A major problem in the statistical analysis is making inferences about individuals from the groups of which those individuals are part. In Britain, naive analyses of the recent election and referendum results may make this kind of error.

Net, not individual, movements

In a Twitter post shared over a thousand times, a user stated:

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Voters do not stay in blocs. (Image: John Ross/Twitter)

Let us look at an illustrative election to show the problem with this reasoning. Imagine a prior election with three parties. 45% voted Blue, 40% chose Red, and 15% backed Green.

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This is an illustrative example. (Image: ggplot2)

The same voters cast ballots again, but there is switching.

5% of the electorate voted Blue last time, but now voted Green. 5% went from Red to Blue. Also, Red and Green swapped 5% of voters in both directions.

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Looking at net changes gives the wrong impression. (Image: ggplot2)

Result:
Blue: 45 (=);
Red: 35 (-5);
Green: 20 (+5).

The net change between Red and Green was zero. Red lost voters to Blue.

We cannot draw inferences about switching by individual voters from the total votes for each party. We need surveys to understand how individual voters changed.

The latest YouGov Blumenau-Lauderdale model of vote intention was based on surveys from 5th — 11th December 2019. Here, 2017 Labour voters were estimated to defect at roughly even rates to the Conservatives and the Brexit Party (13%, in the ‘Leave’ bloc), and the Liberal Democrats, Greens and the Scottish National Party (12%, in the ‘Remain’ bloc).

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The central estimate of Conservative seats was 348 seats. (Source: YouGov/UCL)

A similar conclusion can be drawn from the Datapraxis analysis of YouGov responses, the Lord Ashcroft Poll-badged internet survey, and YouGov’s post-election vote recall survey.

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Labour lost slightly more voters to the Conservatives than the Liberal Democrats. (Image: YouGov)

Labour Leave

Another example of the ecological fallacy at work in British politics is the belief that most Labour voters (in the 2017 General Election) backed Leave in the 2016 EU referendum.

Lord John Mann, formerly the Labour MP for Bassetlaw, claimed:

This is untrue. Most Labour voters, in both 2015 and 2017, backed Remain in the 2016 EU referendum.

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The dilemma was often misunderstood. (Image: Prof John Curtice/UK in a Changing Europe)

If a constituency elects a Labour MP and was estimated to vote Leave, it does not follow that most Labour voters in that seat also voted Leave.

There are other voters in that constituency. Disproportionately, it was the Conservative and UKIP voters in those constituencies that backed Leave. As an analysis of YouGov data on behalf of Best for Britain found:

Not everything is a fallacy

It is important to remember that constituency-level associations can provide indications of individual movements.

As John Burn-Murdoch (Financial Times) highlights, there is a reduced association between the type of jobs in constituencies and the difference between Labour and Conservative vote share:

This is reflective of the reduced importance of social grade in vote choice.

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Social grade is based on what types of jobs people do. (Image: Financial Times/Twitter)

People seeking to understand election results should be aware of the ecological fallacy. The siren call of seemingly clear conclusions muffles more complicated electoral rhythms.

This blog looks at the use of statistics in Britain and beyond. It is written by RSS Statistical Ambassador and Chartered Statistician @anthonybmasters.

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