Is five seats the most that Cameron can hope for?

There has been much discussion on whether regional swings may provide a hidden bonus for the Tories at the next election. In particular, so the logic goes, the Tories are underperforming in Scotland, so they must be doing above average in England (and/or Wales.)

True enough, but how can we measure the differences, and calibrate any possible benefit? In truth we can’t, for the simple fact that regional poll breakdowns are based on samples of about 100 people – in statistical terms, garbage….

But in the absence of reliable poll data, we can still make reasonable hypotheses, based on quantifiable aspects of the electoral system, and previous experience.

The above graph of Labour’s battleground seats shows, in rank order, the number of marginal Labour seats where the Tories are second-placed to Labour. I have split the seats into those requiring up to a 5% swing, and those requiring up to a 10% swing. A 5% swing would surely see the Tories as the largest party, forming a minority government.

Notice the big difference in the sizes of the orange-coloured columns. In the North-East, no seats at all would fall on a 5% UNS, while in the East Midlands 11 seats would fall. Our own Nick Palmer’s place on the battleground is noted (NP on the graph). The red 10% bands broadly follow this pattern too (apart from the North West, which has a surplus of seats in the 5%-10% band)

What would be the optimum swing pattern for the Tories across the regions?

It should be intuitively obvious that to maximise their gains the Tories should hope for a relatively low swing in the North-East and a relatively high swing in the East Midlands, with swings rising across the graph from left to right. In other words, swing perfectly correlated to the number of marginal seats in each region. For example, in the North-East it makes no difference whether the Tories get a 5% swing, or no swing at all – no seats will fall, whereas in the marginal-rich East Midlands an extra 5% swing would deliver another 7 seats on top of the 11 UNS gains.

How likely is it the regions shown on the graph will magically line-up in ascending order of swing? Those familiar with permutations will realise the answer is 11!:1 due to chance alone.. (or about 1 chance in 40 million…..) In other words, so unlikely it’s laughable…

But, the swing would not have to be perfectly correlated for the Tories to derive some benefit….. So long as it was broadly increasing left to right – even if a few regions bucked the trend – the Tories might make some gains over and above UNS. How many? That is very difficult to answer algebraically – there are too many constraints and permutations. The method I have used is to run thousands of simulations, generating thousands of random regional swings, subject to differing levels of constraints.

What constraints? Well, not all swing patterns are equally likely. Despite regional differences, the nation still broadly moves as one. London is not going to swing 10% to the Tories while the North West swings 10% to Labour. Or even 5% in opposite directions. Such divergences have never occurred in a British General Election, and there is no evidence things are about to change dramatically.

Two common measures of dispersion are Range and Standard Deviation. Range is simply the gap between the highest and lowest regional swing, and standard deviation is an overall measure of how different the swings are from one another. If every region followed the UNS both the range and deviation would be 0, and there would be no regional seat bonuses. Here is a table of these statistics over recent elections.

One thing to notice is that the past two elections have been significantly more uniform than previous elections, with about half the range and standard deviation exhibited during the period 1987-97. Why that is I’m not sure, nor can I predict whether it will continue that way or reverse. I don’t have the stats prior to 1983, but the consensus is elections were relatively uniform until the 1980s.

The model uses the maximum range and standard deviation thus far exhibited in a British general election, with increments up to these levels. Thousands of random swings have been generated within these constraints, and the net seat difference summed across the regions. If ever there was a case of swings and roundabouts, this is it!

In all tests the average net bonus is close to zero, and 95% of results show a difference of less than plus or minus 6 to 11 seats, depending on the range and deviation selected. The higher the deviation and/or range the slightly larger the maximum potential bonus or penalty.

The 95% range of results can be interpreted as a confidence interval. In other words, only about once in every 80 years might we expect a party to obtain a regional swing differential in excess of 11 seats, and the odds indicate it will be considerably fewer. For example, John Curtice calculated that the Tories only obtained a 2 seat bonus in 2005. In 1992 Labour obtained a 5 seat bonus due to regional swings.

A political party clearly does not have the power to force the regions to swing in a way that best suits them. Such outcomes are determined by long-term trends, third-party performance, differential turnouts and a huge amount of randomness. But, as posters have noted, there is a hint the Tories have at least one data-point in the right place. In Scotland the swing will in all probability be below average next time. But look at “next-door” Wales. The long-term trend there is in the Tories’ favour. So if Wales swings above-averagely, that would largely cancel out the benefit obtained in Scotland.

Looking at the top end of the scale, the East Midlands, North West and West Midlands would pay rich dividends if the Tories could boost their performance here. Unfortunately, for the past three elections they have all swung nearly identically to the nation as a whole, and previously when they have diverged it has been in opposite directions! Again, the natural tendency is for variations to cancel out.

So the answer to our question seems to be. Yes, regional swings might help the Tories a bit, but they largely cancel out, and are insignificant in the overall context. Perhaps 5 seats may be attributable to regional swings next time.