The UK 2017 result–Comparative data forays

Well, the election that I thought would be just a boring “typical” snap election in which the incumbent takes advantage of the unprepared opposition… did not quite turn out that way.

Some things happened that are not supposed to happen. And some things about the result are glaringly off the mark of what we should expect from the Seat Product Model (which, of course, is meant to predict average trends, not individual elections).

Top two dominance but no majority

A party is not supposed to gain votes, but lose seats. It is hard to exaggerate how extraordinary this is. The top two parties combined for 82.4% of the votes, the highest in the UK in a long time. The last time it was over 80% was in 1979. The last time over 75% was 1992, and in the three elections immediately before this one, the figure had been around two thirds.

Yet, despite the recovery of the top-two vote shares, there is no majority party. Parliamentary majorities have been won on far less in the past, and one would not expect such dominance of the two leading parties (42.4% and 40.0%) under FPTP to fail to produce majority government. But here we are.

I was curious to know just how common it was for both parties in a FPTP parliamentary system to have at least 40% of the vote, but there to be no parliamentary majority. In my dataset of FPTP elections, consisting of 210 observations, I find one case: Trinidad and Tobago 1995 (two top parties on 48.8% and 47.2%, tied in seats with 17/36). (I have not kept this updated in recent years, and perhaps I am failing to remember one that would be included if I had.)

If I drop my threshold a little lower, to the top two parties both being at at least 38% (but no seat majority), I get one more case: Canada 1957. Of course, the main reason why a leading party with 40% or even 38% of the votes so often gets a majority under FPTP is that it tends to have a more substantial lead over the runner-up, implying many districts are competitive.

Thus it is not only the top two absolute sizes that matter for getting a majority, but also their ratios. How common is it for the top two parties to have votes so similar? First of all, let’s define a ratio of the top two in votes; the mean of this ratio in the data sample is 1.67 (median 1.26). In this UK election, it was 1.06. Approximately 15% of the elections are this close. However, only around 3% of all the elections are both this close and result in no majority party, including UK 1974 (Feb.).

Thus the UK17 combination of two-party dominant, close, and no seat majority is pretty unusual!

Campaigns and leaders

Campaigns and leaders matter. That is not in itself surprising, but many political scientists (sometimes including me) consider them less important than “fundamentals”–whatever those might be. But May did not look like someone who could provide “strong and stable” government. And indeed, she may not get to provide any government at all, if she can’t survive a seemingly inevitable challenge to her position from within.

On the other hand, does Labour’s success relative to low expectations suggest leaders do matter? Did voters actually come to like Corbyn? I am aware of no evidence that such was the case. I suspect he was still a drag on the party, but will leave it to other analysts to try to sort this out. It seems to me that any reasonably competent Labour leader could have won this election, which in turn would never have happened, because May would not have called it had the main opposition had a reasonably competent leader.

The numbers compared Seat Product expectations

On the quantitative indictors, the effective number of vote-earning parties (NV) was, by my calculations from data at BBC, 2.88. The last time it was that low in the UK was 1987, when the leading party (Conservative) won a vote share about the same as this time (42.3%), but it won 57.8% of the seats.

The effective number of seat-winning parties (NS) was 2.47. This is not so unusual, by UK standards, as the figure was 2.53 in the 2015 election and 2.57 in 2010, the last time no party won a majority. In fact, the UK has tended to have a less fragmented parliamentary party system than expected from the Seat Product Model, which would be NS=2.94. The maximum observed since 1945 was the just-reported 2.57 in 2010.

For NV, the Seat Product Model says to expect 3.32, based solely on the large assembly size. Although the post-WWII mean is much lower than that, the electoral party system was finally behaving in the 1992-2015 period, with all those elections seeing NV>3, and the last three (2005, 2010, 2015) all being at 3.6 or higher. Then came 2017, and the party system stopped behaving properly!

It should be emphasized that the Seat Product Model does not expect a majority party; with this large an assembly, even FPTP “should have” a largest party size of 44.5%. At 48.9%, the Conservatives are only a little higher than where they should be. But, of course, actual UK experience usually returns a majority in parliament, and this election was certainly expected to do so–where those expectations are based on political factors and the opinion polls, not the humble Seat Product Model.

Governance and policy

As for government-formation, clearly it is a Tory minority government. Claims by a few pundits that Corbyn could somehow assemble parliamentary support are pure fantasy. And there almost certainly won’t be a coalition. The most likely formula is backing from the Democratic Unionist Party (DUP), of Northern Ireland. The DUP’s 10 seats plus the Conservatives’ 318 combine for just over half the seats.

What will it mean for policy, especially Brexit? I can’t claim to know! But the DUP does not want a “hard border” with the Republic of Ireland, and that implies a “softer” Brexit. On the other hand, if the main motivation May had in calling the election was to boost her standing against restive members of her own caucus who want a harder Brexit, she failed. It will not be easy governance or policy-making for May or an intraparty successor.

Funny how elections don’t always turn out how we expect them to. Democracy! FPTP!

Appendix: Effective Number of Parties and the Seat Product Model

The effective number of parties is a size-weighted count, where each party’s share (of votes or seats) is weighted by itself through squaring. The squares are summed, and you take the reciprocal. See Michael Gallagher’s excellent website for details.

I am not going to explain here the logic behind the Seat Product Model. For that, see Taagepera (2007) or Li and Shugart (2016), or the forthcoming Shugart and Taagepera book, Votes from Seats (2017, due out in October). But the equations are as follows, where M is the mean magnitude (1, in the case of FPTP) and S is the assembly size (650 in recent UK elections).



Seat share of the largest party: s1=(MS)-1/8.

The important thing to understand about these equations is that they are not post-hoc regression fits. They are logical models, derived without reference to the data. When tested against the data from hundreds of democratic elections under various electoral systems, they are astonishingly accurate.

Related earlier posts and comment threads:

UK 2017: Green Party won’t stand in Ealing constituency

So much for fixed terms

UK 2015 and Diverter’s Law

Does UK 2015 mean the death knell for Duverger’s Law?

31 thoughts on “The UK 2017 result–Comparative data forays

  1. That is an astounding drop in Nv! I suppose it remains to be seen whether this is the beginning of a trend or whether this election was simply the confluence of many one-off events. The post-BREXIT referendum collapse of UKIP, a sharp decrease in the SNP vote, and only small gains for the Lib Dems could all be unusual features of 2017 — or they could be the start of a new electoral reality in the UK! It seems to me that a Lib Dem or far-right party resurgence would be necessary to drive Nv back up. There’s not much room to the left of Labour anymore!

  2. So 35.2% of votes won Labour under Tony Blair 62.4% of seats in 2005, but 40% won Labour under Jeremy Corbyn 40.3% of seats in 2017.
    Are we still going to hear “But STV-AV isn’t always monotonic!” lectures from the Posties (usually cribbing their examples from the Borda or Approval fans)?

  3. To respond to Rob’s comment on the earlier thread, you can blame the Lib Dems for the Conservative not getting a majority despite both major parties getting over 40% of the vote.

    The Lib Dem vote actually dropped, and it was small enough that they shouldn’t have won any seats under single district plurality. But they won 14. And the 10 seats in England, and maybe one in Scotland as well, were “natural”Tory seats, basically areas that would have elected Conservative MPs with the absence of the Lib Dems. Taking all of those would have put the Tories at 328 or 329 seats, out of 650.

    Usually the Lib Dems and their predecessor parties won a handful of natural Labour seats as well, but not in England in this election, though one of their Scottish seats historically did vote Labour before 2010.

    This was due to a combination of the Lib Dems betting the farm on getting “Remain” voters, and the Tories going hard for the UKIP vote with the government’s Brexit policy. The Lib Dems did succeed in getting pro-EU Tories, at the cost of losing whatever appeal they had left as a protest party. The Tories gained half a dozen seats that had voted Labour in 2015 by hovering up UKIP voters, but it probably cost them more Remain seats to the Lib Dems at the other end. But the election may have been called on the false premise that they could add the 2015 UKIP and Conservative votes together without much leakage. These things never work out that way.

    • Who says Democracy is Boring, this is the first ever FPTP election that I know where the plurality winning party that won more than 40% didn’t win a majority, technically the Tories got a 6% seat bonus, reminds me of a party list proportional representation system, this election looks very proportionate, who says the UK needs electoral reform. Those predictions came true that the UK was doomed to have hung parliaments of coalition governments and minority governments and this all happened without the Alternative Vote. I know the British have their pride, it is starting to look a bit like Belgium and shades of Italy with all of the political drama.

      If the UK were to embrace an alternative to FPTP, we know the Alternative Vote system is crossed off, what system of PR would be best for the UK?

      • What system of PR would be best for the UK? This is surely worth a separate planting. But the UK Electoral Reform Society has not yet even published any comment on the 2017 vote. Let’s see what they said about options after 2015:

        1. Single Transferable Vote, District Magnitude unspecified. But they published a study on the 2015 election, the most disproportionate result in British election history. It shows how their favourite low-magnitude STV model would have let Lib Dem voters elect 26 MPs when they deserve 47, and the Greens 3 when they deserve 20, while giving Conservative voters a bonus of 32 MPs and Labour a bonus of 28. Why this is their favourite model I have never understood. Seven-seat STV districts are common in New Zealand, and were recommended by the BC Citizens Assembly. But the ERS does not look at anything but low-magnitude STV, not even seven-MP STV.

        2. The Additional Member System, also known as the Mixed Member Proportional system (and in Germany the “personalized proportional system” which, considering they pioneered it, might be a good name). But the ERS considers only the Scottish closed-list version, despite Scotland’s Arbuthnott Commission having recommended a change to open lists. They even repeat anti-PR myths like “constituency MPs receive local casework, whilst the party list MPs do not” which is not even true in Germany, and certainly not in Scotland and New Zealand. Oddly, when explaining their third option, party-list PR, they carefully explain closed-list, open list, and semi-open list, but not under AMS. It is more widely used in the UK than their favourite system, so they seem to want to disparage it. Their 2015 study says about AMS “a system with a 50/50 ratio of FPTP MPs to those elected from the list would be likely to produce similar results to our list-PR projections” but suggests it “could” damage the link between MPs and constituents. In Scotland AMS has accountable-sized regions of 16 MSPs (nine local, seven from top-up regions). And it could have had accountable regional MSPs by now, it the Arbuthnott Commission’s 2006 recommendation for open-list had been followed. AMS “could” damage the link between MPs and constituents? How would that be true under the open-AMS variant recommended by Arbuthnott (just like Canada’s Law Commission model)? With nine MPs directly elected, and seven more by open list? Sounds like an accountable link to me.

        I think AMS (MMP) with 40 regions, with an average DM of about 16, ranging from 12 to 22, would work well: 356 local MPs and 294 regional MPs, 45.2% regional, slightly better than Scotland’s 43.4%.

        Another option would be lower-magnitude MMP, with an average DM of about 8, as some academics have proposed, and which the Jenkins Commission also recommended. This would make more sense in a large country like Canada than in the more compact United Kingdom, but would be worth considering.

        3. Pure party list, which they used for European Parliament elections, but which no one seriously proposes for the UK Parliament.

      • I’d guess that the ERS can possibly take be given a longer than 48 hours to publish their analysis.

      • The ERS needs longer than 48 hours? But I’m astonished how fast the UK moves. Election: June 8, Parliament to resume sitting for a confidence vote: June 13.
        By comparison, see British Columbia. Election: May 9, Legislature to resume sitting for a confidence vote: June 22.

      • What is the logical relationship between the speed of an electoral process and the speed of analysing that process?

    • I think this was definitely a factor. The electoral map has not been changed for over a decade now and still has a pro-Labour bias. The Conservatives will undoubtedly have a notional majority under the new 600-seat map.

  4. I stand with Owen Jones at The Guardian newspaper that a Blairite would have performed much below Corbyn. Corbyn appears to have brought out many enthusiastic and young voters who may have sat out.

    One may say two things about the election structure in the UK: land still probides the Tories a larger number of seats than is reflected in the popular vote margin and clusters of voters who vote uniformly for local reasons (Scots and Ulster parties) get far more proportionate seats than dispersed voters in the Lib Dem Party.

    Bonus structural point: I leave it to number crunchers, but I think if this was a 90 day sprint to the election, meaning two weeks longer, Corbyn and his Labour Party would have won outright. Such are fortunes fortuitously made or lost.

    • Counterpunch has an article comparing Corbyn in 2017 to Blair in 1997, and Corbyn stands up well over most metrics:

      Where Blair 1997 does better of course is in number of seats and margin over the Conservatives, the two popular vote percentages are close, and Corbyn got a bigger increase in Labour’s vote over the previous election. The 2017 election result also compares well to any since the UK stopped being effectively a two party system in 1974 (second or third best in popular vote percentage since that election).

      We will see what happens in the next election, but the whole unelectable” thing isn’t tenable anymore. Campaigning was also suspended twice during the campaign due to terrorist attacks.

  5. A new point: who will be the first British MP to raise the possibility of a grand coalition between the Conservatives and Labour? So far, the punditry says only that it appears unthinkable, and there is essentially no chance of it, even though it would be an obvious solution in many other countries in Europe. There is a strong majority of MPs in favor of a soft Brexit. Theresa May could be unseated as Conservative leader by a soft-Brexit Conservative, but would be unable to govern in the face of the hard-Brexiters in the Conservative caucus. Only a grand coalition would be able to negotiate the terms of a soft Brexit. Will it really take another election to reach that point? The unthinkable election result has already become reality. Could the unthinkable grand coalition be next?

    • I forgot to mention: Theresa May’s problems are complicated by the unexpected growth of her Scottish caucus, which has jumped from one to 13. Since Scotland wants to stay in Europe, they are another voice for a soft Brexit. Since the only reason Theresa May did her 180, from “Remain” to “hard Brexit,” was as an electoral tactic to pull the UKIP vote — and look how well that worked — it seems the Conservatives have every reason to look for a dismount strategy from their failed “hard Brexit” tactic. Step one in the dismount may be to unseat the leader.

      • I have to give credit to a Wikipedian with a sense of humour, who has written “In 2015, after the SNP landslide, David Mundell narrowly defeated his SNP rival to remain as the only Scottish Conservative MP elected. However, following the SNP’s loss of vote share and a third of their seats in the United Kingdom general election, 2017, the Conservatives gained 12 seats, proving that Pandas do occasionally breed.”

    • I asked who will be the first British MP to raise the possibility of a grand coalition between the Conservatives and Labour? Answer: Liberal Democrat Vince Cable, in an excellent analysis.

      “In a sensible, modern, democracy like –say- Germany, the two main political parties would sit down together, right now, to provide reassurance to the public after a General Election that had produced a ‘hung parliament’. A Grand Coalition in the interests of stability would be one of the serious options.
      “There will have to be a compromise in which the 48% accept the reality of Brexit and the 52% accept that a ‘hard Brexit’ is no longer an option.”

      • A more cynical man might suspect that such a coalition would leave Mr Cable’s boss, Tim Farron, as the effective leader of the opposition, and place the Liberal Democrats in a position to gain handsomely from any anti-government backlash. Mr Cable well knows what would happen to Labour were they to try such a deal.

        While I would never accuse Mr Cable of this, I suspect the electorate would view Labour shifting from its most leftist election position since the 1980s to participation in a grand coalition with some confusion. Mr Cable well knows what would happen to Labour were they to try such a coalition. It seems plausible that Theresa May would seek to come to some understanding with Labour on the exact terms of the Brexit deal (assuming this parliament lasts to Brexit) in order to get it past her backbench, but the other obstacles to a broader deal would seem insurmountable.

      • I think the Lib Dem’s experience as being the junior partner in the 2010-2015 coalition, as well as recent experiences in Europe such as the dwindling vote share for the SPD in Germany since 2009 (though that may finally be reversed this year) and the near-wipeout of the PvdA in the Netherlands would make such a thought quite unpalatable to the Labour Party.

        Indeed, I can’t possibly see the appeal to any party to become the junior partner in a two-party coalition. The senior partner takes the credit if the government is successful and both governing parties lose votes if it is not.

      • I think we could confidently expect that part of the price would be guarantees that the Conservatives would not act the way they did during the coalition with the Liberal Democrats. How convincing prospective coalition partners would find those guarantees is another story.

      • Yes, what Alan said. Running a referendum campaign on “This proposed voting system is far too complicated for anyone to understand, but don’t worry about the details. just focus instead on how deeply you hate Nick Clegg for being [a right-wing tertiary-fee-charging sellout/ a left-wing Eurocrat (strike out one)], and vote ‘No2AV'” is not good coalition politics if one has an eye to the long-term (ie, if one realises that FPTP is no longer reliably fit for its advertised purpose of suppressing votes for, and denying seats to, third parties).
        Unfortunately the Tories seem to have believed a lot of their own mantras. How many times did one or another pundit take at as settled science that “England [sic] does not love coalitions” because, hey, Disraeli said “England does not love coalitions” just under two centuries ago?

      • I wouldn’t say Labour needs to actually form a Grand Coalition cabinet with the Tories. What I do maintain is that if Labour are genuinely serious with their pants-wetting about gay-hating misogynistic extremists (or, more accurately, gay-hating misogynistic extremists who don’t have a “You’re raaaaaaacist!” card up their sleeves to play when called out on their gay-hating misogynistic extremism), Corbyn would announce that he forswears the Bob Carr/ Tony Abbott tactic of seizing every available opportunity to defeat the Government on the floor.
        It doesn’t even have to be for the full five-year term. Labour need only guarantee May/ Boris some parliamentary breathing space for the next, say, two or three years. If Boris/ Delingpole screws up badly in the fourth or fifth year of this Parliament, Corbyn can drop the axe, boot them out and get on with turning Britain into Venezuela with cricket pitches.
        I always bet on revealed preferences over asserted preferences.

      • If Boris/ Delingpole screws up badly in the fourth or fifth year of this Parliament, Corbyn can drop the axe,

        So, after the electoral boundaries change significantly against Labour then?

      • According to the Electoral Calculus projection, the Tories wouldn’t even have got a majority under the new boundaries. (No, not what I expected).

      • A soft Brexit is not an option. It is in the same territory as Trumpcare providing ‘healthcare that is far less expensive and far better’. A soft Brexit requires EU approval and it is simply not in the EU’s interest to agree to terms for Britain that are more favourable than the terms enjoyed by the remaining EU countries, Norway or Switzerland.

      • “Bob Carr/ Tony Abbott tactic of seizing every available opportunity to defeat the Government on the floor”

        Tom, is the dynamic here not somewhat changed by motions of confidence in the House of Commons being regulated by the Fixed Term Parliament Act (hence any motion of no confidence must be explicit)?

  6. And very quickly a fine point: the Conservatives did win a narrow overall majority of 317-315 in Great Britain proper last Thursday (318-314 if you count the Speaker as a Tory). I think this is the first time that Northern Ireland – which has a completely different party system – has actually prevented the winner of a British election from having a parliamentary majority.

    • Throughout the nineteenth century successive Liberal governments come under huge criticism because they depended on Irish MPs for their majority, although obviously the party system was radically different and the Irish MPs were home rule advocates rather than Unionists. I don’t think it has happened since the independence of the Irish republic but I will check it when I get time.

      A confidence and supply arrangement with the DUP would make the Good Friday agreement almost unworkable, as would the appearance of a hard border between the republic and the province. The British government cannot very well act as a neutral umpire between the DUP and the other Northern Irish parties while it depends on the DUP for its survival.

      If the DUP talks fail, or if a DUP agreement fails further down the road, there are some fascinating alternatives to a grand coalition, although they would all come at a price. In some ways, it’s as though May were a US Democrat attempting a confidence and supply arrangement with the Freedom Caucus.

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