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 referenda*, 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!