How will Scotland's voters impact on the next election?

Anyone who hoped that the “no” victory north of the border would quickly move Scotland out of the headlines must be bitterly disappointed. Two linked questions will ensure that it will continue to remain in the news and affect what happens at Westminster. The first, of which this week’s report of the Smith commission provides the latest instalment, is, what new powers will Holyrood gain—and how will this affect the arguments about “English votes for English laws?”

This blog addresses the second question: what impact will Scotland’s voters have on the outcome of the next election? A recent YouGov/Times poll showed the SNP 16 points ahead of Labour when people are asked their Westminster voting intention. An Ipsos-Mori poll reported an even larger lead. The two polls led to talk of a Labour meltdown next May and the end of any chance of Labour emerging as the largest party across the UK as a whole.

The conventional way to assess the prospects is to assume a uniform swing. That is, we convert poll numbers into a change in the percentage share for each party since the last election, and apply those changes to each constituency. The following table provides uniform swing projections to different Lab-SNP swings, ranging from a repeat of the 2010 result, when Labour enjoyed a 22 per cent lead over the SNP, to the opposite—a 22 per cent SNP lead:

In other words, there is a bias in Labour’s favour, in the sense that Labour could lag the SNP in votes but still have more seats. And that is not simply a theoretical calculation: in the 2007 elections to Holyrood, the SNP edged ahead of Labour in votes, 33-32 per cent, but won fewer constituencies: 21-37. (The SNP ended up as the largest party overall because the regional top-up system redressed the imbalance.)

So is Labour’s terror overdone? No, and for two reasons. The first is that SNP is currently on course for a substantial win—and the pro-Labour bias disappears once the SNP’s percentage lead in the popular vote reaches double digits.

The second is more technical. Uniform swings never happen. Swings vary from seat to seat, often quite significantly. However, uniform swing calculations often provide a good guide to the final outcome on the principle of swings and roundabouts: Some seats that should change hands on a uniform swing end up as “no change”—while other seats do topple on above-average swings. In other words, uniform swing projections can work in terms of overall numbers, even if individual seats buck the trend.

However this depends on the swings roughly equalling the roundabouts. Sometimes they don’t. In the 2005 general election the Conservatives gained more Labour seats across Britain than they “should” have done, given the overall 3 per cent swing. The main reason was that, while Labour was defending just 23 seats that would fall to the Tories on a 3 per cent swing, it was defending as many as 45 seats where the swing the Tories needed was 3-6 per cent. This meant that random variation either side of the overall 3 per cent swing meant that the extra seats Labour lost on slightly above-average swings exceeded the number of seats it clung onto on below-average swings.

Something similar could happen next May in Scotland. If SNP and Labour are level in terms of votes, there are many more Labour seats that could fall on slightly above-average swings than the party is likely to retain on below-average swings.

So: how many seats will the SNP actually gain? I don’t know. Once again, my ambition at this stage can be no greater than to raise uncertainty about the outcome of next year’s general election to a higher level of sophistication.