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?

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

Here is something we do not see in First-Past-the-Post elections* as much as the Duvergerianists seem to think we should: one party agreeing not to have a candidate in order to avoid vote-splitting in a district.

The Green Party has pulled out of a crucial election seat in a bid to help the Labour Party beat the Tories – the first tactical withdrawal of its kind ahead of the general election.

The decision is expected to allow more votes to go to Labour MP Rupa Huq, who beat the Conservatives with a majority of just 274 votes in 2015, when no other party managed to attract more than seven per cent of the vote.

Green Party members in Ealing — where the party won 1,841 votes in the 2015 election — voted not to field a candidate last week, after Ms Huq promised to campaign for voting reform and the environment.

* Except in India!

So much for fixed terms

Barring a further unexpected turn of events, it seems the UK government has an answer to the question of whether an early election can be called, despite the Fixed Term Parliaments Act. [Update: the measure to call the election has passed.]

Prime Minister Theresa May has indicated that she wants a snap election. In May, of course–Alas, no, it is actually on 8 June.

Under the FTPA, parliament can be dissolved early only if (1) the government loses confidence and a resolution of confidence in a government (whether the original or a new one) is not passed within 14 days, or (2) the House of Commons votes by two-thirds of its total number to dissolve itself.

May is seeking the latter, and with opposition Labour leader Jeremy Corbyn saying he “welcomes” an election, the vote is likely to go ahead.

May’s Conservatives have a narrow majority in the current Commons. The snap election is likely to give the party a much bigger one. This may not do much to strengthen the government’s hand with the EU in Brexit negotiations (the ostensible justification), but it should strengthen its hand against its own back-benchers.

Recommended: Alan Renwick’s take.

‘MP not 4 sale’

I am looking through my photo archives to see if I have anything that would be good for a book cover. The one below is a favorite, although not likely to make the grade as a cover image. It is the office front of the campaign of Tamsin Osmond in the constituency of Hampstead & Kilburn, UK, just before the 2010 election. The office was located on Finchley Rd. at Frognal. Across the street was a billboard for David Cameron and the Conservative Party, reflected in the office window.

Tamsin Omond for MP_1.JPG

The posters on the door are interesting. One refers to Osmond as “The election’s most enthusiastic candidate” and the other says “party politics is dead.”

The constituency was a three-way marginal in 2010. In fact, that was one of the reasons for choosing to stay there. We rented an apartment (at the Langorf–Frognal spelled backwards). An advantage of staying in a short-term rental rather than a hotel during an election campaign is you get campaign flyers through the mail slot! Such as this one:

We also obtained this very optimistic one.

Optimistic, but not absurdly so, at the time. The weeks we spent in the UK were the height of “Cleggmania” and if the LibDems were going to make the breakthrough that some polls hinted could be coming, Hampstead & Kilburn was the sort of place in which they were likely to be winning. And the Conservatives were worried. Note how Philp’s flyer points out how far behind the LibDems were in the local elections (upper right of front) and thus they “can’t win”; thus only the Conservatives can beat Labour in this constituency. On the lower right of the flip side, “vote LibDem, get Gordon” Brown (the Labour leader and incumbent PM).

In the election, Osmond won 123 (presumably most enthusiastic) votes. The incumbent MP, Glenda Jackson (the actress) was reelected with 32.8% of the vote and a margin of 42 votes (yes, forty two) over Philp. The margin over the third place candidate, the LibDem, was 841 votes. A Green Party candidate had 759 votes, just short of the total votes separating first from third. In addition to Osmond, there three other candidates (including one each from the BNP and UKIP) combining for 827 votes. It was quite an interesting constituency!

Other reasons for staying there: It was close to a stop on the express bus to Luton, where we were catching our El Al flight to Israel a few days after the election. It was also walking distance to a fascinating synagogue* (which we attended for Shabbat), which also happened to serve as the local polling station.

Sign to the polling station in front of the church on Belsize Square. The synagogue where the polling took place (and which I was able to spend a few minutes in on election day) is just past the church.

* Note that “helping out on Mitzvah Day 2009” is among Chris Philp’s demonstrations of his local leadership. The constituency includes one of London’s major Jewish communities.

Brexit vs. BC-STV: Help with my principles!

As I noted earlier, I happened to be in British Columbia while the British were voting to leave the EU.

[Note: If you want to make general comments on Brexit and what happens next, please comment at the earlier thread. I’d like to keep this one on the narrower topic raised here.]

I never liked the BC-STV vote having been “defeated” in 2005 despite a clear majority (57%), due to a threshold of 60% having been set. But I do not like the UK “mandate” to leave the EU by a vote of 51.9%.

Is there a principle that reconciles my two positions? Or do I just have no principles regarding referendums*, and assess the rules for passage by whether I like what is being proposed? Help, please!

(I have written about referendum approval thresholds before.)


* Other than that, in general, I’d rather not have them. I rather like representative democracy and deliberative institutions.

Brexit (open planting hole)

I was in British Columbia during the Brexit vote (for both a vacation, and a public forum on Canadian federal electoral-system reform). So no time for a full post. But by popular demand**, here’s a discussion opportunity for F&V readers. Clearly, the outcome raises a whole host of F&V-relevant issues…


* About which, more later
** I might note that Brexit reminds one that following the popular demand can be risky sometimes.

The new UK constituencies

For the next (expected 2020) UK election, the assembly size will be reduced from 650 to 600, and the balance in the number of constituencies across the UK’s component units (including English regions) will be shifted. Ron Johnston, at the LSE blog, has a rundown of the changes.

Imagine the research-design opportunities for analyzing personal-vote behavior:

Some current MPs will see their current seat dismembered, and may worry whether they will be selected for another; David Cameron has promised all current Conservative MPs that they will have a seat to fight in 2020, but it may well be very different from the one they currently represent. And so much change will break the bonds between MPs and both their constituents and their party organisations – some of them of long standing – that will have to be rebuilt before the 2020 contest. Many MPs may spend a lot of time building support in their new constituencies rather than serving their existing ones – let alone debating and decision-making in Westminster.

The partisan effects also could be substantial: “The Conservative lead over Labour will probably be widened with the new seats,” says Johnston. However, the extent of this impact is unclear as, given the LibDem collapse and the rise of UKIP and Greens in 2015, “there are fewer marginal seats than at any time since 1945.” Conservatives, especially, have many very safe seats. Still their path to a majority in the House of Commons looks better for 2020 under the constituency revisions than was the case in 2015, when the manufacturing of their majority by the FPTP system was a close call.



Imagining the 2015 UK general election under AV

What would the last UK election have been like be under the alternative vote (AV)? I was discussing this question with Henry Schlechta, and I thank him for bringing it up.

The 2011 attempt at electoral reform failed, but let’s imagine it had somehow succeeded, say, for example, if the referendum had turned the other way, or if the Liberal Democrats had succeeded in getting it passed without a referendum.

In the referendum, one of the challenges the Liberal Democrats faced was that they were seen as by far the main beneficiaries of the proposed change. Conservatives and Labour alike would have been expected to rank the Lib-Dems second, and in all projections of previous elections under AV, the Lib-Dems were estimated to gain about two-dozen seats on average, even becoming the official opposition had AV been in place in 1997.

However, according to the Electoral Reform Society’s report on the 2015 general election (which presents several projections of the results of the election had it been held under a different electoral system)[1], the 2015 general election would have hardly been any different under AV:

Party Seats under AV Difference from actual seats
Conservative 337 +6
Labour 227 -5
SNP 54 -2
Liberal Democrats 9 +1
Plaid Cymru 3
Greens 1

In fact, not only would the Liberal Democrats have received just one seat more than under First Past the Post, the main beneficiaries apparently would have been the Conservatives, who were hell-bent on preventing the system’s adoption in the 2011 referendum campaign.

It would seem that the Lib-Dems lost so much support in 2015 that there would have been far fewer seats where they were among the top two parties in first-preference terms, thus being able to survive exclusion until the final round where they could benefit from Labour or Conservative lower preferences. Perhaps they also lost so much credibility that they would get fewer lower-preferences than in previous elections (I couldn’t find the full poll results on which the projection is based – I would be very grateful if someone else were able to share them with us).

Of course, this is just a projection, with some serious limitations. Firstly, it appears votes under FPTP were simply translated into first preferences. In reality, many voters who voted strategically under FPTP would use the opportunity given to them by AV to rank their real first preference first. Secondly, AV might incentivise parties to pursue different campaign strategies, and maybe even have an impact on manifestoes and candidates, as the need to get a majority of the vote would change what it takes to be elected in many constituencies.

In any case, there would probably have been more 1st-preference votes for smaller parties, including UKIP and the Lib-Dems. But the Lib-Dems might also have benefitted from second preferences from parties such as the Greens, who would usually get eliminated from the count first. Might this have evened out the effect of the Lib-Dem collapse in some constituencies and allowing the Lib-Dems to beat the Conservatives to the final ‘round’ on preferences, by getting second preferences from parties smaller than UKIP?

What would have become of the Conservatives’ campaign warning against a minority Labour government dependent on SNP support? Could it easily have become a campaign for voters’ second preferences?

In Scotland, would Unionist parties have recommended preferences to each other to block the SNP?

These are just a few of the questions that should be considered when constructing this alternate history, and I’d love to hear our readers’ thoughts on these as well as other potential changes to the campaign and results if the UK had adopted AV in 2011 (or any other country – there’s at least one that has been discussed here where the question is becoming increasingly relevant).

[1] Based on second- and third-preference polls. The methodology is stated in appendix of the report (page 33).

The Lib Dems’ demise–and what might have been

I have long been something of a fan of the Liberal Democrats (and their immediate predecessors in the Alliance). So the result of the election saddens me to an extent. While (ex-)party leader and Deputy PM Nick Clegg held his seat, several of their best MPs, like Vince Cable and Simon Hughes, were dumped. This is a loss for British politics.

It is obvious that the party was punished by many of its previous voters for choosing to go into coalition with the Tories when many of their supporters would have expected them to partner with Labour if the opportunity ever came up. However, let’s put the strategic choice in context and ponder the alternatives the party’s leaders faced.

I suspect they would have fared worse from a coalition with Labour given that (1) Labour had clearly lost the 2010 election going from a majority to second place, and (2) It would have been a minority coalition dependent for survival on the SNP (and others).

The more interesting question is what would have happened if they had just agreed to back a minority Tory government, which was what I expected at the time.

The reason for not doing that was probably the fear that the Tories would call an early election and win a majority. The coalition, and the passage of the Fixed Term Parliament Act, prevented that. However, the political situation, as it turned out over the five-year term, meant that an early election was never in the Tories’ interests anyway, and in the end the Tories still won a majority. Would the LibDems have benefitted in this election from not being in power, and making the case that only liberalism could save the union? Yes, I think they would have. Maybe we’d be looking today at a real chance of a Lab-Lib coalition, which would have 4-5 seats in Scotland and an ambitious program of political reform.


On the (minimally) bright side: The LibDems retain seats in England, Scotland, and Wales. Liberal ideas, still bridging divides. I hope the party will recover from this setback. It is too long and significant a fixture of the UK scene to whither away.

And I still agree with Nick.

UK 2015 and Duverger’s Law

Before the election, I said that it was premature to declare Duverger’s Law dead. With an apparent late swing, relative to what opinion polls were showing, in English votes from Labour and especially from Liberal Democrat to Conservative, I am going to say that my “prediction” was not the worst one on this election!

The swing from Labour might be interpreted as nationally focused voting–“which government would I prefer?”. English voters certainly seem to have recoiled from the idea of a Labour government dependent upon keeping the Scottish National Party content. The swing from Liberal Democrats was far greater than had been anticipated, and looks like the district-level “psychological effect” working as anticipated. The party generally benefits more than others from incumbency, given its incumbents’ reputations as good constituency MPs. In this sense, the Lib Dems could be thought of as the party that made FPTP “work”–it is supposed to be a system in which local representation matters, after all. In this election, however, it seems the LibDems suffered major desertion even in districts where they were up against Conservatives. (Defection to Labour from Lib Dem was widely expected, ever since they entered the coalition in 2010.)

In making the case for Duverger’s Law not being dead yet–even if it has been on life support in the UK for some time–I suggested that this election would be more “top two” than the last one, at least in England. That looks like a good call. The following table shows the percentage of votes and seats for Conservative + Labour in 2010 and 2015 in the UK as a whole, and in England.

UK UK England England
votes seats votes seats
2010 65.1 86.8 67.7 91.7
2015 67.3 86.7 72.6 98.5

Even with Scotland included, there was a slight increase in the top-two percentage, back up over two thirds (which is still low for a “classic” FPTP system!). In England alone, it was more dramatic, and the collapse of the Lib Dems, plus the failure of either UKIP or the Greens to win more than a seat apiece despite major growth in votes, sure is noticeable in the top-two seat percentage. The UKIP vote in England was 14.1% in this election, compared to 3.5% in 2010. The Greens won 4.2%, up from 1.0%. The mechanical effect is especially alive and kicking!

The increase of these two small parties’ votes obviously cuts against the notion of a Duverger’s Law rebound. Yet in spite of their increases, we still see an almost five percentage-point increase in the Labour + Conservative percentage, thanks to the major third party having collapsed to fourth place: the Lib Dems, in England, fell from 24.2% to 8.2%! Their seats–still England only here–fell from 43 to 6 (57 to 8 in the UK as a whole).

So, yes, overall a more Duvergerian result. But let’s not overstate it. UK-wide, the effective number of vote-earning parties (NV) went to 3.93. That is by far the highest it has been in the entire post-WWII era. The next highest were 3.71 (2010) and 3.60 (2005). So the trend as of 2015 remains upward, and fairly substantially so. The effective number of seat-winning parties (NS), on the other hand, did decline, although only a little bit: to 2.53 from 2.57. As I pointed out in the previous post, based on Taagepera’s Seat Product, the UK’s large assembly should lead us to expect NS=2.9. So it is still much more a “two-and-a-half” party system than expected–even with the massive SNP win (56 of Scotland’s 59 seats).

Speaking of the Scottish result, that near sweep certainly is a gift from the electoral system. The SNP’s 94.9% of the seats in Scotland comes on almost exactly half the votes. By contrast, the formerly dominant party in Scotland, Labour, in 2010 had 69.4% of the seats on 42.0% of the votes. In 2010, the SNP was a distant second in votes (19.9%) and an even more distant third in seats (6), compared to the Lib Dems (11 seats on 18.9%). What a difference a 30 percentage point swing can make under FPTP!

It is also noteworthy that the SNP received 1,454,436 votes in the parliamentary election. The YES side in the independence referendum last September obtained 1,617,989. Given the turnout differences, the YES vote was 44.7%, so just over five percentages point less than the SNP obtained in this week’s election. (In the last Scottish Parliament elections the SNP had 902,915 votes, which was 45.4%.)

Finally, below is a table of NS, NV, and the gap between them since 1945. The final column is an “expected NV” derived from NS, based on another (as yet unpublished) Taagepera formula that I will put below the table. The noteworthy thing is that we could expect the NV– NS gap to be around .4, given the actual  NS, values in UK elections. In most elections since the resurgence of the Liberals (in votes) in 1974 it has been above that. The gap has been more than 1 in each election since 1997, but surged all the way to 1.4 in 2015. This is extraordinarily high; in fact, I record a gap that high in only 31 of 517 parliamentary elections worldwide (details in the first comment below).

The 2015 result thus appears to confirm that there is demand for more party representation than the electoral system can deliver, but due to what we might call the “Duvergerian rebound”, I have to agree with Alan Renwick that the probability of electoral-system reform has gone down, rather than up, as appeared at least somewhat likely (despite many obstacles) if the result had been as anticipated in pre-election forecasts.

year Ns Nv Nv-Ns ‘Expected Nv’ from Ns
1945 2.12 2.58 0.46 2.56
1950 2.08 2.44 0.36 2.52
1951 2.05 2.13 0.08 2.49
1955 2.02 2.16 0.14 2.47
1959 1.99 2.28 0.29 2.44
1964 2.06 2.52 0.46 2.50
1966 2.02 2.42 0.4 2.47
1970 2.07 2.46 0.39 2.51
1974a 2.26 3.15 0.89 2.68
1974b 2.25 3.13 0.88 2.67
1979 2.15 2.87 0.72 2.58
1983 2.09 2.83 0.74 2.53
1987 2.17 2.85 0.68 2.60
1992 2.27 3.03 0.76 2.69
1997 2.12 3.23 1.11 2.56
2001 2.17 3.33 1.16 2.60
2005 2.46 3.6 1.14 2.87
2010 2.57 3.71 1.14 2.97
2015 2.53 3.93 1.4 2.93
mean 2.18 2.88 0.69 2.61
mean, 1983- 2.30 3.31 1.02 2.72
mean, 2005- 2.52 3.75 1.23 2.92

‘Expected Nv’ here is NV=(NS3/2 +1)2/3.

Trust me, it works amazingly well across hundreds of elections under different electoral systems. To see the derivation, you will have to wait for some forthcoming Shugart-Taagepera work!


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

Patrick Dunleavy, writing at the LSE blog, says that the “UK’s current general election looks certain to put another nail in the coffin of the most famous proposition in political science – Duverger’s Law.” This “law” is, of course, that the plurality rule in single-seat constituencies (FPTP) tends to result in a two-party system. With projections generally indicating that the largest UK party will not win much more than 35% of the vote and 45% of the seats, it does indeed look bad for our famous law.

On closer inspection, however, the UK has been drifting away from the law’s expectations for some time now, and yet even this election does not look like it will mean a break with the “law”. Assessing the performance of the law as a set of expectations for election results depends on just how we define what the “Duvergerian” norm should be, so let’s look at a few different standards and how the UK stacks up, both over time and in this current contest.

1. It is not exactly news that the UK voters and party elites have been less than conformist to the law. Consider the following graph.


The graph plots the effective number of parties, which is the standard way that electoral-systems specialists measure the fragmentation of a party system–it gives us a size-weighted measure of the party system, where each party’s weight is its own vote or seat share.* We can calculate the effective number on either votes (NV, the red line) or seats (NS, in blue).

We see that since 1945, and especially since 1974, there has been a mostly steady upward trend in the effective number of vote-winning parties (NV). Only in two elections in the 1950s was NV under 2.25, and in every election since 1992, NV has been greater than three. If Duverger’s Law means that the effective number of vote-winning parties should not be three or higher, then the law was broken in the UK some time ago.

Of course, maybe Duverger’s Law does not require the effective number of vote-winning parties to be less than three. After all, Duverger did say in his original presentation of what he said was closest to a true sociological law of all the propositions in his book Political Parties, that the national effect meant a two-party system in the legislature. He also said that the impact on the voter (which he called the “psychological effect”) was most felt at the district level.

The graph above shows that the effective number of parties in the legislature (NS) has indeed lagged well behind Nv. In fact, it had never been much above 2.25 until 2005 or above 2.5 until 2010. So we could say Duverger’s “mechanical effect”–the electoral system punishing parties other than the major ones–has continued to work even in the face of fragmentation of the vote. I would point out, however, in response to Dunleavy’s piece, that if NS creeping up above 2.5 signals an end to Duverger’s Law, that is nothing new in 2015.

What about the district level? The next graph compares NV in the average district to the national value of NV. (Note that NS is always one at the district level in such a system!)

It is not surprising that NV is higher nationality than in an average constituency. After all, some parties are more present in some parts of the country than others, and some seats are safe for one or the other (which results in a sharply lower Nv for such districts than for the nation as a whole). Still, district-level mean Nv has been above 2.5 in every election since 1983, and reached almost 3.0 in 2005, before actually tapering back just a bit in 2010 (despite that being an election with no majority party in seats at the national level). So, either Duverger’s Law has been on something like life support for decades, even at the district level, or at any rate, 2015 is not newly non-conformist to the law.

2. This election will actually be somewhat more “Duvergerian” than 2010 was. I mean in a more qualitative sense, as in “how top-two is the election?”, as opposed to the perhaps overly blunt instrument of a single indicator like the effective number of parties.

The big threat to Duverger’s Law is not the presence of regional parties like the Scottish Nationalists (SNP), who will do smashingly well in this election. Duverger explicitly recognized that regional parties were favored by the FPTP system. What is a threat to the claims of the law being in effect for a given FPTP country is a persistent third national party. In 2010, as in 2005 (and some earlier elections), there was such a party in the form of the Liberal Democrats (and their predecessors). However, with the LibDems’ impending collapse in this election, the top two parties–Labour and Conservative–are going to be much more dominant over the rest than they were in 2010. We should see each of these parties on 40-45% of the seats, and no UK-wide party with even 5% of seats. (Two non-regional parties could have 8-15% each of the votes, but the mechanical effect will squash them down in seats, as expected.)

What about the district level? I will venture that here, too, the mean district effective number of vote-earning parties (NV) will drop, compared to 2010. This is mostly due to the collapse of the LibDems, but also due to strategic/tactical voting in English constituencies where voters concerned about the close national contest between Labour and Conservatives lend their vote to whichever party is best placed in their constituency to defeat their least-liked national party. (Such trends are evident in some of Lord Ashcroft’s polls of marginal seats.) As for Scotland, most districts should be much more two-way fights between SNP and Labour, and a few LibDem-SNP, than was the case in 2010.

The 2015 election thus will have more of a top-two flavor than 2010 in both the UK as a whole and in Scotland.

3. The UK is actually under-fragmented, according to the most fully developed quantitative model of the “Duvergerian Agenda”, by which I mean Taagepera’s (2007) Seat Product Model (SPM). This says that the effective number of seat-winnng parties (NS) at the national level tends to be about the sixth root of the Seat Product, defined as mean district magnitude (M) times assembly size (S):

NS = (MS)1/6.

In both Taagepera’s own work and follow-up work I am doing, we find that the SPM is an excellent predictor of seat fragmentation in countries with various “simple” electoral systems (a category that includes variable-magnitude districted PR, single-district PR–and FPTP). For the UK, with M=1 and S=650, the models says that we should expect NS=2.9 in the UK. Note: 2.9, as in almost THREE, not TWO.

The graph below shows how well the SPM works on just those countries that use FPTP. Each country’s long-term average is shown with its abbreviation at the plotted position. The red line is the expectation of the Seat Product Model.


Apparently it works pretty well, overall.** However, the UK really stands out as one of the big outliers! Its average NS is much too low for its very large assembly, despite the single-member district system. In fact, it is more of an outlier than India, on the high side! (It is not, however, as egregious a low-outlier as the US.)

What about 2015’s likely result? Using the Election Forecast projections, the effective number of seat-winning parties would be around 2.6 in this election. So it is creeping upwards towards its expected 2.9, but it still won’t be there. In other words, the UK’s likely 2015 result still remains substantially more top-two dominated than we should expect, given its electoral system–when we include the size of parliament in our definition of “electoral system”, as we should.

In summary, it is hard to sustain the claim that the 2015 election is some sort of final nail in the coffin for Duverger’s Law. We looked here at several ways of defining what a “conforming” election result might look like. In some ways, the UK has been deviating for some time: the effective number of vote-earning parties has long been too high to really be a “two-party system”. While the effective number of seat-winning parties has been lower (as expected, due to the “mechanical effect”), it has crept up in recent elections, meaning 2015 is not really new. Even at the district level, it is not as if we have had consistent two-party dominance in recent times. Moreover, this election result will be more focused around the top two nationally than were the last two elections, and this pattern should be true of the district level as well as nationally. Finally, the UK’s electoral system actually should be able to accommodate an effective number of parties a good deal higher than it will in 2015 (or has in preceding elections), according to the most detailed quantitative model yet of the Duvergerian effect of electoral systems.

Duverger’s Law may be on life support, but it actually has been for some time, and it is not dead yet.

* For those unfamiliar with the index, a quick summary of what it does: It offers a summary of how many hypothetical equal-sized parties would be just as fragmented as the actual constellation of unequally sized parties. Thus if there are three parties, each with a third of the vote, we get NS=3.00. But if one of them is bigger than the others, the index will trend downwards towards two. If one of them splits in half (so the party shares become 1/3, 1/3, 1/6, 1/6) we now have four parties, but as they are unequal, the effective number will be less than four (but more than three–the actual value being around 3.6). It is computed by squaring each party vote or seat share, summing the squares, and taking the reciprocal of the sum.

** Sri Lanka and New Zealand are shown here only in their FPTP eras.

UK 2015 forecasts

With the UK general election three weeks away, Chris Hanretty of the team offers a comparison of their forecast with those of two other academic teams, and Polling Observatory.

The forecasts must estimate a nationwide vote share for each party, and then devise a means of projecting these figures on to the 650 individual plurality (FPTP) contests that make up a UK House of Commons election. Given these two stages for any forecast, Chris’s comparison includes running their own seat calculator on other projections’ vote shares.

One thing all the projections agree on is that no party will be close to half the seats, although the confidence interval on the ElectionsEtc and ElectionForecast figures for the Tories include the majority mark (barely). All agree that Labour has almost no chance of winning a majority.  Another point of agreement is that the leading party in votes will be the Conservatives, but on only 34%, with Labour just a percentage point or two behind. In each projection, the confidence intervals on vote shares overlap. So, yes, the race remains more or less tied.

For those of us who enjoy anomaly watches, the PollingObservatory forecast (as of 1 April) has Labour ahead in seats, 276-271, despite being just behind in votes. The other two put Conservatives ahead on seats as well as votes, although again with overlapping confidence intervals.

On the eve of the 2010 elections, I ran some numbers from FPTP elections around the world up to that time, asking how uncommon it was for the largest party have less than 36% and the third party have more than 25%. The answer, in my sample of 210 FPTP elections, was one (Nova Scotia 1998). There was at least one other that was missing in my data, Quebec 2007, where all three leading parties were within a range of 33.1 to 28.3. The question arose, because it was the consensus of the final polls that the UK was going to have such an election. However, it did not quite get there. The Conservatives made it just over 36% and the third-place Liberal Democrats slipped to 23.0. In other words, there may have been some last minute tactical (strategic) voting by just enough voters to make the result just a little more “Duvergerian”.

If we think of Duverger’s Law as a baseline expectation for an electoral system like the UK, the projections for this election might be said to conform, if all one cares about is the relative dominance of the top two over the rest. Thanks to the fall of the Liberal Democrats since entering the coalition in 2010, all projections agree that there will be a big gap between second and third. Of course, the top two on around 33% each is not exactly what we normally think of as a Duvergerian outcome, regardless of the gap between second and third. The interesting thing to watch is if there is sufficient late desertion of the UKIP (on 10-13%) and Greens (less consequentially, as they are under 5%) to push the leading party up over 36% again. If that is the Conservatives, there might be an outside chance of a majority government, depending on the constituencies where such tactical voting takes place. UKIP leader, Nigel Farage, recently called on supporters to vote Conservative in seats UKIP can’t win, and there is some evidence of UKIP slippage in recent Ashcroft polls of marginal constituencies.

For now, let’s suppose that the seat projections are about right. Are there any combinations of two (other than Labour-Tory) that would control a majority? The House contains 650 members, but Sinn Fein (of Northern Ireland) does not take the seats they win, which were five in 2010. That makes the majority threshold probably at 323. A combine of Labour and Scottish National Party (SNP) gets there, according to Polling Observatory–barely: 325 (or 324 if using ElectionForecast’s seat model).

How likely is Labour-SNP cooperation? Nicola Sturgeon, SNP leader, has been appealing for it–not for a formal coalition, but for blocking a Tory government. An exchange in the final debate (opposition parties only; video) was telling. Labour leader Ed Miliband forcefully refused, saying he had fundamental disagreements with the SNP, mainly over the possibility of a second Scottish independence referendum. He said no to a “coalition”. However, he pointedly did not directly say there could be no cooperation short of a governing coalition, although he shook his head dramatically when Sturgeon appealed for him to join her to block the Tories. He is in a bind, for sure. Sturgeon is probably right when she says left-leaning voters would never forgive him if he refused cooperation and allowed a Tory minority government to form. On the other hand, he certainly has to be careful not to signal intention of working with a party that would break up the UK.

A path to a stable Conservative-led minority or coalition government is hard to see, on these projected numbers. However, two of the projections have Conservatives and Liberal Democrats at 311. I find it hard to believe the Liberal Democrats would enter a coalition again with the Tories, but less hard to believe they could enter a looser arrangement. However, such a combination would still be a around a dozen seats short, and even the Northern Ireland Democratic Unionists (not in the projection models, but 8 seats in 2010) would not quite get them there.

Absent a late surge for the Tories, it still looks like a government led by the party with the second largest number of seats, and needing support from Scottish separatists, is the most likely result. Let me close with an understatement: This will be interesting.

The most dysfunctional and undemocratic parliament in the Commonwealth?

On, Frances Russell reviews Democratizing the Constitution — Reforming Responsible Government, by Peter Aucoin, Mark D. Jarvis and Lori Turnbull.

Russell begins the review by declaring that “Canada has the most dysfunctional and undemocratic parliament in the British Commonwealth.” She subsequently indicates that the book’s proposal is that:

Canada should follow the lead of its sister Commonwealth countries Britain, Australia and New Zealand and codify the principles of parliamentary democracy to ensure the players — voters and politicians — understand the playbook and stay within the rules.

Because themes of this sort are a frequent topic of discussion around here, I thought I would open up a new thread.

Thanks to Wilf Day for the link.