Uniform versus proportional swing: which is best?

Presenting a new analysis of the merits of the two main ways of converting party vote shares in to seat number projections:

Although uniform national swing (UNS) calculations are widely used to extrapolate likely seat numbers from party’s national ratings and have the merit of simplicity, they are not without their critics. For example, in November ConservativeHome ran a piece from Quentin Langley which said,

That it [UNS] continues to be used when a superior system was developed more than three decades ago is a testament to incompetence in the media…

The Proportional Loss Hypothesis (PLH) developed by Dr Gordon Reece of Bristol University is a much more useful and accurate

Although as Quentin Langley has pointed out there was evidence at the time of Gordon Reece’s work in the 1970s that his method was superior, that has not been an uncontroversial view. For example, the Butler & Kavanagh book on the 1979 general election, The British General Election of 1979, concludes that uniform swing was superior at predicting results in that election than proportional swing and had also been at previous general elections.

Regardless though of the 1970s evidence, there have been sufficient changes in British politics since then that what worked best then does not necessarily work best any more.

I have therefore re-run the last three general elections, using both uniform and proportional swing calculations to see how the two perform. For each election I have applied the known swing since the previous election to that previous election’s results and seen how those predicted results compare with the actual results.

2005 general election

Conservatives: 197 seats. UNS prediction: 184 (-13). Proportional prediction: 181 (-16)
Labour: 355 seats. UNS: 369 (+14). Proportional: 371 (+16)
Liberal Democrat: 62 seats. UNS: 62 (+/-0). Proportional: 68 (+6)

Proportional swing is consistently slightly less accurate than uniform swing.

2001 general election

Conservatives: 166 seats. UNS prediction: 181 (+15). Proportional prediction: 177 (+11)
Labour: 412 seats. UNS: 402 (-10). Proportional: 401 (-11)
Liberal Democrat: 52 seats. UNS: 47 (-5). Proportional: 51 (-1)

Proportional swing is slightly more accurate than uniform swing.

1997 general election

Conservatives: 165 seats. UNS prediction: 207 (+42). Proportional prediction: 207 (+42)
Labour: 418 seats. UNS: 395 (-23). Proportional: 394 (-24)
Liberal Democrat: 46 seats. UNS: 28 (-18). Proportional: 29 (-17)

Proportional and uniform swing perform the same.


There is no evidence from this data that proportional swing calculations are superior to uniform swing calculations.

Although UNS projections from opinion polls are often used to predict majorities to the nearest seat, in addition to the margin of error on the poll result there is a consistent error in the majority predicted by UNS or proportional swing calculations. On average, the majority predicted by UNS is out by over 30 seats, though there is no consistent pattern to the error.

In general elections of relatively little change (2001 and 2005), both are fairly good predictors, though it should be remembered that on the historical record there is a large enough margin of error to be significant not just in knife-edge elections but also those that are moderately close.

Across the three elections there is a modest trend of the Conservatives improving their actual result compared to swing projections and Labour slipping.

Finally, for the Liberal Democrats the accuracy of the predictions is mixed. Whilst both UNS and proportional projections get close in 2001 and 2005 they were significantly wrong in 1997. If the Liberal Democrats are making significant inroads in the governing party’s support in a set of winnable seats in 2010 as in 1997, then the predictions may again be significantly off.

Calculations details

  • Electoral data taken from Pippa Norris’s British Parliamentary Constituency Databases http://www.hks.harvard.edu/fs/pnorris/Data/Data.htm
  • Calculations have been carried out across Great Britain; i.e. excluding Northern Ireland.
  • Calculations have been based on GB-wide figures; i.e. without any regional breakdown. This is because published poll results do not give reliable regional or national breakdowns and this, combined with the absence of regular Wales-wide polling data, means any attempt to project from poll results to seat numbers has to be done on a GB-wide basis.
  • Calculations exclude the Speaker seeking re-election from party totals as well as seats where the election was postponed due to death of a candidate.

UPDATE: Andy Cooke has subsequently done an analysis comparing UNS over several elections, including looking at how UNS predictions based on opinion polls would have fared.

UPDATE 2: This academic article looks at the reasons why uniform swing may work better than proportional swing.

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This entry was posted in Polls.


  • interesting but not sure what conclusion to make apart from both systems are only any good the final prediction.

    the son of PoliticalBetting.com owner has come up with a third system, which although untested seems to address some of the issues with UNS.

    more info here http://www.resolversystems.com/election2010/

  • There is a new posting on http://www1.politicalbetting.com/ It shows that swings are mostly between Labour and LibDem voters, and with Labour behind in the polls I can see a danger of a large swing to Brown very near to the election.

    I can not understand that why the LibDem % is so low in the polls at present, and think it show be about 22%. Any ideas?

    Would replacing Brown be bad news for Clegg?
    Thanks to Ryans on a previous thread for highlighting the detailed finding in the week’s first YouGov poll on the party split when respondents were asked if they would be more or less likely to vote Labour if Brown was replaced.

    Normally I think we should be quite sceptical about such questions and I don’t think we should read too much into the scale of potential switching. But one thing stands out from the numbers – that 27% of Lib Dem voters said they would be more likely to vote Labour if it had a different leader.

    What makes this segment so important is that the LD-LAB cross-over could be the key factor that decides whether there is a Tory majority or not.

    For in almost all polls from all the firms the Tories are pretty solid on 40 – 42%. At the same time the LD-LAB aggregate is staying remarkably constant in the 45 – 49% range – it’s how that is splitting that is driving the size of the Labour deficit.

    So when Labour is up the Lib Dems are down and vice versa. Thus anything that could move more Lib Dems to supporting Labour has to be taken seriously.

    Taking YouGov’s 27% LD proportion then that would mean a 4 point switch from Clegg’s party to Labour. I don’t think it would be anything like that but 2% could make a dramatic difference in terms of seats gained and lost.

    There’s also the factor that we’ve looked at many times of “tactical unwind” – what happens when electors revert to their main allegiance after at previous elections voting for the party in their constituency most likely to stop, generally, the Tories.

    One survey in 2005 suggested that one in ten of all votes for Labour were tactical – mostly, one would assume, in the marginals. So if some of those slip back then that could make it easier for the Tories in key targets.

    Maybe because more people are at home because of the weather the YouGov poll sample was pretty large and there were 564 LD voters.

    Mike Smithson

  • I really wouldn’t take anything posted on politicalbetting.com seriously if I were you. PB.com is full of innumerate and quite mad posters.

    Mike Smithson thinks he is some sort of political analyst FFS.

  • I think that’s a bit unfair to Mike Smithson, Colin. You can’t really dismiss someone who makes serious money out of betting on politics in that way. I quite agree about many of the posters though – the site seems to have been colonised by no-nothing Tories who contribute nothing in the way of political expertise, which is why I rarely read the discussion any more.

  • I did my PhD thesis back in the 1970s using regression analysis to predict the Liberal vote. In those days it meant submitting trays of punched cards to the university’s central computer along with the subroutine one had written. The next day it would come back as a pile of zigzagged computer paper, usually very few pages because I had made some mistake. It took me five years to do the analysis and two years to write it up. These days the analysis could probably be done in a few weeks, although the data collection might take a while still. Good luck Richard!

  • Richard: I think the really interesting approach would be to do regression analysis on who votes, so that we can acvoid wasting effort on people who don’t. If any local party in a held seat has an ears officer who can extract the data into a more general programme (excel) then I would delighted to talk to them. tim [at] leunig [dot] net. If we can work out who not to canvas, we could deploy that effort onto more useful things. But I agree, regression analysis with no priors is the way forward for your question

  • Quentin Langley 5th Feb '10 - 8:05am

    Good piece, Mark, and thanks for the credit and link.

    Your point that we need to consider the combined errors of both polls and projections is especially important. Note that in the 2005 election – one rogue poll in the FT aside – the actual Conservative vote was in line with the highest projections and the actual Labour vote in line with the lowest projections. I believe this pattern was similar over the last four general elections – two in which the Conservatives were in government and two in which Labour was.

    LibDem performance is especially difficult to predict. Geoffrey Payne raises the point of local factors, which include, but are not limited to, tactical voting. Consider also that the standard margin of error in opinion polls is a larger proportion of 18% than it is of 42%. LibDem candidates are also most likely to be competitive in seats that are either three or four way or in seats where the vote of the larger parties has been heavily squeezed. The Uniform Swing Hypothesis performs particularly badly in both these instances. How can you possibly project a uniform -10% for Labour onto, say, North Cornwall?

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