DMP Part 3: the real world.

Originally posted on my (now-defunct) WordPress blog

The sporadic blog returns! This installment has been a long time coming, partly because of all of the beautiful maps. They’re worth it, I promise. When we left the wonderful and weird world of Proportionalia and its Dual Member Proportional (DMP) voting system, we’d just explored some of its more interesting quirks using some highly contrived examples. In creating these, I was helped along by some janky MATLAB/Octave scripts I knocked up to do all the calculations nice and quickly; the plan in the future is to upload these for public consumption. After plenty of necessary sanitiation. It may never happen. (Update from 2024: it never did — L)

Snapping back to reality, in this post I’ll be asking the big questions, such as “is Wales real?”, “what’s so special about North Devon Council from 2015-2019?”, and “can we use Haida Gwaii as the basis for a new measurement system?”.

But first…

Wales 2017

Ahhh, Wales. Where the men are men and the sheep are nervous. The existence of Wales is still unproven, and there is evidence to suggest that the whole country is an elaborate prank devised by the British and Irish governments to secure drilling rights in the Irish Sea (much like Finland). In any case, this country sends 40 members to the UK House of Commons using the abhorrent first-past-the-post (FPTP) system. The Labour party was thus able to win 28 of these seats (70%) on 48.7% of the vote — a hugely inflated majority.

The system is hardly representative, and fosters a rural/urban divide: Labour hold a monopoly on the former mining heartlands of the valleys (that big red blob in the south for those unfamiliar with the topography), whereas the sparsely populated rural areas are dominated by Plaid Cymru and the Conservatives.

Side note: it is surprisingly difficult to find style guides for political parties, and hence have an idea what colours to use for greatest accuracy. Fortunately Wikipedia has a list! I can therefore show you Labour in beautiful #DC241F, Plaid in ravishing #008142 and the Tories in sublime #0087DC.

To convert this to a simulated DMP election, all I did was to pick a handful of the most sparsely populated constituencies (and Ynys Môn because it’s an island and therefore special), then pair up the remaining ones and sum the vote totals for those. This approach obviously has downsides: I am pairing constituencies up sort of randomly rather than considering possible cultural or community bonds, and I am assuming that people’s voting habits would not change under the new system. DMP greatly reduces the incentive to vote tactically, as a vote for a losing candidate may help them gain the second seat or another seat for their party elsewhere in the region.

With this in mind, this is what we end up with:

Here are some points I find worth mentioning:

• Labour are so astonishingly popular in South Wales that they take both seats in three constituencies!
• However, they do not have a monopoly on the region. There is much greater party diversity in the two-seat system, with Plaid, Tories and Lib Dems all being represented.
• UKIP does not appear on this map, despite gaining enough votes across Wales to be allocated a seat. They were unable to fill it, and the Liberal Democrats also forfeited one seat. These were snapped up by Labour and the Tories.
• Plaid Cymru was already spot on with four seats under FPTP, but here they lost Arfon as it was merged with Aberconwy. Strangely enough they didn’t pick up the second seat here, instead nabbing this from the combined Caerphilly/Merthyr Tydfil & Rhymney seat.

One trouble with UK general elections is that independent candidates are largely shut out by FPTP, so their vote counts don’t even come close to testing out the DMP mechanisms designed to give them a shot. To test this out, we need something a bit more local.

North Devon 2015

Local elections in England & Wales often feature a variant of FPTP called ‘bloc voting’ (the lucky bastards in Scotland and Northern Ireland get to use the Single Transferable Vote). In effect, bloc voting is FPTP applied to multi-seat districts. In a three-seat ward, voters have three votes, parties will put forward three candidates and all three seats will be most often won by one party. It’s abominable, and can result in electoral deserts where one party holds every single seat on a council (e.g. Sandwell).

So why look at North Devon? Before 2019, it was one of the few councils that only had one- or two-seat wards, and in just the right proportion to lend itself to a DMP simulation! Most other councils have three-seat wards, including North Devon currently after boundary changes. Therefore we must cast our minds back to 2015, even though it feels like a completely different world. Here’s how the electoral map looked in North Devon then:

Thanks to bloc voting, one party holds both seats in 12 of the 16 two-seat wards. Shockingly, the Green Party won not a single councillor with 16% of the vote — UKIP won a seat with four times less.

This election is pretty much ready-made to run the DMP algorithm on, but some tidying is still needed. In two-seat wards, I halved the vote totals for every candidate to reflect that DMP voters have one vote instead of two in bloc voting. Then vote totals for candidates in the same party were combined, and that’s it. It’s a little crude but it’ll have to do. Of course, single seat wards can just be left as-is.

As expected, the Greens are the major beneficiaries here. However, I am impressed with how well the Independent vote matches their seats, even with the weird DMP hack-job second-seat gift compromise (you should probably read the previous blog posts to understand what I mean). If this would repeat in a different election, I do not know.

Sadly, North Devon redrew its boundaries before the 2019 local elections, so I can’t update this map for the present day. Let’s turn to something a little closer to home - and more relevant to DMP!

British Columbia 2017

British Columbia is a hippie province that most often elects right-wing governments. It is easy to blame FPTP for this, and weeeell you’d be right. Take the 2001 provincial general election for example: the BC Liberal Party won a very respectable 58% of the vote, but this translated into a whopping 77 out of 79 seats! They remained in power for sixteen years until the 2017 election, during which they lost their majority… by one. Currently, BC is being run by a New Democratic Party minority government supported by the three Green MLAs (Members of the Legislative Assembly). The map looks like this:

Side note: BC politics may require a bit of explanation for my UK audience. The red party here is the centre-right BC Liberal party, which is not affiliated with the Liberal Party of Canada for reasons (reading into this a little further, the LPoC only has local parties in four provinces, which would be like the UK Conservatives only contesting local elections in the South East). The social-democrat NDP (orange) and the… green Greens (green) are much more closely related to their federal counterparts.

One challenge with introducing proportional representation in BC is that it is big. Really big. In fact, two of its electoral districts (ridings) are bigger than England. They’re the two at the top of the map, Stikine and Peace River North, with a combined population of 59,670 as of 2011. This population is just higher than the smallest riding (Vancouver False Creek, pop. 52,565) but is spread around an area a good 60 thousand times larger. For some reason, the inhabitants of the north of BC are vehemently opposed to any system that requires larger ridings, and this was one of the reasons DMP was designed: sparsely populated areas can keep representation as it is, while denser regions pick up the proportional slack.

How DMP would work in BC we may sadly never know, as it was defeated as an option in the 2018 electoral system referendum. But I’ve crunched the numbers so you don’t have to, just for a taste of that sweet sweet alternate reality.

While running this simulation, I used the whole province to calculate proportional seat allocations. However, this results in an extremely low bar for small parties to clear to be given a seat (they only need about 1% of the vote across the province). Somehow in this case, the Communist party managed to scrape enough votes together to be awarded a proportional seat, which they promptly forfeited to the Liberals. To avoid unnecessary forfeits, it’s probably worth dividing your legislature into regions of about 20 seats each.

Sadly, because the three main parties have such a stranglehold on provincial voters in BC, we didn’t see anything crazy with the introduction of DMP, just a redistribution of seats between these parties. However, DMP’s impact on provincial politics would still be profound. At least in this simulation, the NDP and Greens would no longer be working with a wafer-thin majority. In reality, people’s voting patterns could change dramatically. For example, even in the vast interior where it seems only Liberals can survive in the single-seat wastes, NDP supporters can be encouraged that their votes help elect MLAs elsewhere in the province. That’s the beauty of DMP. It fosters both dramatic change and ensures continuity.

…

Just don’t think too hard about how it does it.