Mathematics Politics

What would Parliament under STV look like?

This image shows what an STV-elected House of Commons would look like.

As I said in my first posts, I am a believer in the Single Transferable Vote: it devolves power to the people, is preferential, and is proportional. I’m voting for AV as it does the first two, but I really want the third as well. But we can’t win them all. Indeed, as recent polls show, the No campaign — which has been running mostly on the “you’re too thick to count to three” message — may scupper the chances for even AV.

The Electoral Reform Society did some research into this, but I found the results somewhat… strange. In Brighton, which has a strong Green Party presence, no Green candidate was elected under the ERS’s calculations. So I decided for myself, in my free time, to do a simulation for myself. The rules I set myself by were to:

The rules

  • A limit of 600 MPs
  • Apportionment by country, region, and constituency in turn, using the harmonic mean of the lower and upper integer values of a division’s share by population. The number of seats apportioned depended on comparing the quota with the mean.
  • Any left-over seats at each stage are apportioned to the “best runner up”.
  • A minimum of 3 and maximum of 6 seats per constituency, except the Isle of Wight, the Northern Islands, and Eilean Sarr.
  • No dividing local government areas except Birmingham and Leeds, which are split into two constituencies.
  • All constituencies are to be contiguous.

Because I’m one man, I didn’t run the election on a constituency basis; I ran it on a regional basis. As I was effectively creating new constituencies, to run it on constituency basis I would have had to find the results by ward, which I would have had considerable difficulty doing so. I also made the general assumptions about voter preference which, I admit, I took some liberties in running those elections:

  • Representatives are elected regionally using “pure” PR, with the Saint-Lague method.
  • Voters transferred their votes to candidates of the same party wherever possible. Hence if the quota was 20% and the Labour Party got a vote of 45%, two MPs would be elected.
  • Tactical voting, taken on average over a region, was minimal and did not affect the election of a representative.
  • After electing representatives, each party has a fractional value of the quota (in the above case, Labour would have 0.25). Unallocated seats are filled by transferring preferences until all unallocated seats are filled. Once a party reaches quota again, they receive a new fractional value.
  • The British National Party and Traditional Unionist Voice, as “extremist” parties, are penalised, by being eliminated for being second last when allocating unfilled seats.

I am fully aware that these are fudges designed to make my job easier. I’m not saying that my work is better than the ERS’s work either.


Using the above rules, we get 147 constituencies. Most constituencies are within “acceptable” limits for size; the only deviations from the mean are the three constituencies listed above. However, linking those three to the mainland would be problematic in itself.


By running the election for 2010, we get the following representation in a 600-member Commons.

  • Conservatives and Unionists: 219
  • Labour: 180
  • Liberal Democrats: 140
  • UK Independence Party: 17
  • Scottish National Party: 10
  • British National Party: 8
  • The Green Party: 5
  • Sinn Fein: 5
  • Democratic Unionist Party: 4
  • Social Democratic and Labour Party: 3
  • Plaid Cymru: 3
  • Alliance Party: 1
  • Traditional Unionist Voice: 1
  • Sylvia Hermon: 1
  • Kidderminster Hospital Health Concern: 1
  • RESPECT The Unity Coalition: 1
  • Speaker John Bercow: 1

More detailed results are available here. Interesting results include UKIP picking up seats in every region, George Galloway holding onto his seat in East London, and the Greens and BNP picking up quite a few seats (most likely for the Greens: Southwark and Lewisham, Leeds West, Brighton and Worthing, South Gloucestershire and Stroud, and South and East Norfolk; for the BNP: Calderdale and Kirklees, Blackburn and Burnley, Barnsley and Rotherham, South Derbyshire, Stoke and Newcastle, Epping Forest, Dagenham and Havering, and possibly Teesside).

Changing the rest to STV

Even if the referendum on Thursday fails, we’ll probably get a proportionally elected Lords. Bringing it in is in the Coalition Agreement and in both manifestos. How would an elected Lords look like?

Well, we have to change the name. The hypothetical Senate should be elected by STV by halves; this prevents both chambers being controlled by a party that is popular for one year and unpopular for three or four. This does require larger constituencies. Using the above constituencies, I’ve created twenty-three Senate constituencies:

  • North East (6-7)
  • Manchester (6-7)
  • Cheshire and Merseyside (6-5)
  • Lancaster and Cumbria (5-4)
  • West Yorkshire and York (6-7)
  • North and South Yorkshire and Humberside (7-6)
  • Derbyshire and Nottingham (6-5)
  • Northamptonshire, Leicestershire, and Lincolnshire (5-6)
  • The West Midlands (6-7)
  • Birmingham and Wolverhampton (7-6)
  • Essex and Hertfordshire (7-7)
  • Bedfordshire, Cambridgeshire, and East Anglia (7-7)
  • Inner London (7-8)
  • North and East London (5-5)
  • West and South London (7-6)
  • Kent and East Sussex (5-5)
  • West Sussex and Surrey (6-5)
  • Hampshire and West Berkshire (6-5)
  • Chilterns (4-5)
  • South Coast (5-6)
  • West Country (7-7)
  • Highlands and Islands (5-5)
  • Central and South Scotland (8-7)

Another good idea would be council elections by STV. This already happens, in Scotland, and the Conservatives may be amenable to changing the rest as they’re on the receiving end of disproportionality (having only one councillor in Manchester, for example). As councils are often “hung”, there would be little change for most councils. We could also make moves to electing the devolved assemblies (and setting up regional or an English assembly) and European Parliament by STV too.

Looking forward: Election cycles after introduction

The problems with extrapolating FPTP results to STV is that FPTP skews results in favour of big parties and against small parties. We can see this in Australia, where their House elections (under AV) see less Green votes than Senate elections (under STV) at the same time. After a few election results, the Con-Lab-LD-UKIP-Green-BNP vote shares will probably go from 35-29-23-3-1-1 to, say, 27-22-19-12-7-3. Yes, the BNP could get more votes, but that’s democracy. Politics would be more consensual: instead of Labour over-spending and Conservative over-cutting, we’d have responsible spending and responsible cutting. And we won’t have people elected from England ruling a Scotland that never voted for them, or Scottish Labour using their clout to legislate against England. Nearly everyone will be represented in Parliament, as opposed to the small percentage of voters in safe seats and marginals.

Regardless of the result on Thursday, we need to keep the fight up for proportional representation. Even if the fight doesn’t take itself to the Commons sooner than a Yes result will, we need to keep pushing for PR for the Lords and for local government, and AV for mayoral elections. We’ve ignited the spectre of proportional representation in the vast public for the first time in years, and we need to make sure it doesn’t go out.

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