Was Labour's purge worth it?

Last month the was a huge hoo-hah over the fact that the Labour party had been weeding out non-supporters from people who had signed up after the general election, removing the vote from people they suspected didn't "support Labour values". I'll declare now that I think this was the wrong thing to do, so this is the background from which I am writing this post.

I'll also declare up front that I signed up as a registered supporter and paid my £3, before the general election, on the basis I wanted a say in who the London mayoral candidate would be for Labour. Getting a vote in the leadership election was a surprise. You can see me above supporting Labour values at People's Day back in the heady days of July when no one thought Jeremy Corbyn stood a chance.

Anyway, the point of this post is to determine whether the purge of 3,000 people who had signed up to vote in the leadership election was worth it, statistically and then following on from that from a PR point of view. It's clear from the post I linked above that the purge has removed some people who were in fact genuine supporters of Labour, so from that position I argue straight off it wasn't a wise thing to do.

But onto the stats. In order to determine whether or not the purge was "worth it" we need to determine whether or not those purged could influence the result. This requires a bit of information about who gets to vote in the election and their likely voting intentions and it requires you to make a few assumptions about those who were purged.

I have taken the data on Labour party membership from the Guardian live blog on the purge (yes, they liveblogged it...) and the data on likely voting intentions from a compilation of opinion poll results on wikipedia.

So the total electorate for this leadership election was made up as follows:

Pre-election members  187,000
Post-election members 105,973
Affiliates            148,182
Registered supporters 112,799

This gives a total of 553,954.

According to the Guardian, 3,000 people were "purged". My first assumption is that all these were registered supporters, not members. In fact I know this to be false, but I think it's reasonable to assume the majority were so let's stick with that.

This gives an electorate of:

Pre-election members  187,000
Post-election members 105,973
Affiliates            148,182
Registered supporters 109,799

Next we need to decide how these people will vote. I have taken a range of opinion poll results to try to reflect the views of the different categories above. Obviously these are all assumptions. I have also assumed that 12% of the electorate won't vote and that all these are pre-election members.

I've assumed the pre-election members vote as the Ipsos MORI poll for the Evening Standard of 14-16 June:

Burnham 23%
Cooper  20%
Corbyn   9%
Kendall 11%
Unsure  37% (it's these people I have removed from further calculations).

I've assumed the post-election members vote as the Opinium poll of 21-25 August:

Burnham 27%
Cooper  22%
Corbyn  39%
Kendall 12%

I've assumed the affiliates vote as the Opinium poll of 11-14 August:

Burnham 29%
Cooper  19%
Corbyn  37%
Kendall 15%

I've assumed the registered supporters vote as the YouGov poll for The Times of 6-10 August:

Burnham 21%
Cooper  18%
Corbyn  53%
Kendall 8%

And lastly I have assumed that every single purged supporter was an infiltrator intending to mess up the Labour party good and proper by voting for Corbyn.

Following through these numbers, it follows that if the purged voters were removed this would be the outcome:

Burnham 28.4%
Cooper  22.4%
Corbyn  35.9%
Kendall 13.3%

Removing the purged voters has the following effect:

Burnham 28.6%
Cooper  22.5%
Corbyn  35.5%
Kendall 13.3%

That's right. Removing those 3,000 people affects the result by 0.4 percentage points. That is it has absolutely no impact on the first preference results.

The eventual winner of the contest depends on what you assume happens to the second and third preferences but making some assumptions about who transfers to whom, the impact on the outcome is still 0.3 percentage points, that is keeping or removing those 3,000 people does not affect the result.

So was it worth it? I argue on the basis of the stats the answer is no. Those 3,000 people couldn't influence the eventual outcome and it's certain that some of them were genuine supporters, who may now be lost to the party forever. And that's before we get started on how incompetent and petty it makes the party look - a PR disaster.

And who will be the eventual winner? Well that really does depend on the distribution of second preferences. I worked out two, both plausible, scenarios, one of which leads to eventual victory for Burnham, the other for Corbyn. No doubt there's a third way that would lead to Cooper being victorious. The one thing that's certain is it won't be Liz Kendall. But she's philosophical about it:

Nope, Malbec & steak https://t.co/Kcahcs8r02

— Liz Kendall (@leicesterliz) September 10, 2015