Proportionalising the results

I was curious to see how this election would have played out under a proportional representation system. We can’t easily guess what an STV result would have looked like, since it would involve very different voting dynamics – but we can make a rough guess at what would happen if we had used multi-member regional seats, similar to the regional section of the system in Scotland.

(Scotland, for those unfamiliar, has a mixed system – every person is in an individual constituency, where they cast a normal FPTP vote; they then cast a second vote to elect members from their region, which returns about half a dozen MSPs. Regional votes are counted in a moderately complicated way so as to benefit parties with lower local representation; it actually comes out pretty representative of overall vote-share.)

Let’s say we do away with local seats entirely, and implement simple voting in county-based seats, with as many members from that county as it gets under the current system. Because people only cast a single vote, their preferences are likely to be broadly similar to their preferences under FPTP, and so we can use the existing data from the past two elections… and why counties? Constituencies are already grouped to follow county boundaries, and it provides a reasonably natural way of dividing them up.

What would it look like? A handful of arbitrary examples (2005 results are using 2010 boundaries; seat allocation uses the nice simple D’Hondt method):


  • FPTP 2005 – 6 Con, 1 LD
  • PR 2005 – 3 Con, 2 Lab, 2 LD
  • FPTP 2010 – 6 Con, 1 LD
  • PR 2010 – 4 Con, 1 Lab, 2 LD


  • FPTP 2005 – 1 Con, 13 Lab, 1 LD
  • PR 2005 – 3 Con, 9 Lab, 3 LD
  • FPTP 2010 – 1 Con, 13 Lab, 1 LD
  • PR 2010 – 3 Con, 9 Lab, 3 LD


  • FPTP 2005 – 4 Con, 1 Lab, 1 LD
  • PR 2005 – 3 Con, 1 Lab, 2 LD
  • FPTP 2010 – 5 Con, 1 Lab
  • PR 2010 – 3 Con, 1 Lab, 2 LD


  • FPTP 2005 – 3 Con, 3 Lab
  • PR 2005 – 3 Con, 2 Lab, 1 LD
  • FPTP 2010 – 6 Con
  • PR 2010 – 3 Con, 2 Lab, 1 LD

That last one is perhaps the most interesting – under FPTP it swung wildly from 3-3 to 6-0, but under PR it remained a balanced 3-2-1.

Some open issues with this model, though, frivolous as it is –

a) To what extent are the figures we’re getting from FPTP data representative of tactical voting, not of true preferences? That would drive down the results of third & fourth parties in any given region, and boost the second-placed.

b) What’s the optimal size for a region, and how do we allocate them? My gut feeling is that around half a dozen members is approximately right – big enough to iron out local oddities, small enough not to be too unwieldy – but I’m not sure if this is based on anything in particular. (Seven-member seats mean that each has approximately 700,000 people in it – the same size as the average US congressional district)

c) Shouldn’t we be using STV in these regions anyway? (The answer to that one is: probably yes. But see above.)

5 thoughts on “Proportionalising the results”

  1. Counties, though, you get the problem that some of the unitary authorities are tiny (York, or Darlington, for instance). I suppose York would go back into North Yorkshire and Darlington into County Durham when the boundaries were rearranged.

    I did the same with the regions – which, admittedly, are too large for anything other than closed-list or AV+/FPTP+ to really work – and got (using 2005’s notional result for Thirsk and Malton, which should be close enough). Big winners are the Lib Dems (of course), the SNP, and the far right.
    Conservative 238 -68
    Labour 201 -57
    Liberal Democrat 152 +95
    UK Independence Party 15 +15
    Scottish National Party 12 +6
    British National Party 8 +8
    Sinn Fein 6 +1
    Democratic Unionist Party 5 -3
    Plaid Cymru 4 +1
    Social Democratic & Labour Party 3 +0
    Green 2 +1
    Alliance Party 1 +0
    Ulster Conservatives and Unionists – New Force 3 +3
    Independent Unionist 0 -1

  2. Yeah, in many cases you’d want to bundle the unitary authorities into a neigbouring (often traditional) county. Cambridgeshire figures above incorporate Peterborough, for example. Some of the Scottish ones would need quite vigorous grouping – you could stretch from Argyll to Caithness, with the Western Isles and Orkney & Shetland, and still need to swallow up Inverness to make a six-seat group.

    You get a similar problem at the other extreme – Manchester has 27 MPs across ten boroughs, West Midlands 29 across seven, and West Yorks 23 across five! And this is without even thinking of how to deal with London, which approaches the scale of an entire region in its own right.

    Doing it on this large a scale is going to benefit the smaller parties more – whether that’s intentional or not I leave as an exercise to the reader – but, in a more practical sense, it’s going to provide unwieldy lists. I suspect in terms of someone in a polling booth, you don’t want to bombard them with more than half a dozen names per party, especially since they’ll all run…

  3. Probably the guidance would need to be to aim for 5-8 seat constituencies, merging small unitaries into the nearest traditional county as you say, and then splitting the larger counties and unitaries into geographically sensible constituencies as happens now.

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