Chris Prosser @caprosser
I’ve been thinking a lot about why people seem to have a hard time grasping the idea that the Brexit Party is more of a threat to the Conservatives than it is to Labour and realised that it’s a classic example of people finding conditional probability unintuitive (A thread) 1/
Specifically people seem to have trouble accepting that both of these things could be true at the same time:
1) Lab Leavers are more likely to defect to the Brexit party than Con Leavers.
2) More Con voters are likely to defect to the Brexit party than Lab voters.
2/
This isn’t because people are stupid. As David Spiegelhalter – one of the top statisticians in the country – has said, it is because probability is unintuitive and difficult!
There’s quite a lot of research showing that people are bad about thinking about probability, and one of the most common errors is failing to take base rates into account (e.g. that there are more Con Leave voters than Lab leave voters) 4/
There’s also a bunch of research that shows that people find probability much easier to understand when you express it in terms of expected frequencies. So I’m going to do just that, and try and explain why the Brexit Party is more of threat to the Conservatives than Labour 5/
Imagine a seat with 100 voters. The seat is an ultra-marginal and last time 51 people voted Lab and 49 voted Con. About 35% of Lab voters voted Leave = 18 people, and 70% of Cons voted Leave = 34 people (52 Leave/48 Remain). 6/
I haven't just plucked these numbers from nowhere - our @BESresearch data suggests the proportion of 2017 Lab voters who voted Leave was about 31%, and about 73% of 2017 Cons voted Leave. And this doesn’t vary that much by constituency (see t.co/oFG6p77Wa1 ) 7/
Lets say the Brexit Party is better at recruiting Lab Leavers than Con Leavers – in my scenario 1 in 2 Lab Leavers defect to BP and 1 in 3 Con Leavers. With 18 Lab/Leavers that means 9 defect to BP, and from 34 Con Leavers 11 defect. Lab still win the seat 42 votes to 38. 8/
These numbers are very generous to the ‘Brexit Party is a threat to Labour’ argument. At the EP election BP was better at recruiting Con Leavers than Lab Leavers. Newer data suggests that if Lab Leavers are more likely to defect, it’s not by much: t.co/EJXZWKYIEQ 9/
Now let’s imagine another seat, this one went Con 51 votes to Lab’s 49. Otherwise the numbers are the same: 35% of Lab voters voted Leave = 17 people, and 70% of Cons voted Leave = 36 people (53 Leave/47 remain). 10/
1 in 2 Lab Leavers defecting to BP = 9 people and 1 in 3 Con Leavers defecting is 12 people. Now – even though the seat is more Leave-y than my other example, Lab win the seat 40 votes to 39! 11/
To cut a long story short, if you’re a politician/journalist/canvasser/etc: you might talk to Lab Leavers and find that more of them are defecting to the Brexit Party than Con Leavers. But you need to remember there are many more Con Leavers out there than Lab Leavers! 12/12