Posts Tagged ‘elections’

Deal > Remain > No-deal > Deal: Brexit and the Condorcet paradox

With the possibility of a second referendum gaining increasing support, what happens if more than two options are on such a ballot paper for voters to rank? Simon Kaye explains the prospect of a Condorcet cycle and considers alternatives. He concludes that, whatever the route taken, there will always be a majority who will find the outcome of the Brexit process to be far from their first choice.

After more than two subsequent years of Brexit negotiations, manoeuvres, follow-up polls, and parliamentary debates, the UK has arrived at a political impasse. There are now widely believed to be three potential future outcomes: leave with no deal, remain and forget the whole thing, or approve the government’s Withdrawal Agreement (and its attendant, carefully vague Political Declaration on the UK’s future relationship with the EU). There are frequent attempts by all parties to suggest that one or another of these potentialities is effectively ruled-out or illegitimate, but clearly this has not yet been persuasive.

What is striking is that many polls now indicate that a Condorcet cycle – a paradox of preferences – exists between these three options. This is a paradox which seemingly runs throughout UK politics, from the general public to the dispositions of elected MPs. But what is a Condorcet cycle? Famously explored by Kenneth Arrow, this is about an underlying paradox that can emerge when translating individual preferences into social choices. Imagine three voters choosing between three options.

Voter 1:            A > B > C

Voter 2:            B > C > A

Voter 3:            C > A > B

It is clear that there can be no majority winner among them: the vote is deadlocked, because by pairwise comparisons, each option is at some stage preferable to every other. Different methods of counting these votes will therefore produce varying outcomes, and in any situation a majority of participants will be disappointed by the result. They’ve tried to be democratic, but the final decision will always feel, to some extent, arbitrary.

When people are polled directly on these three options in pairwise comparisons, a similar pattern emerges. At least a few polls now indicate a majority would prefer May’s deal to remaining in the EU outright; almost all polls show that a majority prefers remaining in the EU to leaving; and a subset of these show an even clearer majority preference for remaining over a no-deal exit. Finally, a majority prefers leaving the EU without a deal to the government’s Withdrawal Agreement. Deal > Remain > No-deal > Deal.

To simplify further: the referendum showed that more people oppose remaining than support it. Polling shows that more people oppose the government’s deal than support it, and that more people oppose a no-deal exit than support it. Under all circumstances, a majority will end up displeased.

Reflective of this, at present no outright majority exists in the House of Commons for any of these three outcomes. Even with a strong pro-remain tendency in the average MP, the political mandate created by the 2016 referendum leads to a similar preference-impasse. Intuitively, it makes sense for a median position to be marginally preferred to simply forgetting the whole Brexit idea, among both public and politicians. It also makes sense that the risks associated with no-deal would create a majority preference around remaining if it were the only alternative, and that the compromises and gaps represented by the government’s deal would lead to overarching preferences for that no-deal Brexit in a pairwise comparison.

What can we do in a deadlock situation like this? Here are some possible escape routes:

1. Articulating deeper preferences. Going further than finding out everyone’s first choice through a simple vote – is one. This doesn’t rule out the possibility of Condorcet cycles, as in the example given above, but it does make them more unlikely. See the illustration from a recent Deltapoll survey below. In this poll, the government’s withdrawal agreement emerges as a ‘Condorcet winner’ – a middle option that trumps either outright remain or outright no-deal, as discussed by Simon Fisher. This could be achieved by a referendum using a voting system that allows voters to set out their preferences in order. But this is not uncontroversial: we’re not used to finding ways of endorsing an outcome that’s everybody’s second-favourite. And, perhaps worse, this could ultimately reveal an even deeper level to the Condorcet cycle.

2. Hand-off the decision to a smaller subset of representatives who are empowered to make an informed final decision. Or, more simply – representative democracy. The problem here is that our representatives may be liable to be just as divided as we are, but this is effectively the option that is being trialled now, over days of debating and voting in the Commons. A crucial component that can be added under these circumstances is deliberation, which is impossible to accomplish meaningfully for a whole population, but could make all the difference among 650 legislators. By hearing and offering reasons for the different alternatives, deliberation can sometimes eliminate Condorcet cycles through meta-agreement, where participants find they can agree on the most important benchmarks against which the alternatives should be measured, and/or the emergence of more rational preferences, which will tend to favour the ‘middle’ option in a set of three. This is effectively what the government is counting on. Unfortunately – as any MP can tell you – the Commons is seldom reflective of an ideal deliberative environment, and even if it were, you might nevertheless fail to resolve the deadlock.

3. Formulate a new alternative to disrupt existing preferences or to become a clearer overall preferred option. This could be the product of a deliberative process, or it could be suggested from outside and gather enough support to come into real contention. We might think of the often-mooted Norway model/EFTA Brexit in these terms: a different plan that could end up generating wide appeal among MPs, if not the general public. There are issues here too, though: a new option could simply further complicate the whole picture, leading to a Condorcet paradox between four alternatives instead of three, and further weakening the mandate for any one option.

4. Boil the options down to two alternatives. Condorcet cycles can’t emerge between fewer than three options. If the final decision is between just two options, then a clear winner is likely to emerge. This is probably the simplest response, but also arguably the most arbitrary one. Which two options should be on the table, when at least three seem to be quite equally disliked? How legitimate would a subsequent vote or referendum be in the eyes of those participating? And, of course, even a straight-forward two-way vote can result in near-deadlock. The 2016 referendum itself ended up with a result so close that it has been the backdrop for endless disputes ever since: a more emphatic victory either way would surely have led to a very different political reality now.

Option 2, rolling through the Commons as I write, may yet yield results. Nevertheless, it now seems clear that, however things play out, there will always be a majority in the UK that will find the ultimate outcome of the Brexit process to be very far from their first choice.


About the Author

Dr Simon Kaye is Research Director at the Project for Modern Democracy think tank, having previously worked at King’s College London.




All articles posted on this blog give the views of the author(s), and not the position of LSE British Politics and Policy, nor of the London School of Economics and Political Science. Featured image credit: Pixabay (Public Domain).

Why 2017 may have witnessed a Youthquake after all

While prominent immediately after Labour’s performance in the 2017 election, the idea of a ‘youthquake’ has since been challenged by the British Election Study team. Using the latest data from the Understanding Society survey, however, Patrick Sturgis and Will Jennings show that there was, after all, a large and significant increase in turnout amongst the under 30s.

The 2017 snap general election saw a substantial reconfiguration of party support during the short campaign from 18 April to Election Day on 8 June. From polling as low as 25% in mid-April, Labour surged to as high as 40% in the final polls, an estimate that matched their actual vote share. While not historically unprecedented, such large shifts in voting preferences are rare during the course of a campaign.

Commentators have offered a variety of explanations for the surge in Labour support in 2017. These include disaffected Conservative Remainers switching to Labour, weaknesses in the Conservative manifesto and campaign strategy – in particular the so-called ‘Dementia Tax’ and widespread tactical voting for Labour as a means of preventing the Conservatives from winning a landslide. In the weeks after the election, however, the most widely held view was that Jeremy Corbyn had particularly appealed to young people, who turned out to vote at historically unprecedented levels – the so-called ‘Youthquake’.

The Youthquake theory was supported by an analysis of constituency level vote shares carried out shortly after the election by Oliver Heath and Matthew Goodwin, which found the largest increases in turnout were in constituencies with larger numbers of young people. Pre- and post-election polls conducted by The Stream for the music magazine NME and by Ipsos MORI also showed large increases in turnout amongst 18- to 30-year-olds between the 2015 and 2017 elections. YouGov’s own polling, as well as polls it carried out for the Essex Continuous Monitoring Survey, provided further corroborating evidence of a large increase in voting amongst those aged under thirty. As this all tallied with anecdotal evidence, such as Corbyn’s ecstatic reception at Glastonbury, the idea that Labour’s electoral gains were driven by young voters soon became established as conventional wisdom.

The British Election Study (BES) team, however, were not convinced. In a widely reported study, they showed that there was no relationship between the proportion of 18- to 30-year-olds in a constituency and the level of turnout increase once population density was controlled for. Turnout just happened to have increased most in constituencies with more young people, and it could not be concluded from this aggregate evidence that more young people actually turned out to vote. They also noted serious limitations of opinion polls for studying voting behaviour, namely that polls substantially over-estimate turnout. This is for two reasons. First, UK polls employ non-random sampling procedures which include too many politically engaged people and too few non-voters. Second, a substantial minority of people tell pollsters that they voted when they in fact didn’t.

The BES team undertook their own individual-level analysis of turnout amongst young people using the 2015 and 2017 waves of the BES. The BES is a post-election cross-sectional survey that has been fielded at every election since 1964. It adheres to the highest methodological standards, using face-to-face interviews and strict random sampling at all stages. The survey also includes a vote validation component, in which respondents’ self-reported vote is validated against electoral records. This means that estimates of turnout are not biased by misreporting.

Using these higher quality data sets, they found little in the way of change in turnout for the under 30s in 2017, concluding, “there is no evidence to suggest the relationship between age and turnout changed substantially between 2015 and 2017”. The same conclusion was drawn by John Curtice and Ian Simpson in their analysis of the 2015 and 2017 British Social Attitudes (BSA) surveys, which also employ random sampling and face-to-face interviews. While the BSA showed a 6 percentage point increase in turnout for the 18 to 24 group, this was not statistically distinguishable from no change.

So, case closed? Perhaps not. In November 2018, the University of Essex released Wave 8 of the Understanding Society survey. Understanding Society is a longitudinal household panel survey which interviews a random sample of the UK population annually on a range of different topics, including voting and party support. Like the BES, Understanding Society uses ‘gold standard’ methods. A key feature is its very large sample size (around 40,000 respondents at Wave 8). This is important for our purposes here, because the primary limitation of both the BES and the BSA is their comparatively small sample sizes for sub-group analysis. For the BES, the sample size for 18- to 24-year-olds in 2017 was just 53 using validated vote and 157 using self-reported vote, while for the BSA (which only has a self-report question) the sample size was just 162. These small samples make it difficult to statistically detect even quite large changes in turnout between elections (particularly when weights are applied, as this tends to reduce the effective sample size still further).

In Waves 2, 7, and 8 of Understanding Society respondents were asked whether they had voted in the most recent election and, if they had, which party they voted for (corresponding to the 2010, 2015 and 2017 general elections, respectively). The number of 18 to 24 year olds was 1,897 in Wave 2, 1,363 in Wave 7, and 919 in Wave 8. (These are the sample sizes for respondents who were asked the turnout question and provided a valid answer. The full sample sizes for this age group are larger. The sample size is lower in Wave 8 partly due to attrition and partly because some respondents were interviewed before the election, so were not asked whether they voted.) These larger sample sizes make it possible to assess the evidence for change in turnout among young people at a higher degree of granularity than has been possible to date.

Figure 1 plots non-parametric regression estimates of the relationship between age and turnout. The dark blue line, which represents turnout in 2017, is clearly and substantially higher for the youngest voters, aligning with 2015 turnout at around the age of 35. Interestingly, the figure also reveals a significant increase in turnout for the youngest voters between 2010 and 2015, a change which has not, to our knowledge, been previously noted – indeed the focus of Ed Miliband’s Labour on youth engagement in the run-up to the 2015 general election was widely derided at the time.

The estimates in Figure 1 are unweighted, so do not account for the greater tendency of non-voters to drop out of the Understanding Society panel over time. We therefore also compare turnout proportions within age-bands using a weighted estimator. The results are reported in Table 1. These show that there was an 8 percentage point increase in turnout for 18-24 year olds between 2015 and 2017, although this difference is marginally non-significant at the 95% level of confidence. For 25- to 29-year-olds, the increase in turnout is 13 percentage points and this difference is statistically significant. Differences in turnout at higher age bands are smaller and none are statistically significant.

The thresholds used for age bands are essentially arbitrary (i.e. why use 24 years as the cut-off point for the youngest group?). We therefore also present estimates in Table 2 using 18-25 for the youngest group with age bands increasing at five-year intervals thereafter. Using this age banding, the increase in turnout is statistically significant for both the 18-25 group (9 percentage points) and 26- to 30-year-old group (14 percentage points). While the statistical significance of the increase does, then, depend to some extent on how the age bands are defined, these estimates nevertheless support the claim that there was a large increase in turnout amongst voters under the age of 30 in the 2017 general election.

Figure 1. Nonparametric smoothed local polynomial regression probability of turnout by age in years, Understanding Society Waves 2, 7 & 8.

This increase in turnout amongst young people, combined with the greater tendency of young people to vote Labour in 2017, means that the party drew particularly heavily on the support of younger voters in this election. This can be seen in Figure 2, which plots predicted probabilities of voting Labour by age. Strikingly, the probability of someone in their 20s voting Labour is estimated at around 0.7 compared to 0.4 in 2015 and 2010.

Figure 2. Nonparametric smoothed local polynomial regression probability of Labour vote by age in years, Understanding Society Waves 2, 7 & 8.

Like the other sources of data discussed here[1], the Understanding Society survey has its own limitations and weaknesses, most notably a low response rate – although the wealth of information on nonrespondents available from earlier waves means that powerful weights are available to correct for differential nonresponse – and the use of self-reported turnout (rather than validated vote). It over-estimates turnout at each of the past three general elections by between nine and 13 percentage points, no doubt a combination of nonresponse bias and mis-reporting. Nevertheless, it is not unreasonable to assume that these biases are largely stable across waves, i.e. the levels of estimated turnout may be too high but there is little reason to assume that changes in turnout or party support should be subject to systematically different biases across elections. And, while the size of the turnout increase we see in this data may not be as of great a magnitude as some have contended, it would seem that 2017 may have witnessed something of a Youthquake after all.


[1] Interested readers are directed to Roger Mortimore’s excellent chapter on data sources for measuring turnout in the UK in the forthcoming book Political Communication in Britain.


About the Authors

Patrick Sturgis is Professor of Research Methodology in the Department of Social Statistics & Demography at the University of Southampton and Director of the ESRC National Centre for Research Methods.


Will Jennings is Professor of Political Science and Public Policy at the University of Southampton.




All articles posted on this blog give the views of the author(s), and not the position of LSE British Politics and Policy, nor of the London School of Economics and Political Science.

Vote switchers: the two groups of voters whose values the main parties must understand

Looking at voters’ values helps explain the UK’s changing electoral landscape, write Paula Surridge, Michael Turner, Robert Struthers, and Clive McDonnell. They look at vote switching between 2015 and 2017, and explain why the two main parties need to understand the values of two specific groups of voters in order to appeal to them.

The period between the 2010 general election and that of 2017 has been marked by very high levels of voting volatility. The collapse of first the Liberal Democrats between 2010 and 2015, and then UKIP in 2017 appears on the surface to have led us back to a two-party system, with Labour and the Conservatives gaining the highest two-party share of the vote since the 1970s. This apparent return to the two-party system masks high levels of individual level volatility as well as the potential for existing (and new) ‘3rd’ parties to be resurgent as the voters struggle to fit themselves into a party system which barely reflects their values and preferences.

Having previously introduced the values clans here, this piece uses this framework to look at vote switching between 2015 and 2017, and considers the values of the clans which had the greatest prevalence of vote switching.

Taking only those who voted in both the 2015 and 2017 elections, we can calculate the proportion who changed parties within each of the values clans. As shown in Figure 1, this proportion was highest among the Proud and Patriotic State clan – who combine left-wing economics with socially conservative values – and lowest among the Notting Hill Society – with broadly right-wing economic instincts. This strongly mirrors the two-party (Labour plus Conservative) share of the vote in each clan and is indicative that much of the switching between parties occurs between a ‘minor’ party and one of the two major parties, with direct switching between Labour and the Conservatives rare. Overall, around 1 in 20 voters switched directly between Labour and the Conservatives between 2015 and 2017.

Note: see here for a detailed explanation of the various clans illustrated above.

Considering how the different clans behaved, and the characteristics of those with higher levels of switching helps us understand where potential volatility still lays. Two clans stand out as having higher levels of vote switching, these being the Proud and Patriotic State (PPS) and the Modern Working Life (MWL) clans – the latter being more likely to believe in individual responsibility for financial well-being but liberal on social issues and the environment. Nonetheless, the two groups are very different in their behaviour. The PPS were the clan most likely to have voted UKIP in 2015 (1 in 5); there was therefore a substantial proportion of this clan ‘up for grabs’ by the major parties as UKIP collapsed in 2017. By contrast, the MWL clan did not have a particularly large share for UKIP (or any other minor party) in 2015. Around half this group voted Conservative in 2015, a further quarter voted Labour, and around 1 in 8 voted for the Liberal Democrats. As a result of these very different profiles in 2015, switching in these two clans is different too. For the PPS group this is primarily switching from UKIP to one of the main parties, while among the MWL 1 in 10 switched directly between Labour and the Conservatives, such that in 2017 Labour had a very slight lead among this group.

Looking more closely at the values of these two groups provides us with further clues as to how values influence political behaviour. The clans are described according to their positions on a set of 27 items which can be further grouped into 11 broader categories. Spider diagrams then illustrate the values profiles of the clans. The diagrams are drawn so that positions close to the centre of the ‘web’ are the most ‘left’ or ‘liberal’ positions and those furthest out are the least liberal or most right-wing positions.

The spider diagram for the Proud and Patriotic State group shows a values profile that lies close to the outside of the web on a wide range of issues; notably Immigration and Multiculturalism, International Affairs, and Crime and Punishment but who also have notably ‘left’ leaning views on the Economy and Workers’ Rights. In an earlier piece we described this as one of the ‘cross-pressured’ clans for this reason.

Looking at how these voters switched between 2015 and 2017 reflects this cross-pressure. Most of the switching in this clan is between UKIP in 2015 and one of the main parties in 2017. This is not all to one party, however: a mistake often made in the run up to the 2017 election was to assume that all the ex-UKIP vote would go to the Conservatives. Among this clan those who switched from UKIP went to the Conservatives over Labour in a ratio of 2:1. So, around one third of those who switched from UKIP in this clan voted Labour in 2017. By contrast among the Bastions of Trade and Industry (BTI) group (the clan with the second highest proportion voting UKIP in 2015) those who switched from UKIP overwhelmingly supported the Conservatives in 2017 (almost 95% of the UKIP switchers went to the Conservatives).

The Modern Working Life spider diagram contrasts sharply with that of the PPS. This group are much more liberal on issues of Immigration, Gender and Sexuality, the Environment and Religion. They are close to the ‘mid-point’ on the Economy but somewhat less liberal on issues of Welfare and Crime. Having less obvious and clear ties to a party on economic grounds, this clan are a key ‘swing’ clan for the major parties. While only representing a small proportion of the electorate they are nonetheless a crucial group electorally given this heightened tendency to switch directly between the two main parties.

Aside from high levels of vote switching, these two clans share another feature. They are the two clans (apart from the Apathy group) with the lowest levels of political interest. Just 1 in 10 of these groups say they are ‘very’ interested in politics. This may mean that they are less likely to have strong attachments to parties and therefore make them more volatile, but it also means they are less easy to reach with political messages.

For future elections these groups are likely to again be volatile, but with rather different possible scenarios. The MWL group could prove central to the competition between the two main parties whilst the PPS group are the most likely source of any resurgence in the UKIP vote. In both cases the main parties will need to understand the values of these groups in order to make success appeals for their support.

About the Authors
Paula Surridge is Senior Lecturer at the University of Bristol.



Michael Turner is Research Director & Head of Polling at BMG Research.



Robert Struthers
is a Senior Research Executive at BMG Research.



Clive McDonnell
is a Data Analyst at BMG Research.

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