted for the party. In the middle of the final row in grey is a dot indicating the position of the average (mean) voting-age adult.

The Economic Values of Actors in the Conservative and Labour Parties
These data show that Labour's members (-1.4) are indeed more radical on the economy than Labour MPs (-1.2) and Labour voters (-1.1), thus conforming to May's 'special law of curvilinear disparity'. However, these differences are not massive, and, contrary to the implicit assumptions of May's theory (and a lot of accepted wisdom about political parties), there is almost no difference between the different types of members depending on their levels of activism.
Things are, however, very different when we consider the Conservative Party. Rather than being closer to the average voter (-0.7), Conservative MPs (0.8) sit significantly to the right of party members (0.3) and councillors (0.4) on economic questions. And, in turn, the rest of the party (again with only a little difference between the various levels of activism, even if members are indeed more 'extreme' the more active they are) sits some distance to the right of its voters. The result of this disjunction is that there is a clear gap between the views of Conservative voters and the Parliamentary Conservative Party. Rather than May's special law, it adheres most closely to May's heuristic of 'leaders as extremists'. Figure 3 then breaks down the aggregate data into the five constituent questions for Conservative voters, members as a whole (given the aggregate differences are insignificant) and MPs. For the Conservatives, there is the same pattern on all five questions: MPs sit to the right of the rest of the party, which in turn is to the right of the voters. At times, the gap is very large -as with whether there is one law for the rich and another for the poor: fewer than a quarter (22%) of Conservative members, and just 5% of Conservative MPs, agree that 'there is one law for the rich and one for the poor', yet this is a view held by 72% of the public. Some 67% of the public agree that 'management will always try to get the better of employees if it gets the chance' -a view held by only 5% of Conservative MPs.
In almost every case, the spread of views within the Conservative Party is greater than that for Labour. On only one of these five questions -regarding redistribution -is the Conservative family more united than Labour: fewer than a quarter (24%) of Conservative MPs say they agree that the role of government should be to redistribute income from the better off to those who are less well off -not that far off the 17% of Conservative Party members who say the same. Contrast this with Labour. When aggregated, as in Figure 2, Labour appeared to conform to May's Law, although Figure 3 shows that is not true of every question that made up the overall scale. But for the most part the differences within Labour are not especially great on any of these five questions, and on four of the five questions Labour are closer to the average voter that Conservatives.
For example, on whether 'there is one law for the rich and one law for the poor', the 72% of the public who agree is near-identical to the 71% of Labour MPs that say the same, as do 92% of Labour members. The idea that big business takes advantage of ordinary people is the perception of 75% of the public, 83% of Labour MPs and 92% of Labour members. When asked, 67% of the public say that 'ordinary working people do not get their fair share of the nation's wealth'; this is a view held by all our representative survey of Labour MPs, and 95% of Labour members. Strikingly, on four of the five questions asked in the survey, those voters who backed the Conservative Party at the polls in 2019 have more in common with every section of the Labour Party than they do with Conservative members, activists and MPs.
It is only on the principle of income redistribution where a large gap exists between the Labour Party and the country, with Labour members and MPs being more to the left -and this anyway is a question where there is a similar gap between the Conservatives and the country, this time on the right. The average British adult supports the principle of income redistribution, unlike the average Conservative Party member or MP -just (unsurprisingly) not with the same overwhelming enthusiasm as Labour Party people.

The Social Values of Actors in the Conservative and Labour Parties
As Figure 4 shows, on questions of social values, the Conservative Party once again does not conform to May's special law. Conservative party members (0.8) are, in fact, more liberal on the liberal-authoritarian scale than the average Conservative voter (1.0). More pronounced is the difference between Conservative MPs (0.3) and the party's voters, with some evidence for an adapted version of May's mooted typology of 'leaders as deviant liberals'. The effect of this spread of views is that the average British adult (0.6) is more socially conservative than the average Conservative MP. Indeed, on these issues Conservative MPs have views that more closely align with the average Labour voter in 2019 than they do with their own supporters.
For Labour, there is the same pattern, but with a bigger gap between the party's voters (0.1) and party members (-0.6), and a smaller gap between the MPs (-0.7) and the rest of the party. This has the effect of creating a serious disconnect between their voters -who are on balance in aggregate and absolute terms more socially conservative than socially liberal -and the party. This gap between the party's MPs and members and the average voter (0.6) on social values questions is striking. Labour MPs cannot claim, as per the expectations derived from May's Law, to hold social values that are more aligned with the average voter than those of grassroots members; rather, they are the single most liberal group examined here -further evidence of 'leaders as liberal deviants'.
Figure 5 again breaks these data down into its five constituent questions, and while there is some variation between the five graphs, there is relatively little that looks like anything May's special law of curvilinear disparity predicts. There are three cases where Labour MPs are closer to the Labour voter than the Labour membership, although in all three cases the MPs are still a fair distance away from their voters, and the effect of these in the aggregate scale is anyway dwarfed by two questions where the MPs are the most liberal group. The argument for tougher sentences is accepted by only 24% of Labour MPs and 25% of members, but it is backed by over half (53%) of those who voted Labour in 2019 and 70% of the public-at-large. Support for the death penalty sits at 31% among Labour voters but just 11% of members and a grand total of 0% of the Parliamentary Labour Party surveyed.
On the Conservative side, we see a similar pattern, but one that brings Conservative MPs closer to, or even to the left of, the centre ground. There are two areas where Conservative MPs hold significantly more liberal views than the average member of the public: these are the death penalty (which 21% of Conservative MPs support, compared to 50% of the public) and the idea that young people do not have respect for traditional values (44% of Conservative MPs agreeing, and 63% of the public and 46% of Labour voters). On law and order, 70% of the public think that those who break the law should get tougher sentencesvery close to the 66% of Conservative MPs who feel the same way.

The Effect of Education
In general, therefore, these data show almost no support for May's special law of curvilinear disparity. Of the four sections of analysis presented here -on both social and economic values across the Labour and Conservative parties -only one appears to show congruence with May's law -the distribution of economic views within the Labour Party, with MPs and voters closest to the average voter.
What we are less sure about is the extent to which these findings reflect recent developments. Given the paucity of previous systematic studies, it is at least possible that the two parties have always had these distributions of views, or at least something similar, largely undetected. Or, indeed, they may have had a different distribution entirely. That said, we are able to test a number of possible explanations for our findings and the extent to which they may have changed over time.
We start with existing structural explanations on the connection between education and values. After all, one plausible reason for the distinctiveness of members of the House of Commons as a cohort -for the leaders as deviant liberals thesis concept that May set out, and that partly transpires in these data -is their socio-demographic characteristics as an elite group. Both parliamentary parties have a disproportionate number of graduates -83% of Conservative MPs and 84% of Labour MPs have a university education to undergraduate level (Barton, 2020). While representation of graduates has always been higher in the House of Commons than in the general population, the percentage of graduates has risen at a disproportionately higher rate in the Commons, largely as a result of a relative increase in graduate representation within the Parliamentary Labour Party. Since 2005, the percentage of Labour MPs who are graduates has increased by 20%, among Conservatives by 2% and the percentage of the population with a degree has risen from 27% to 40%.
Yet, as Figure 6 demonstrates, education characteristics in and of themselves have limited explanatory value in explaining why MPs as a cohort are more socially liberal. Holding the data for MPs constant, we created weighted scores for party members and voters, weighting each cohort of voters and members to the same educational level as their MPs. The dotted line shows the original finding; the bold line is this weighted result. It is true that Conservative and Labour graduates are more liberal than non-graduates across each liberal-authoritarian question. However, these effects are marginal, and in many cases, it is fairly difficult to differentiate the original and the weighted results. There are some exceptions. The lower propensity of graduates does appear to drive some of the higher level of support for the death penalty among Conservative members and voters when compared to MPs, for example. But even when the differences are relatively large, they are not sufficient to change the overall findings. All of the fundamental points noted earlier remain even when we control for education.

Longitudinal Change in the Values Coalitions of the Conservative and Labour Parties, 2015-2019
We are also able to examine the extent to which voter coalitions have changed in recent elections. Figure  electoral coalition has moved to the right and in a socially liberal direction. This is entirely consistent with the churn in the demographics of both parties that others have identified: the collapse of working class support for the Labour Party, and the relative success they have had in retaining middle class support. The Conservative's electoral coalition moved further leftwards between 2015 and 2019 (−0.1 to −0.4) than it moved in a more socially authoritarian direction (0.8-1.0). Since 2015, the party's coalition has moved 0.22 to the left and 0.15 in a more authoritarian direction. Even accounting for the slight movement towards social liberalism in the electorate as a whole -driven principally by cohort effects (Surridge, 2020) -the party's coalition has become more left wing compared to the median voter than it has become more authoritarian. This gives succour to the idea that the Conservative government's victory in 2019 was delivered by a set of voters that have stretched the party's coalition on the left-right spectrum.
The Labour Party's coalition moved in roughly as liberal (0.4-0.1) a direction as the Conservative Party moved towards an authoritarian one. Consistent with realignment creating more heterogeneous internal coalitions on the left-right spectrum, the Corbyn project appears -somewhat ironically -to have created a voter coalition that was marginally more, not less, right wing on economic issues. The voters it attracted were more liberal, and less left wing. In other words, the process of realignment and entrenchment on the liberal-authoritarian axis lead to the creation of broader coalitions of support for both main parties on the left-right spectrum.
We see something similar when we profile the attitudes of voters who switched parties from Labour to the Conservatives in 2019. 5 Figure 8 sets out the position of these 2019 'switchers' on both economic and social values, highlighting the disconnect between these voters and party they voted for in 2017 on liberal-authoritarian questions, and from the party they backed in December 2019 on the economy. Conversely, Figure 8 also demonstrates that these voters converge around a near-identical position on the liberalauthoritarian axis to the one taken up by all Conservative voters.
On economic values, 2019 Labour-to-Conservative switchers are a considerable distance away from the views of the party they have now backed. A full 81% think that big business takes advantage of ordinary people, compared to 34% of Conservative members and 18% of MPs. Some 81% think there is one law for the rich, another for the poor, compared to 22% of Conservative members and just 5% of Conservative MPs. Similarly, a mere 5% of Conservative MPs think management will take advantage of workers, compared to 77% of those who switched parties.
On social values, they are also some distance away from the values of their new party -they sit to the right of Conservative members and (even more so) Conservative MPs. And they are a very long way from the Labour Party they abandoned. Some 17% of Labour members and 9% of Labour MPs think that 'young people don't have enough respect for traditional British values'; but this view was held by 88% of Labour-to-Conservative switchers in 2019. The idea that schools should teach children to obey authority is also supported by 81% of this group, against just 28% of members and 41% of Labour MPs. Stiffer sentences are supported by 82% of these voters, significantly more than the public as a whole (68%), Labour voters (53%), Labour members (25%) or Labour MPs (24%).
In this, and all of the above, we lack systematic data on the evolution of the party membership and the MPs. These may also have changed over time, for example, as Labour's membership expanded under Jeremy Corbyn's leadership between 2015 and 2019. We know, for example, there were differences between the views of Labour members who joined the party before and after Corbyn became leader (Whiteley et al., 2019). However, we lack contemporary data on MPs' attitudes to the questions posed here at the time.
Yet, the most marked changes that we do detect -the movement of the Conservative coalition to the left, and the Labour coalition towards the liberal axis -are less sizable than the structural differences we find within both parties. It may be that despite a process of realignment taking place, the broad intra-party picture we find -with Conservative voters more left than the party's MPs and members, and Labour voters more authoritarian -was true in 2015; it just happens to be more true, as it were, in 2019. In other words, given what we know about voters, for these findings not similarly to have held in 2015, there would need to also have been dramatic changes in the views of MPs and members in the same four years. This seems to us unlikely, even if we cannot prove it.
That said, the movement of the Conservative coalition to the left -while overall UK voters have not moved at all -suggests that the distance between the party's voters and its members on economic values is now nearly equivalent to the gap the Labour party has had to manage on social issues. There is, therefore, some clear evidence of May's 'leaders as extremists' thesis in the Conservative Party: that is, that their leadership in the House of Commons holds a set of economic values not shared by the party's voters, or indeed their members.
On social values, for both parties, the pattern is clear: the Conservatives and Labour have a parliamentary elite with more liberal social instincts. There is, therefore, clear evidence from the UK case to support the idea that party elites are significantly more socially liberal than the country-at-large -and the idea of 'leaders as liberal deviants', that appeared to manifest itself in opposition to Brexit in 2016. This is a deeper structural problem for the Labour Party than the Conservatives. Within Labour, the difficulty in managing this disconnect was exacerbated by the contingency of Brexit, which increased the salience of social values questions.

Conclusion
The approach in this article builds on some of the conceptual ideas of Kitschelt (1989), whose revisionist analysis of May's law called for a greater degree of interaction between the literature on party systems and party organisations. Kitschelt (1989: 87) claimed analysis of systems and cleavages structures had a tendency to 'treat party organization as a black box in which actors adapt rationally to the constraints and opportunities offered by the electoral market'. In contrast, he (Kitschelt, 1989: 88) argued that theories of party organisation ignore the varied patterns of party competition that influence how political actors act within party organisations -a tendency to which he felt May's theory had succumbed.
Our findings provide important further evidence for the idea that the UK has undergone a profound period of political change, and that these new patterns of party competition are fundamentally redefining the Labour and Conservative parties as internal coalitions. This has created some important strains -creating a Conservative party with a parliamentary wing that is economically more neo-liberal and a Labour Party whose MPs are more socially liberal than their respective party members and target voters. Our article also points towards areas in need of further exploration -most obviously understanding the causal factors that explain why elites within mainstream parties hold more liberal views independent of the variable of education.
The evidence here suggests that Labour's struggles over Brexit between 2016 and 2019 were arguably symptomatic of a disconnect on a wider set of social values between its MPs, activists and members, on one hand, and many of its potential voters, on the other hand. We show here that a wider set of social attitudes underpinned these struggles over Brexit and the growing disconnect between Labour voters, and members and MPs. Consequently, it would be a mistake to assume that 'getting Brexit done' will see this strategic problem disappear. The disconnect in economic values between Conservative MPs and the party's voters is plausibly both a symptom of their success in realigning politics towards the authoritarian-liberal axis, and a warning of the fragility of its connection with its voting coalition.
If the tilt towards a social or cultural values divide was contingent upon a relatively benign economic context and the contingency of Brexit as a policy issue that amplified divisions over values, then a period of economic disruption following the pandemic and the declining salience of Brexit could plausibly reverse these trends. Indeed, there is growing evidence that public reaction to the pandemic and the UK state's response have led to a reassertion of the left-right economic division among the public, rather than further reinforcing divisions on social values (Green et al., 2020). Yet, among political elites, particularly in the Conservative Party, COVID-19 clearly posed a set of ideological questions about attitudes to authority and regulation that have often looked to have quite a lot in common with the Brexit debates that dominated pre-pandemic. This disconnect in elite and public responses to COVID-19 speaks to the divisions between leaders and led that we set out in this article, and the relatively favourable public attitudes towards a bigger role for the state that we have found give a clue as to why this disjunction exists.
The public policy response to COVID-19 also demonstrates that these value positions are not destiny: the Conservative government's economic and health measures to counteract COVID-19 cannot be meaningfully described as libertarian, and the salience of governing competence and administrative capability is a question distinct from value judgements of left or right, and liberalism or authoritarianism. The policy questions posed by the long economic recovery from COVID-19 are likely to see the Conservative party's voter coalition favouring a markedly different response to its MPs. Yet, recovery could see the differences in social values that drove an electorally damaging wedge between Labour and its erstwhile voters reassert themselves once more.

Declaration of Conflicting Interests
The author(s) declared no potential conflicts of interest with respect to the research, authorship and/or publication of this article.

Funding
The author(s) disclosed receipt of the following financial support for the research, authorship and/or publication of this article: The Party Members Project's research was made possible by the support of the Economic and Social Research Council's grant ES/M007537/1, which we gratefully acknowledge. The MP survey was conducted through the UK Economic and Social Research Council's UK in a Changing Europe initiative (grant number ES/S014608/1). Fieldwork for this research -both the representative sample of UK members of Parliament and data drawn from the Party Member's Project -was funded by the Economic and Social Research Council.

Supplementary Information
Additional Supplementary Information may be found with the online version of this article.

Notes
1. Further information and full data from the British Election Study (BES) Internet Panel Survey can be found here: https://www.britishelectionstudy.com/bes-resources/about-the-bes-internet-panel-study 2. Further information on the Party Member's Project can be found here: https://esrcpartymembersproject. org/ 3. Each member of parliament who participated in the survey was paid £200. 4. The first known COVID case in the UK was identified on 31 January, and by the end of February 2020, when our survey of MPs concluded, there had still only been 23 known cases. The UK's medical officers did not move the COVID risk level from moderate to high until the following month. Obviously, we cannot preclude the possibility that what subsequently unfolded will have adjusted the social and economic ideological priors of respondents. 5. Due to a small n problem, we did not analyse the reverse grouping of Conservative to Labour switchers in 2019.