Tectonic Voter Migrations hurt the Conservatives

This article first appeared in the Daily Telegraph online on 20 April 2015

The headline polls inch towards the Tories, but underneath big changes have happened

The polls now give the Conservatives a lead over Labour both in vote share and in predicted seats. Although both parties are within 3 per cent of their vote shares in 2010, there have been tectonic movements in the electoral make up of the nation.

The graphic shows the various migrations of one hundred typical voters from 2010 to now. Voters who have switched from one party to another are shown moving along the corresponding arrow. "Lost" supporters are shown in grey, and "gained" supporters carry a white plus sign.

There are four key changes: the collapse of the Liberal Democrats; the rise of UKIP; the SNP surge in Scotland; and the growth of the Greens. On the graphic, we see five outbound arrows from the Lib Dems, and several inbound arrows into the three insurgents.

Armchair Conservative strategists welcome most of these changes (apart from the rise of UKIP), believing that they hurt their opponents relatively more. But that is not true. Even for the Conservative party on its own, the changes are at best neutral. And the Conservative party is not on its own. A hung parliament is probable and the Conservatives will need allies. Their most likely ally is the Liberal Democrat party. Indeed, two rival blocs are taking shape: Conservatives plus Lib Dems, and Labour plus SNP. Let's call them the "Blue" and "Red" groups.

How do these voter flows affect the predicted seats won by the two groups?

The decline of the Liberal Democrats, even in terms just of the voter movements to Labour and the Conservatives, is emphatically bad for the blue bloc. It loses 36 Westminster seats, which are all gained by the red team.

The growth of UKIP is also unambiguously bad for the blue bloc. By differentially taking more votes from both its parties (more LD than Labour supporters have switched to UKIP), this voter migration costs another twenty seats. Despite the obvious propaganda in the slogan "vote UKIP, get Labour" repeated ad nauseam by Tories, it is psephologically correct.

Even the surge of the SNP is bad for the blues. Although it seriously weakens Labour, those seats lost by Labour stay within the "red" column. But the SNP will also take seats from the Liberal Democrats in Scotland, such as those held by Danny Alexander and Charles Kennedy. This takes a further eight seats away from the coalition parties.

Finally the growth of the Greens is neutral for the major parties. Labour and the Conservatives each lose about half a voter (out of a hundred), and the Lib Dems don't lose many further seats from these defections.

Although the Conservatives are now ahead in the polls and the predicted number of seats, they are facing strong headwinds from the change in electoral circumstances.

Appendix: Data and sources

The raw data for this article comes from looking at the detailed tables of four YouGov surveys from 10-17 April 2015 (Sunday Times, Sun, Sun, Sun) with a total sample size of 7,938. Combining these polls together gives us a table of current voting intention against how people voted in 2010:

These raw data are then adjusted and extended to make a "transition matrix" for the six major parties and "Other". Each column of the transition matrix should sum to 100, and shows where one hundred supporters of that party in 2010 have migrated to. Most voters stay with their original party (for example, 80 out of 100 Conservatives have stuck), but many Lib Dem voters have switched to other parties leaving only 39 voters out of their original 100.

The adjustments made are the minimum necessary to make the matrix consistent with the measured levels of support in both 2010 and the Electoral Calculus predicted vote share (as at 18 April 2015):

In particular, the matrix product of the transition matrix with the 2010 vote share should be equal to the April 2015 predicted vote share. For instance,

Some assumptions about the minor parties had to be made to do this. These were:

• No 2010 supporter of UKIP, Green or SNP migrates
• A 2010 supporter of "Other" can only migrate to UKIP or Green
• Nobody migrates into "Other"

Finally, the transition matrix can be scaled by the 2010 vote share to get the number of voters in each category:

(Note that not every row and column exactly adds up due to rounding.) On the actual graphic, there were some additional simplifications:

• Voters were rounded to the nearest integer
• The "Other" category was not shown
• The flows between Conservative and Labour (two voters in each direction) were omitted
• The flows between the Lib Dems were netted for both Conservative (2.3 voters) and Labour (5.6 voters)
• The flow between the Conservatives and the Greens was rounded up from half a voter to one voter.