The Lib Dem collapse in Scotland

Here's something interesting. Normally the best prediction (or at least, the least flawed prediction) of how votes translate into seats is a uniform swing projection - that is, if a party has increased it's national share of the vote by 5 percentage points, you add five percentage points to the share it gets in each seat, and vice-versa if it loses support.

Broadly speaking, uniform national swing has been a pretty good predictor of elections - or at least, a good starting point to analyse elections and where parties have done better or worse than average. However, it is mathematically inelegant, particularly when it comes to the extremes. Say a party loses 5 percentage points in its national support - what happens in a seat where they only had 4% at the last election? On a UNS model they'd get minus 1% support, which is clearly impossible. Generally speaking though UNS doing odd things to parties with minimal support doesn't matter, as it is all about the marginal seats and predicting overall seat numbers, how well it models changes in support in safe seats is irrelevant.

However, it has been playing on my mind how it will work with the Liberal Democrats at the next election if they maintain their present low levels of support. How would it cope with a drastic collapse in support for a party? It varies from pollster to pollster, but roughly speaking the Lib Dems have lost about half their 2010 vote, about 12 points or so. To start with there were 57 seats where the Lib Dems got less than 12% support in 2010, they can't lose 12% in those. Equally, if their vote did collapse to what extent would their sitting MPs be insulated from the fall?

The Scottish Parliamentary election gives us a chance to see. Below is a scatter chart of the Lib Dem performance in 2011 - plotting the change in the Lib Dem share of the vote in each seat against the share of the vote they recieved in 2007. Gold dots are those seats that were notionally or actually held by the Lib Dems in 2007, blue dots are non-LD seats.

The green line is what we would expect to see if there was a uniform swing - the Lib Dem vote falling by 8% in each seat. The red line is what we'd get if the Lib Dem vote fell proportionally to their support in 2007 - basically if they lost half their support in each seat. The actual distribution of dots is clearly closer to the proportional line than the uniform swing. If this was repeated at a GB general election then the Liberal Democrats would do even worse than a uniform swing would predict.

On the other hand, look at the distribution of the blue and gold dots - in seats where the Lib Dems had incumbency the Lib Dems did better than a proportional loss would have suggested (and they do worse than than this in seats without incumbency) - while the Lib Dems did end up losing all their mainland seats in Scotland, they did actually perform somewhat better in the seats they held... just not by enough to save them.

I wouldn't presume to make models or predictions about what would happen to the Lib Dems at a general election on this basis... just that UNS national swing may not be a very good predictor if the Lib Dem vote does remain in dire straights at the next general election.