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!

 

5 thoughts on “UK 2015 and Duverger’s Law

  1. I should have noted just how uncommon a value of Nv-Ns as high as 1.4 is. Among parliamentary systems in the datasets we are using (drawn mostly from Matt Golder’s, but augmented to some extent), the 90th percentile is 1.14, and the 95th is 1.48. This is for 517 elections. Only 32 elections have values of 1.4 or higher. So pretty unusual.

    I restrict the sample here to parliamentary because presidential systems are more extreme. The same average pattern is found, but many more of the low and high outliers are presidential than parliamentary. (The 95th percentile for presidential systems is 1.93.)

  2. Pingback: Could a third-party candidate win the U.S. presidency? That’s very unlikely. | modica news

  3. In relation to the linked article, I’ve often wondered whether third party candidates may actually be somewhat advantaged by the Electoral College, compared to a vanilla national FPTP election. Using the national popular vote, a vote has the same chance of influencing the contest whether it’s cast in Montana, California or Pennsylvania, thus meaning that every voter for Jill Stein or Gary Johnson is ‘wasting their vote’. On the other hand, under the Electoral College, voters in safe states may feel more free to vote for a third-party candidate without tipping the national contest to the lesser of two evils, while only voters in the marginal states have to think about tactical concerns.

  4. Pingback: Could a third-party candidate win the U.S. presidency? That’s very unlikely. | meschugge.net

  5. Pingback: Could a third-party candidate win the U.S. presidency? That’s very unlikely. | web02003

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