Just Look What You Could Have Won

Shortly after the election the Electoral Reform Society published a bar chart which showed the results under “Proportional Representation”. Basically they had treated the whole of the UK as one constituency, and apportioned the votes into seats using something known as the d’Hondt mechanism, which is what we use to determine MEPs in elections to the European Parliament.

Put simply, the d’Hondt mechanism sees how many votes each party has got, and repeats a calculation (dividing that number of votes by the number of seats already allocated + 1), giving a seat to the party with the largest result, until all the seats are allocated. It’s pretty proportional – if you get 15% of the votes, you’ll get around 15% of the seats.

However this is not the only form of proportional representation. My main criticism of it is that it only allows people to vote for parties – and I think there is significantly less loyalty to parties now than there has been for quite some time. It ignores the perspective that parties are, themselves, coalitions of views, and that people might want to distinguish between, say, a euro-sceptic Conservative and a euro-phile Conservative. Additionally, it places a lot of power in the party hierarchies again, because the parties determine which order candidates appear on the list – so determining the most (and least) likely candidates to actually be allocated seats.

As I stated before, my preferred mechanism is called Single Transferable Vote, abbreviated to STV. The way it’s implemented in Ireland seems to work well.

Basically, the country is divided into constituencies which return 3, 4 or 5 MPs. If an area is big enough to return 6 MPs, it’s divided into two constituencies, each returning 3 MPs. The ideal size is 4 MPs. People then rank individual candidates in order of preference, so you put a 1 next to your most favoured candidates, 2 against the next one, and so on. You don’t have to write numbers against all candidates – so if there are some you really don’t want in, you don’t write a number against them.

The benefits are that (a) it retains a link between an MP and an area they represent, (b) it ensures that people are more likely to have an MP in their area who represents their views, and (c) it allows people to vote for independent candidates – it removes some power of patronage from parties. Sure, parties will still determine who goes on the list in their name, but it’s entirely up to the electorate which, if any, of their candidates are returned.

So, as an exercise in futility, I decided to see what would happen with both 2010 and 2015 election results using STV. It’s an exercise in futility for a number of reasons: the main one is that people will vote differently when they can express a preference, as tactical voting is minimised. But I thought it would be interesting, nonetheless.

The first thing to do would be to try to split the country into constituencies that returned 3, 4 or 5 MPs. I decided I’d use current constituencies as the base. Again, this is another area where reality would diverge from this projection – as the boundary commissioners would be able to (and probably would) apportion seats differently within local areas. I also decided that I would leave Northern Ireland alone. One change I did make was to set my Highlands and Islands constituency to return 5 MPs, even though it was made of 6 existing constituencies. There will be a number of ways to aggregate the seats but, where a county or city could be divided into more than one region, I tried to use district boundaries or natural features – for example, using the River Clyde to split Glasgow into two.

There remain some issues, particularly for Wales where the number of electors per MP is a lot lower than the UK average – for example, keeping Gwynedd as a single entity means that it becomes the smallest constituency by far, and boundary commissioners would probably merge it with Clwyd to create fewer, bigger constituencies. At some point I may revisit this analysis to see if it’s possible to resolve some of the electorate issues.

The next thing was to total up the votes for each party within each of my larger constituencies. I decided I’d use the d’Hondt mechanism to allocate seats within each constituency. Again, not ideal, but given the lack of any detailed “how would you actually vote” surveys, it’s the best I could do.

In summary, my results diverge from the Electoral Reform Society’s ones. Subject to all the caveats, the results would have been:

Party 2010 2015
Conservative 264 298
Labour 205 236
Liberal Democrat 150 18
SNP 9 35
Plaid Cymru 2 2
Speaker 1 1
Green none 2
UKIP none 39

There are some interesting, if predictable, changes. For example, rather than the Conservatives only having 1 MP in Scotland in both 2010 and 2015, this model gives them 8 in 2010 and 5 in 2015. UKIP gain single MPs in lots of eastern Conservative and urban Labour areas.

The upshot would have been, for 2010, the Liberal Democrats would have had a real choice between Labour and Conservatives as coalition partners, and, for 2015, the most likely result would have been a Conservative / UKIP coalition or Conservative minority government with UKIP support.

I would also argue that this result is more representative of the country’s views in both 2010 and 2015.

The raw data is attached for you to play should you really wish to – PR Estimate – May 2015


  1. I was doing very similar for elections from 1983 onwards. STV based on 3 to 5 seaters, with the 3 single-member island constituencies. Results I had were

    1983: Con 287, Lab 172, Lib 96, SDP 71, NI 17, SNP 5, PC 2

    1987: Con 290, Lab 198, Lib 90, SDP 47, NI 17, SNP 6, PC 2

    1992: Con 291, Lab 233, LD 92, NI 17, SNP 16, PC 2

    I had a bias towards 3 seaters when doing it, as I think that would be the most likely compromise as in Ireland. I never got around to finishing 1997.

  2. […] in 2015 and 2017, I’ve done a little thought exercise about what would have potentially happened in the recent […]

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