by Stephen Fisher.

The SNP went into yesterday’s Scottish Parliament elections defending a majority of 9, and with many expecting that they would manage to achieve another majority on the strength of their performance in the constituencies alone.

Indeed the SNP managed to improve on their 45.4% share of the constituency vote in 2011, with 46.5% this year. Moreover, Labour dropped from 31.7% in 2011 to 22.6%. This represents a Lab to SNP swing of 5%, which should have been enough for them to take 13 seats from Labour. That number, on top of the 53 constituencies they won in 2011 would have yielded the SNP 66 constituencies on a uniform swing, a majority of 3 before looking at the regional list seats.

What went wrong for the SNP then? They did manage to pick up 11 seats from the SNP, just short of the 13 expected from uniform swing from Labour. But they were not quite the ones uniform swing predicted. Labour’s former leader, Iain Gray, managed to hold on to what was formerly their most vulnerable seat. They also held on to Dumbarton despite the swing. Compensating for this, Labour lost Glasgow Provan and Coatbridge & Chryston with bigger than average Labour to SNP swings.

What hurt the SNP in the constituency contests were loses to the Liberal Democrats and especially the Conservatives. The both parties took 2 seats each directly from the SNP seats, but the Tories also took 2 Labour seats that would otherwise have been expected to fall to the SNP. In addition both these parties successfully defended the seats they previously held, even though three of them (2 Conservative and 1 Liberal Democrat) were nearly lost to the SNP in 2011. Further analysis is needed but it does look like there was some anti-SNP tactical voting going on in some of the seats that the Tories and Lib Dems won. It is also the case that the two party leaders Ruth Davidson and Willie Rennie did very well, both coincidentally increasing their party’s vote shares by 15.4 points.

Of course, the electoral system for the Scottish Parliament is an additional member system, with regional top-up seats allocated by D’Hondt. So maybe some of the SNP’s short-comings in the constituencies might have been compensated for by additional list seats.

But compensation cuts both ways. Overall the SNP were up 6 constituencies, and these gains resulted in fewer list seats. For example, in Central Scotland the 3 constituency gains were compensated for by 3 losses on the list. Similarly in the 2 SNP constituency gains were offset by 2 losses in the West of Scotland

Overall, the SNP share of the list vote dropped by 2.3%. So to the extent that the electoral system is expected to be proportional overall, and it is commonly referred to as proportional, then we should expect the SNP to have lost seats overall.

In 2011 the SNP won 53.5% of the seats on 44.0% of the list vote. Yesterday they won 48.8% of the seats (63 in total) on 41.7% of the vote. So the system clearly treated the SNP more favourably than pure proportional representation but not quite as favourably as in 2011.

Part of the reason for the deviation of the system from proportionality is that it is possible for a party to be so over-represented in a region’s constituencies relative to the list vote that it is hard to win list seats. Thus the SNP’s 2 constituency loses in Lothian were not compensated for on the list despite just a 2.9 point drop in their list vote in the region.

In other regions they lost list seats at the same time as their regional tally of constituencies stayed constant or dropped. These include the North East (-8.1%), Mid Scotland and Fife (-3.9%), and the South (-2.7%). In the last two of these it might reasonably be considered unfortunate to lose a seat on such a small drop in vote share when the threshold is around 5%. But it is also the case that the D’Hondt system was generous to the SNP in 2011.

Overall then, it is no great surprise that the SNP lost their majority given that they only achieved 41.7% of the list vote.