UK election 2017-any hope for electoral reform?

One of the most remarkable things about the UK election was the total number of votes cast for the top two parties, which increased from 67.3% in 2015 to 82.8% this year. It has been less noticed, however, that this has come with a substantial drop in the Gallagher (least squares) Index of disproportionality. From 15.02 in 2015, it has more than halved to 6.41, a figure actually larger than that in Ireland in 2011, Germany in 2013, or Poland in 2015.

UK_Gallagher_1966-2017

Source: Michael Gallagher

This is largely due to the absence of a large third party discriminated against by the single-seat plurality system. No established minor party outside Northern Ireland gained votes, with UKIP and the Greens both falling to below 2% and even the Liberal Democrats slipping back slightly in terms of votes despite picking up four seats. The (unusual, as Shugart points out) absence of an unearned majority for either party also contributed to the low score.

There also seems to be some evidence from past UK election results that two-party elections tend to be more proportional. Between the 1950 and 1970 elections, when support for the Liberals (the only substantial third party) never exceeded 11.2% (and was generally substantially below this), the Gallagher Index averaged only 6.41; since then, with the until-recent presence of the SDP-Liberal Alliance/Liberal Democrats, it has stayed high as can be seen above.

UK_margins_2015-17

The number of very marginal seats has also increased substantially at this election, as can be seen above. While other readers may disagree with me on this, I personally view a higher number of marginals as good for the status quo, given that it means more voters view their votes as having an impact upon the result. This is not necessarily a result that would appeal to the major parties, but it would seem to act to quell public concern over the current system.

The growth of the top two creates a problem for electoral reform advocates. Which party, exactly, benefits from implementing proportional representation? The Labour and Conservative parties obviously have no personal interest in PR. The Liberal Democrats, at present, are far too weak to extract such a concession (even with 57 seats in 2010, the best they could do was a referendum on AV) in a coalition, as are the Great British regionalist parties (which would probably be heavily expected to go with Labour anyway, weakening their leverage) and the Greens (much the same reason).

Labour’s manifesto makes no specific mention of proportional representation, while the Conservative manifesto goes further, calling for single-seat plurality to be adopted for mayoral and Police and Crime Commissioner elections. Shadow Chancellor John McDonnell has gone on record in the past as being in favour of proportional representation, but I suspect now Labour are at 40% that proposal will be soon forgotten.

While the past two months has demonstrated conclusively that much can change in a short time in UK politics, it’s difficult to imagine that proportional representation could gain any traction in a political system dominated by the top two parties after failing to gain traction (at least for the House of Commons) in nearly thirty years of three-party politics.

Remember: Honeymoon elections matter

On 23 April, when many commentators were lamenting how weak (then-expected) President Emmannuel Macron’s support might be in the National Assembly, I offered an estimate of 29% of the vote for his newly formed party. I based this solely on the mean surge that presidents’ parties tend to have when an assembly election occurs early in their terms–a honeymoon election.

Maybe that was an underestimate. While one poll (OpinionWay/ORPI) has Macron’s party, La République en marche! (LRM), on 27%, Harris Interactive sees it on 32%. Both agree this will be the biggest party (Reuters). Given the electoral system, such a share puts Macron well within reach of having a majority in the Assembly.

And what a party it is!

Half of the LRM preliminary list of 428 candidates for the 577-member National Assembly are women and 52 percent are civil society figures.

Better yet, 95% are not current MPs and one of them is a “rockstar mathematician”! (France24)

Macron has also named his cabinet. The premier will be Edouard Philippe, mayor of Le Havre and a member of the Les Republicans (the party of defeated and discredited presidential candidate François Fillon). Reuters reports:

A leading French conservative accused President Emmanuel Macron of “dynamiting” the political landscape on Tuesday as he put together a government that is expected to include former rivals on both left and right.

In other words, he is being “accused” of doing precisely what he won nearly two thirds of the vote (in the runoff) saying he would do.

Furthermore,

over 20 LR members of parliament, including some party heavyweights and former ministers, issued a joint statement on Monday urging the party to positively respond to the “hand extended by the president”.

All of the above should serve as a reminder of two things: (1) the purpose of the upcoming election is to ratify the new executive’s direction, not to be a second chance for an alternative vision; (2) the honeymoon electoral cycle matters.

What if Canada adopts MMP?

Among the electoral system types to be considered by Canada’s upcoming reform-proposal process is the mixed-member proportional system (MMP). What might we expect Canada’s effective number of seat-winning parties (Ns) to be under MMP?

As noted in the previous post on comparing the Alternative Vote to FPTP, Canada has had almost exactly the Ns, on average, that we should expect it to have, given its assembly size (around 2.6). Thus I will start from the premise here that Canada would continue to have about what we expect if it had MMP staring in 2019 (or whenever). That is, recent elections the country are neither surprisingly under- or over-fragmented, so there is no reason to think the country would over-shoot the expectation under a new system. (It might be more realistic that it would under-shoot, but that depends on how much we believe there is pent-up demand for new parties or for growth of existing smaller ones. I will leave that aside here.)

The answer to this “what if” depends on the precise MMP model. What Li and Shugart (2016) have shown is that a minor addition to the Seat Product Model (of Taagepera, 2007) captures two-tier compensatory systems well. MMP is a type of two-tier compensatory system, so let’s apply that model to a hypothetical Canadian MMP. The formula is:

Ns=2.5t(MSB)1/6.

In this formula, MSB is the “basic-tier seat product”, defined as the mean magnitude of the basic tier, times the total number of seats in that tier. For a typical MMP system, we retain M=1 in the basic tier, so the basic-tier seat product is simply the number of seats elected in that tier. The t in the formula stands for “tier ratio”, which is the share of the total assembly that is elected in the compensatory tier. This is an exponent on a constant term that is empirically determined to be 2.5. (Determined from the broader set of cases on which this is tested.*)

If a country’s electoral system is “simple”, meaning there is just a single tier, as with FPTP, then the above formula reduces to Taagepera’s (2007) seat product model:

Ns=(MS)1/6.

(In a system with no upper tier, t=0, and MSB=MS.)

For purposes of estimating, I am going to assume the assembly size will remain the same, currently S=338. I will further assume that it would be politically difficult to reduce the number of districts (ridings) in the basic tier of an MMP system too much below the current number (which is, of course, 338). I will adopt two thirds of the current number as my estimate of “not too much”. In such a scenario, we get a basic tier of 225 seats, giving us t=.33:

Ns=2.5.33(225)1/6=1.35(2.47)=3.33.

I did not plan my scenario to get to three-and-a-third, but it has a nice ring to it. And seems pretty reasonable. For comparison purposes, this is not much different form what Canada had in 2006 (3.22) or Germany, an actual MMP system, had in 1998 (3.31).

Based on another formula in Taagepera (2007), which is empirically very accurate, we can also derive an expectation for the seat share of the largest party (s1):

s1 = Ns-.75.

For our hypothetical MMP system in Canada, this implies the largest party with just over 40% of the seats.

We can tinker with the scenarios. For instance, suppose the assembly size were increased to 400, with half the seats in the basic tier. Then we get:

Ns=2.5.5(200)1/6=1.58(2.42)=3.82.

As would be expected intuitively, the fragmentation of the House goes up due to the larger compensation tier, and in spite of the basic-tier seat product being correspondingly lower. This scenario would have an expected s1=.366.

Note that I have ignored thresholds here. My ongoing research with Taagepera suggests that thresholds matter, but unless the threshold is very high (more than 5%) or the seat product, MS, is extremely high, the value of the threshold has much less impact than the parameters discussed here.

In conclusion, under common Mixed-Member Proportional (MMP) designs, Canada could expect its House to have an effective number of parties ranging from 3.33 to 3.8, compared to a recent average of around 2.6 under FPTP. Its largest party could be expected to have around 36% to 40% of the seats, on average, compared to majorities or nearly so in recent elections.


* Note that this parameter’s empirical derivation raises the risk that it could be an artifact of the particular sample we have, and thus not reliable for determining an expectation value, as I am doing here. Fortunately, unless it is off by a wide amount, it does not make a large difference. For instance, 2.33 =1.26, whereas 3.33 =1.44. This variance in our prediction is much less than “normal” fluctuation from election to election in many countries.

Does AV mean higher or lower effective number of parties?

There may be a conventional wisdom among people who study comparative electoral systems that the Alternative Vote (also known as Instant Runoff or Majority Preferential) tends to suppress the effective number of parties, compared to plurality (First Past the Post, or FPTP). Or maybe it is just me, but I will admit to having such a notion. After all, Australia is a pretty strict two-party system, isn’t it?

The correct way to approach the question of whether AV means a higher or lower effective number of parties (N) than FPTP is to ask: What we should expect N to be, given the country’s seat product?

As explained by Taagepera (2007) and further elaborated and tested by Li and Shugart (2016), the seat product is a country’s mean district magnitude (M), times its assembly size (S). The Seat Product Model says that the effective number of seat-winning parties (Ns) tends to be the sixth root of this product: Ns=(MS)1/6.

The model is logical, not a mere product of empirical regression work, although regression tests confirm it almost precisely (Li and Shugart, 2016).

When all districts elect just one member, thus M=1, the Seat Product is just the assembly size, S. Hence we take the sixth root of S to get an expectation for Ns. What if we do this for Australia’s House of Representatives? We get an expectation of 2.31.

The actual Ns for Australia’s elections since 1984, the year S was increased from 125 to 148 (subsequently it has increased to 150, a minor change) is… 2.53. However, I believe that figure (I am using Gallagher’s Election Indices) treats the Coalition parties as one in elections before 2010.

In the two most recent elections, Ns has been 2.92 and 3.23. The notes to Gallagher’s Election Indices indicate that for these elections the Liberal Party, the Nationals, and the Liberal National Party of Queensland are treated as separate parties. In my opinion they should be so treated, although I suppose one could have a debate about that.

The actual mean is thus above the expectation for a hypothetical FPTP of the same size assembly. If we use the figure of 2.53, it is obviously not much higher than 2.31 (the ratio is 1.10). However, if we consider the value, at least in recent elections, to be around 3.0, it is about 1.30 times the expectation value.

Contrast this with the UK, where elections of the same period (1987-2010) have a mean Ns=2.30. This is just what we expect for FPTP, right? Not much over 2.0. Not so fast! The UK has a huge assembly, and with S=650 (aprpox., as it varies over the period), we should expect Ns=2.94. The UK actually has one of the more under-fragmented assemblies, according to the Seat Product Model, with this recent-period average being only 78% of expectation.

So how about Canada, where AV is one of the potential reforms being considered? Over a similar period (1984-2011) we get Ns=2.63. With S around 300 during this time, we should get Ns=2.59. So Canada pretty much nails the expectation of the model.

So, should we expect Ns to go down if Canada were to adopt AV, as (what I characterized as) the conventional wisdom would have it? Or should we expect it to go up?

I would not be inclined to say ‘down’. I will just leave it at that for now.

‘Seat Product Model’–audio version

The audio-slides version of Li and Shugart (2016) is now available!

As previously announced, the publication details and abstract are as follows:

The Seat Product Model of the effective number of parties: A case for applied political science

Yuhui Li, Matthew S. Shugart

Electoral Studies 41, March 2016, pp. 23–34.

Abstract

This paper extends Taagepera’s (2007) Seat Product Model and shows that the effective number of seat-wining parties and vote winning parties can both be predicted with institutional variables alone, namely district magnitude, assembly size, and upper-tier seat share. The expected coefficients are remarkably stable across different samples. Including the further information of ethnic diversity in the models hardly improves the estimate of the effective number of parties, and thus the institutions-only models are preferable on the grounds of parsimony and the applicability to electoral-system design or “engineering”.

The Greens, electoral reform, and the Canadian leaders’ debate

Last week, Canadian party leaders participated in a debate. It is currently the only one scheduled to include the Greens leader, Elizabeth May (the party’s only MP).

The debate included an entire segment devoted to, as moderator Paul Wells put it, “Canada’s democracy — how it works, why it doesn’t always work as well as we hoped.” (From my south of the border perspective, I can only admire a debate that actually asks such a question, rather than implicitly assuming that the debate and election themselves are proof of how great democracy is working, but enough of that digression for now.)

The first question within this segment of the debate went to May, and the exchange, which you can read in the transcript, is very interesting.

Paul Wells: Our first question on this to Elizabeth May. Ms. May, you’ve called the government we have now an elected dictatorship and you’ve called for electoral reform, but this election will be won and lost under the current electoral system. Do you worry that Green candidates will take support away from other parties that could defeat this government? Might the Green Party help reelect this government?

Elizabeth May: When I refer to the government as an elected dictatorship, it’s not personal in any way to the Prime Minister nor to his party…

The only job description for a member of parliament is that found in the Constitution, which is to represent your constituencies.

So we need to actually revisit parliamentary democracy, understand that this election isn’t about electing a prime minister — we don’t do that in this country; we elect members of parliament. And their job is to find the government that will hold the confidence of the House, so we can work for Canadians…

As far as Greens being concerned about this, not at all. We have had success and we’ve now had election – my election in Saanich–Gulf Islands, but across provinces — in British Columbia Andrew Weaver, in New Brunswick David Coon, in Prince Edward Island Peter Bevan-Baker. All of us got elected by driving voter turnout.

So instead of fixating on this splitting the vote non-problem, vote-splitting, we need to focus on the real problem, which is 40 percent of Canadians in the last number of elections haven’t voted. And vote abandoning, in my view, is a much bigger problem than vote-splitting…

Paul Wells: You’ve said we don’t elect a prime minister, and that’s true, but we saw quite a mess of a coalition crisis in 2008. Are we headed towards that sort of arbitrage among parties after the next election if there’s no majority?

Elizabeth May: I can’t tell you how committed Green MPs as a caucus will be to working with other parties, working across party lines to ensure that we go from a precarious, perhaps two-year minority parliament to a stable, productive, effective parliament, because you look at really great parliaments in this country, and I refer viewers back to Lester B. Pearson where the small group of NDPers under David Lewis and Diefenbaker in the Conservatives and Lester B. Pearson delivered our social safety net.

I find the exchange interesting for the effort to drive the discussion way from vote-splitting and choosing a prime minister–two common perceptions of elections in parliamentary systems using first-past-the-post electoral systems. These are perceptions that are, of course, harmful to small parties. So May attempts to emphasize local viability of Greens, and the advantages of cross-party cooperation in a non-majority parliament.

Then things returned pretty quickly to business as more-or-less usual, with Liberal leader Justin Trudeau engaging NDP leader Thomas Mulcair in a debate over the Clarity Act (regarding another potential Quebec secession referendum).

A bit later, Wells raises the issue of electoral reform directly, referencing the proposal of the Liberal Party (see p. 8 of the linked PDF). I will just quote a few snippets here. PM Stephen Harper (Conservative):

Well, I think it’s a very fundamental change to the way our political system would work in this country. We have a Westminster system. Voters are able to elect governments. They don’t elect coalitions that make up the government later. And you know, Canadians – Paul, this has come up before. It was subject of a referendum and plebiscite in Ontario and Prince Edward Island and British Columbia. I have not found Canadians who want to make this fundamental change. In fact, whenever Canadians are asked, they reject it. We know the rules. Let’s play under the rules that Canadians support.

Mulcair did not use the immediate opportunity to talk up his party’s stated commitment to introducing proportional representation (MMP, specifically). Instead he talked about the current government’s “Unfair Elections Act” (it is, actually, of course, the Fair Elections Act). Later, however, Mulcair did say, “We think that there are three main things we can do with regard to our institutions. The first is to make sure that every vote counts with a proportional representation system.” (The others were “open up parliament” to more public scrutiny and abolish the Senate.)

Unless I missed it, Trudeau himself never mentioned his own party’s commitment to electoral reform. Perhaps he thought it was enough that Wells invoked it and gave Harper a chance to denounce it.