All women shortlists: now for the bonkers science part…concentrate!

By VoteRedGoGreen

I was expecting my post on LabourList to generate some interest, but 61 comments? Blimey, Charlie!

I think there are three separate issues here, and all of the commenters are trying to address them at the same time (in fairness, so was I when I made the post).

The first point is “Airdrie and Shotts CLP should grow up, and learn to accept collective democratic decisions”. This was the main thrust of the post (which was, alas, ignored by the comments – maybe they all agree?)

The second point is “All Women Shortlists are morally right, or at least, not morally wrong”. Of course, this is purely my own judgement, and clearly, it’s a divisive issue (in and out of the Labour Party).

I’ll probably return to the second point in the future. However, right now I want to address the third point: “open shortlists disadvantage women”.

Unlike the first two, this is actually quite straightforward and objective, because there’s data that we can look at.

Since the 1992 general election, 398 freshly-minted Labour MPs have entered the House of Commons – meaning there were 398 full selections that resulted in the election of a Labour MP. Of these, 289 were men and 109 were women. I’ve illustrated this in a pie chart (because I’m good to you like that).

So, of all of the MPs we elected, only 27% were women. This isn’t so good – and this includes the women who were selected from All Women Shortlists.

If we only include those MPs selected from open shortlists, the picture is even starker: 289 men to just 51 women. I’ll even give you another pie chart for that.

Now, if selections are fair – that is, they are equally likely to produce a man as a candidate as they are a woman – then they’re analagous to tossing a coin. If you toss a coin a couple of times, then you may well find that either heads or tails dominates; but the more you toss the coin, the closer the result will come to 50% heads, 50% tails. This is known as the law of large numbers.

This is because tossing a coin – or, indeed, selecting a candidate in a fair selection process – is a Bernouilli trial with a probability of 0.5 for each outcome: “man” or “woman”.

Hang on, I can hear you say – 340 selections may not be quite enough to really test the system. Could this result be random? In fact, if you’ve really been paying attention and you know your stuff, I might also hear you say, “a repeated Bernouilli trial is defined by a Binomial Distribution; what is its standard deviation?”

If you’re in the latter category of people whose voices I can hear in my head (and it’s not often I say that, I hasten to add) – you’re quite right that this is Binomially Distributed (the Binomial Distribution being used to model a series of n independent identical trials with two outcomes, each with a value of p and 1-p respectively).

The variance is defined by this equation:

So, in this case its value is 340 x 0.5 x 0.5, or 85. The standard deviation – the usual test of the spread around the mean in a set of trials – is the square root of this, which is 9.219.

As the number of trials in a Bernouilli series increases, they tend towards a Normal Distribution – the bell curve we all learned about in school. (This is because of something called the Central Limit Theorem, but going into that would just be showing off).

In a normally distributed set, you expect 68.2% of results of your trial to be within 1 standard deviation of the mean, as shown in the pretty diagram. In this case, this would mean that – 68.2% of repetitions of 340 open fair selections would lie in the range of 160 men-180 women to 180 men-160 women. 95.6% of repetitions would be within 2 standard deviations of the mean – the range 150 men-190 women to 190 men-150 women.

However, our result – 289 men and 51 women – is right down in one of the tails. If you repeated 340 fair open selections loads and loads and loads of times, the likelihood of any one of them being what we have is extremely small – far, far less than 0.01%.

So, we can conclude one of two things. Either, we have a fair system which has thrown up a truly freakish result, with similar odds to me winning the lottery this week; or, open selections are, for some reason, inherently unfair. I’m with the latter as the more likely explanation.