The 2015 election under 3-4 member Single Transferable Vote

Posted by on May 18, 2015 in Articles, Blog | 21 comments

The 2015 election under 3-4 member Single Transferable Vote

When I worked for the Electoral Reform Society I rather enjoyed getting paid for working out what election outcomes might have been under alternative electoral systems. In these straitened times, I seem to be doing it for free as a sort of loss-leader, but this I guess is the way the economy in general is going, so if anyone wants to commission fuller workings, please get in touch…

I am well aware that modelling the consequences of different electoral systems is at best an approximate art. Parties behave differently, in the number of candidates they stand and the way in which they target their efforts. One also has to make up imaginary constituencies or regions to serve as electoral units, which again can affect voting behaviour. Voters also think differently – they are relieved of the tactical considerations that affect voting in First Past the Post (FPTP) and this makes the ‘squeeze’ message (only party X can defeat party Y here) much less effective. Incidentally, anyone who thinks FPTP is simple should have a look at this Daily Mash article…

The model result here is using the Single Transferable Vote (STV) in constituencies returning 3 or 4 MPs each. This if the form of proportional representation introduced for Scottish local elections in 2007 and used for all Northern Ireland elections except Westminster. It is pretty simple from the voter’s point of view – you rank the candidates in order of preference, including quite often the ability to choose between more than one candidate of a larger party – and the (quite elaborate) counting system means that few votes fail to have an influence on the outcome. 3-4 MPs per constituency is a pretty low-end version of proportionality; the larger the number of people elected from the constituency, the more chance there is for smaller parties to gain seats and the more the result will resemble the votes cast. I was somewhat surprised with how proportional even this limited version of PR would have been in 2015.

The STV constituencies are illustrated in the coloured map. The colour scheme is entirely arbitrary and is there solely to differentiate the constituencies from each other. Orkney & Shetland and na h-Eileanan an Iar are treated as single-member constituencies. I have added existing constituencies together, but if this reform ever happened new constituencies would surely be created based on more coherent units.

STV constituencies


(ADDED PARAGRAPH AFTER EDIT) One also has to consider the impact of second and lower preferences on the result. Real-world experience suggests that preference flows are neither as complete nor as clear as is often implied by such models, so this has been deliberately cautious with assuming much about preferences. Broadly, for the cognoscenti of STV, seats are awarded for every whole quota’s worth of support for a party, and then for anyone with more than 80 per cent of a quota. Preferences flows among the remainder are assumed to have small net effects – most Greens in England and Wales going to Labour, in Scotland to SNP; a weak but present unionist preference ordering in Scotland; UKIP votes splitting weakly Conservative in Con/Lab choices and strongly Conservative in Con/LD choices. There may be room to revisit the assumptions when further study has revealed more about preference orders, but the effect of different assumptions is pretty small as most seats are awarded either on whole quotas or large shares of quota that would require implausibly strong adverse transfer patterns to overcome.

The model outcome in seats nationally would be Conservative 280, Labour 241, UKIP 38, SNP 37, Lib Dem 29, Plaid Cymru 4, Green 2, the 18 Northern Ireland seats and the Speaker. In proportions of the whole House this would give the Conservatives 43 per cent of seats for 37 per cent of the vote, Labour 37 per cent of seats for 30 per cent of the vote, UKIP 6 per cent of seats for 13 per cent of the vote, Lib Dem 4 per cent of seats for 8 per cent of the vote and SNP 6 per cent of seats for 5 per cent of the vote. 3-4 member STV therefore would have a significant bonus for the leading two parties (and for the SNP in Scotland) while giving adequate representation to the Lib Dems and UKIP who were ill-served by FPTP. It would not help the Greens all that much, but this may be masked by the greater willingness of voters to support the Greens in a reformed system. One perhaps significant finding is that, surprisingly, UKIP would not elect any MPs from the South West on this model despite the region being one of its stronger areas in many past elections. It may be that there was a late switch from UKIP to Conservative by many voters in this region in particular, and that this would not necessarily happen if the electoral system were different.

The effect of even a modest degree of proportionality in the electoral system on the main parties would be to redistribute their support around a bit – the metropolitan areas would not be devoid of interest to the Conservatives, and Labour would have more representation (commensurate with its vote) in southern England.

When I first posted the headline number on Twitter, someone asked me ‘what sort of government would that produce’? A fair question. My guess would be a Conservative minority with occasional support from the Ulster Unionists (DUP and UUP), UKIP and the Lib Dems, and a measure of passive toleration from the SNP. It might be an easier show to keep on the road than a triumphalist yet divided Conservative majority, but that is even more speculative than any of these calculations.STV table


  1. Could you post your methodology and assumptions and an example of one of your calculations so that we can assess the validity of your numbers. I did a similar exercise a while ago and got nothing like yor level of MPs for smaller parties (Lib Dem or others).

  2. Excellent piece of work – though if that had been the outcome, it’s the sort of outcome that leads to countries running screaming from PR towards something else (as both France and Italy have done). Where I would question your assumptions is how far STV would allow especially Green voters, and perhaps UKIP ones, who were forced to choose a major party to put their real choice first, safe in the knowledge that it won’t be allowing their real enemy in.

  3. People will certainly change the way they vote depending on the electoral system being used.
    This doesn’t detract from this piece of work. It shows that STV can cope with our multi party system far better than FPTP does.

    I note that this model shows that STV is not a proportional system.

    SNP would do well with 37 seats with 4.7% of the vote while the
    Green Party voters would be disappointed. 2 seats – with 3.8% of the vote.
    Lib Dems get 29 seats from 7.9% of the vote.
    The Northern Ireland parties also stand out as far from PR.

    If we justify a switch to a new electoral system for the sake of fairness, that every vote is equal, these results suggest we should look for a PR system rather than a preferential system, and also that the threshold for representation should be low enough to accommodate the Green Party with its current level of support.

  4. Very interesting! Why did you use only 3- and 4-seat constituencies, and no 5-seat ones? Do you think there would be much difference if 5-seat constituencies were used as well?

  5. Thanks for the comments.

    NN: I decided to use 3-4 member STV as it’s the pattern used in Scottish local government and it’s simpler to model – one has to make fewer assumptions about transfers than with larger district magnitude (seats per constituency). There are one or two areas where 5 members would have worked better and I might – when I have a moment – go back and do a model based on say 3-6 with a presumption of 4-5. I expect it would be a bit more proportional, particularly for the smaller parties.

    Stephen, Ender’s Shadow: True enough – STV isn’t party-proportional at these district magnitudes, although every time I do these models I’m surprised by how proportional it is for the major parties. While I think it’s true that Greens would do better in first preferences than in FPTP votes, the threshold is still very high. If I were choosing an electoral system it would probably be STV with a top-up element so that parties with say 5-10 per cent of the vote spread evenly would get more proportional representation in parliament.

    David: The model constituencies are as in the map. FPTP votes cast are regarded as STV first preferences (I am well aware that they would differ, but there’s merit in making minimal assumptions in this and seeing what happens). Preference transfers are as noted in the paragraph above. In most cases allocating to parties with whole quotas or nearly whole quotas is enough to award all the seats. There are only about 20-30 calls for the last seat that I think are at all debatable.

  6. Can you estimate what the proportion of wasted votes would have fallen to under STV?
    Under FPtP I believe it was about 75%.

  7. I see you’ve allowed for 2 single member constituencies with The Northern Isles and Orkney and Shetland. I’d probably also allow for a single 2 member constituency for the Isle of Wight.

  8. Alex – thanks. Reasonable suggestion on Isle of Wight – wonder what the other seat might have been… UKIP? Using classic ERS definition of wasted vote, probably only about 10-20 per cent wastage.

  9. Scotland is very much centre stage at the moment, and the FPTP election result was fairly extreme. It seems to me important to understand the basis on which an electoral system can produce a fair result in such circumstances.

    Lewis, you mention the question of district magnitude in relation to proportionality. If you look again at this it would be interesting to know how you would alter the model so that STV can give a proportional result in Scotland.
    Would redrawing the constituency boundaries help? I suppose this might be seen as partisan and politically vindictive.

  10. Thanks Lewis, However I do think a 3-5 constituency model would be better however, it would give the Tories more of a chance in places like Liverpool, and give them a reason to care.
    The way I’d work it is you’d have a standard of four and rise to 5 or drop to three when needed to keep within major geographic of socially historic boundaries.

    The Greens prefer an additional member system however I don’t think they realise that election thresholds may prove even more of a barrier, the Irish Greens first won a seat in Dáil Éireann with 1.5% of the national vote.

  11. Stephen, Alex – I had a look at what might have been the implications of going up to a larger district magnitude, workings for Scotland only at this point. The seats were uniform 4-5 member other than the two island groups, but the outcome was really not very different – SNP 34, Lab 14, Con 7, LD 4 (i.e. two extra Con and one extra LD seat at the expense of the SNP). There’s still a winner’s bonus, although it’s not massive, and the minority (rather than second place) parties gain most. So probably preferable from a proportional point of view although some of the constituencies are geographically large and diverse (e.g. Dundee, Angus and Perthshire all in a 5-member seat).

  12. Why not have a 3-5 model?

    Anyway this is interesting stuff, will you be doing a projection of what AV would likely have done? I also wonder who would have come out on top in the national Two-party-preferred result.

  13. Unlike your report The ERS report today does not showing the Lib Dems performing better relative to vote share than UKIP, (29-38) which is exactly what I would expect it to be like, it seems to show the opposite(26-54). Is this likely because they’re using more up to date preference data? What preference data did you have?

    • I’m not sure what if any assumptions the ERS model made about preferences, but I note that their model was 2-5 rather than a strict 3-4 seat model and this may be the source of the difference – a party with an evenly spread 15 per cent of the vote or thereabouts will miss out a lot when you have a 3-member seat, while it will almost certainly get one elected if you have a 5-member seat. I think both the ERS model and mine were parsimonious in attributing effects to transfers for the reasons I’ve already discussed. It really makes remarkably little difference unless you make unrealistic assumptions about unanimity and usage.

      • Well, as it was only up to 5 seats, I wouldn’t have thought it would quite have made that much of a difference.

        My initial though to your result was that the Lib Dems do OK at picking up preferences while UKIP are more likely to be not ranked at all by those who do not rank them first. However the Lib Dems unpopularity might mean that they also suffer from being actively not ranked.

        Notice the ERS only give 3 seats to Greens with 3.8% that’s half the 6 seats the Irish Greens got in 2002 with 3.8% and that was out of 150, so equivalent to 27 out of 650.

        Taking the real result then doing a poll to ask people if they voted tactically and what their preferences would be if they could rank candidates then trying to extrapolate what they think the result would be under STV from that, doesn’t really work.
        STV would cause a sea change in the way elections are run.

        Campaigning would be very different under STV, the Tories would make a big effort in Liverpool for instance. We can’t really know what would really happen.

  14. How would you design an STV system with a top-up element?

    • An interesting question (or interesting to me anyway).There are two broad ways of doing it:
      1) Regard the first preference vote share as being indicative of party proportionality, and using MMP type calculations by region or nation to award top-up seats, probably to the candidates of that party with the highest pre-exclusion vote (although there are other ways of picking top-up members). This is by analogy with Malta, which has a national top-up allocation in situations where the plurality of FP votes and seats is reversed.
      2) I did once devise a rather intricate system using the pool of votes for the last candidates not elected, which got around the possible problem that voters for small parties get two bites of the cherry if they affect the STV count and also elect someone on the top up. The wonderfully complex and representative Danish electoral system has compensation tiers from small multi-member PR districts.

      • Your system number 2 is interesting. Can I find a more detailed description of it somewhere?

        A third way would be to use a second vote (a “party vote” like in the Scottish, Welsh and German systems, but preferably without any use of party lists). I found a proposal for such a system here:

        • I ran a model using this system (AV & d’Hondt)

          For example, the 10 Birmingham constituencies are replaced by 5 amalgamated constituencies plus 5 party-list MPs.

          In general, it helped the smaller parties (fairly similar to Lewis’ figures), but single-constituency mavericks (Lucas of the Greens, Galloway) lose out.

    • There should be no need for a top up under STV, most countries with PR have an election threshold of 3-5% to gain seats in parliament, this is to try and block out extremists and fringe parties but it also blocks out more reasonable small parties. STV has no such nation wide threshold.
      On paper having to meet the droop threshold of 25-16.6% in a seat you might think would lock out smaller parties but in reality it’s not been the case, the preferential nature of the system is actually quite kind to them.
      In Ireland reasonable smaller parties do tend to win seats despite only getting a tiny percentage of the vote nation wide, the Irish greens did it with 1.5% of the vote, no where near enough for a seat under most countries’ PR systems, while the preferential nature of STV still locks out the hard right and extremists.

  15. The HG Wells formula was against attempts to enfeeble effective voting, which was: proportional representation by the single transferable vote with large constituencies.

    I think the only real reason behind small STV constituencies is to appease the Tory-Labour duopoly. But the Plant report made it quite clear that at the outside they wouldnt tolerate STV in more than one or two member constituencies. And in their terror of a genuine election recommended any system but STV for various UK elections.

    This puts STV/PR at a wholly unnecessary disadvantage to list systems or additional list systems that use large regional constituencies.

    I have two e-books on electoral reform and research.
    Free from Smashwords:
    Peace-making Power-sharing:

    Scientific Method of Elections:

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