UCL >> Computer Science dept >> Networks research group >> Damon Wischik >> Research interests >> UK election chart 2010

UK elections 2010

To properly show the state of play between the three main parties in the UK, the simple two-way swingometer is inadequate. How would simultaneous swings from Labour to both the Conservatives and the Liberal Democrats affect the result? How big a swing to the Liberal Democrats is needed to relegate Labour to third place?

2010.05.09

Swings, Scots, and swindlers

SUMMARY. There are three distinct sorts of Liberal Democrats seats: those in the South West which are like Conservatives, those in Scotland which are like Labour, and a disparate few in the rest of the country. There is no unified Liberal Democrat party for Nick Clegg to lead. Also, the expenses scandal had no impact at the voting booth.
Overall swing
Three-way swingometer chart [pdf]. There is a point for each constituency. Points are located according to their notional 2005 result, and colour-coded according to their 2010 result. The line from each point shows the swing from 2005 to 2010. A swing line that points up and left means a swing away from Labour; a swing line that points down and left means a swing towards the Conservatives.
Most Conservative seats, and the anti-Labour Liberal Democrat seats, swung away from Labour. It was almost a pure anti-Labour shift, with no deviation in the balance between Conservative and Liberal Democrat. In other words, strong Liberal Democrat seats like Devon North are no different to strong Conservative seats like New Forest West.

It was a completely different story for Labout seats, and for the Liberal Democrat seats that aren't anti-Labour. These seats nearly all had a slight swing away from Labour, but they differ greatly in whether they went pro Liberal Democrat or anti.

Swings by region
Three-way swingometer charts, by region [pdf].
When we break down the swings by region, we see a very striking pattern in Scotland. Scotland showed a nearly uniform swing away from the Liberal Democrats, both in seats that they hold and in Labour seats.

Most of the rest of the country showed a swing away from Labour in Conservative seats, and a mixed bag in Labour seats. Yorkshire & the Humber showed a slight swing towards the Liberal Democrats, and London and the North East showed a slight swing towards the conservatives.

Swings by amount repayable
Three-way swingometer charts, [pdf], stratified by how much the candidate was told to repay in the Legg report. Many MPs stood down. I have grouped seats into four categories according to how much the sitting MP was told to repay; the category labelled 0 is for MPs where the sitting MP was not asked to repay anything. I have excluded seats where the sitting MP was asked to repay but was not in one of the three major parties.
When we break down the swings by how much an MP was told to repay, we see no significant pattern. In other words, the amount that an MP was told to repay had no bearing at all on the swing in his or her vote. Of course many MPs stood down; these charts suggest they might as well have stood for re-election. So much for the outpouring of public anger over the expenses scandal.
2010.05.07

How accurate was betfair.com?

SUMMARY. It did a good job of predicting the national swing. But it didn't predict the resilience that Labour showed in marginal seats.
accuracy of betfair.com
Three-way swingometer chart showing the betfair predictions and the results [pdf]. The per-seat betfair predictions are shown in little pie charts as described below, and the per-seat results are shown by the colour of the outer circle. The predicted swing inferred from betfair.com is indicated by the black dotted lines, and the green arrow shows the actual national average swing.
The seat-by-seat predictions from betfair.com did a very good job of predicting the overall national swing. While national polls were predicting a big surge for the LibDems, betfair.com punters did not believe it.

However, even given this, the swing towards the Liberal Democrats in Labour–LibDem marginals was smaller than betfair.com punters predicted. Furthermore, the swing towards the Conservatives in Labour–Conservative marginals was smaller than predicted. Since Labour held on well to all its marginals, inferred betfair.com prediction of a slight Conservative majority did not come to pass.

The betfair.com market does funny things as the event draws near—on the final days there wasn't enough liquidity for me to make sensible estimates based on the still-open offered odds. Next time, I shall need to think through how to combine still-open offered odds with matched odds.

2010.04.25–2010.05.06

Predictions from betfair.com

betfair.com predictions on 2010.04.30
Three-way swingometer chart based on betfair.com predictions as of 2010.04.30 [pdf]. The chart is very information-dense: data is encoded by position with respect to the axes, by colour, by size, and by background shading.
  • Each mini pie-chart corresponds to a constituency. There are faint text labels next to each constituency; if you load the PDF version of the chart then you can search for your constituency by name.
  • The position of each constituency indicates the 2005 result. The chart area is divided into three by the axes: constituencies in the bottom right went to Labour, those in the bottom left went to the Conservatives, and those in the top went to the Liberal Democrats. The position also shows how the vote was split: for example, constituencies near the top-right axis line were split between Labour and Liberal Democrat, with little Conservative vote.
  • The pie chart for a constituency shows the betfair.com predictions for 2005. The fraction of the pie chart that is blue, for example, is equal to the probability that the Conservatives will win. (Some seats are mainly contested by regional parties or other parties, and this is shown by grey. Some seats are so safe that there is hardly any betting, and these also show up as grey.)
  • The size of the pie chart shows how much betting has been going on: to be precise, the area of the pie chart is proportional to the amount of money matched on betfair.com.
  • The whole plot area is tiled into hexagonal cells, each shaded white, blue, red or yellow. If there were a uniform national swing, say for example a swing to the Liberal Democrats of 12% in every constituency, then every point on the chart would shift up by an appropriate amount. Alternatively, we could represent this swing by moving the axis lines down by the corresponding amount. Any such swing will result in a balance of power in parliament, and the colour coding of each hexagonal cell shows which party would have a majority of seats, if there was a swing big enough to move the axis origin to that cell.
Betfair.com is an online market for gambling; the advantage of predictions from online gambling over predictions from polling data is that gamblers put their money at risk, so they have an incentive to be realistic rather than idealistic, and any deviations from the truth should be corrected by the invisible hand.

Who will win?

It is a very close call between a Conservative majority and a hung parliament. To see this, imagine shifting the axes so that the seats are split according to the majority colour: seats that are predominantly red should be in the lower-right area, seats that are predominantly blue should be in the lower-left area, etc. The shifted axes are shown by a dotted line, and the origin is just inside a white-coloured hexagonal cell, i.e. a hung parliament.

The seats to watch are those that are on a knife-edge, such as

Is there a big swing to Liberal Democrats?

No. (At least, not according to the punters at betfair.com. If you believe otherwise, you should make money by gambling in favour of the Liberal Democrats.) The new axis origin looks to be almost directly south-east of the old, i.e. a swing against Labour, with the ratio of Conservative to Liberal Democrat held constant. That is, there is no shift at all to the Liberal Democrats.

Did Brown's gaffe just lose Labour the election?

Look at the chart from the morning of 27 April [pdf]. Compare it to the chart for the evening of 28 April [pdf], a few hours after The Gaffe. There is virtually no change. Perhaps the punters at betfair.com have simply not reacted yet—or perhaps they had already factored in the likelihood of such an event.

Can the Liberal Democrats change the shape of British politics?

Not in themselves. There are simply not enough seats that are contested between Labour and Liberal Democrat. The richest pickings for Liberal Democrats are in the strongly anti-Labour seats, at the top left of the chart. The size of the swing needed for the Liberal Democrats to become a major party is huge: they would need to win seats like Hemel Hempstead, and according to the gamblers at betfair.com the chance of this is 6.3%.

There is a large number of seats that are evenly contested between Labour and the Conservatives, with the Liberal Democrats a distant third. These are 'middle England', the seats that will swing the election. Zoom into the PDF to see which seats these are—they are places like Milton Keynes South, Hendon, Telford.

What the Liberal Democrats can certainly do is make hung parliaments much more likely (see the large area of white in the middle of the chart).

Available charts

afternoon of 25 April [pdf]
morning of 27 April [pdf]
evening of 28 April [pdf]
morning of 29 April [pdf]
afternoon of 30 April [pdf]
morning of 3 May [pdf]
morning of 5 May [pdf]
early hours of 6 May (election eve) [pdf]
lunchtime on 6 May (election day) [pdf]
*

Datasets and methodology

The data for the 2010 election results is from the BBC Election 2010 website [csv]. I have also used the colour-coding from the BBC [csv].

The data for the 2005 election is from the Press Association [csv]. Because there were substantial boundary changes from 2005 to 2010, they give notional results that show what would have happened had the 2005 votes been cast with the 2010 boundaries. These calculations are by Colin Rallings and Michael Thrasher. In the CSV file, I have normalized the constituency and party names to match those used by the BBC.

The BBC provides a full list of expense repayments from the Legg report [csv]. I have normalized the candidate names and party names to match the list of 2010 candidates, and I have added a column to indicate whether the MP is standing in the 2010 election, using the same constituency names as the BBC.

The 2010 predictions were obtained from betfair.com. Look under Sports | Politics | UK | Next General Election | Constituency Betting. I normalized the constituency names to match the BBC. To turn betfair.com odds into success probabilities, I picked an arbitrary set of probabilities that are consistent with no arbitrage given the odds offered for backing and laying each candidate. When the back and lay odds agree fairly closely, the probability estimate is tightly bounded. In most seats, the candidates most likely to win have back and lay odds that agree fairly closely. To compute the size of a majority, I assumed that six MPs do not vote (the speaker, and five MPs from Sinn Fein).

D.Wischikatcs.ucl.ac.uk