Uniform swing 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.

Conclusions

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.

UPDATE: See my 2010 uniform swing analysis here.

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.