Ecological Fallacies

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:

In approximate terms Labour lost 2 million votes at the election to pro-Remain parties and 400,000 votes to pro-Brexit Parties.

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.

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.

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).

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

A similar conclusion can be drawn from the Datapraxis analysis of YouGov…