*TL;DR, using Bayes’ theorem and UK demographic data, the odds that the United Kingdom Independence Party doesn’t have a racist agenda are 1 in 1.35 billion. Yes, I have that much of a life.*

I know this is getting a bit old now, but it was brought up on the *Mock The Week* clip-show and I thought “what the hell, I haven’t totally over-laboured and nerded-out over a point in a while”.

Take a look at the United Kingdom Independence Party’s (UKIP) cover for its annual conference:

So, apart from the vomit-inducing design and colour scheme, much has been said about the complete lack of non-white faces on it (not least because of the implications of the headline). At least ones that weren’t photoshopped in by the Huffington Post.

But, but, but… says UKIP, *that’s racist*. Why should we care about what the colour of their skin is? They’re just people. Indeed, here’s Godfrey Bloom saying as much in such an eloquent manner:

Aw, bless, he thinks he’s being intelligent… anyway.

I’ve recently edited this because I noticed the original video was taken down. This current one also has Bloom’s “slut” comments at the beginning and him attempting to defend himself over it. I also just love how the woman on the right (I assume a UKIP special advisor?) seems to be fundamentally unaware of how language works. Like, seriously? You really aren’t aware of the common usage of the arbitrary-combination-of-vowels-and-consonants that looks like “slut”? Where have you been for the last… *ever*?

The average social justice nerd will say that this is important because it’s about visibility. If you hide a particular demographic, actively or by accident, you’re ignoring them, you’re pretending they don’t exist, and you’re actively excluding them from important discussions, political or otherwise. Hence why even small groups shown in stock photos are often implausibly diverse; out of a group of six you’ll expect at least two black guys, an Asian and someone in a wheelchair (though she’ll be white, as you can’t stack the under-privilege deck too much), while one will be gay and the last remaining white male will probably represent peanut allergies or something. This has been expressed better (and also far worse) by various others, it isn’t worth covering much further.

Personally, however, I’m more interested in something a bit harder (said the actress to the bishop…). You can argue the benefits of inclusion with idiots all day, but numbers don’t lie. So let’s take Godfrey Bloom at face value. His point is a common one; that if you talk about race, you’re a racist. Supposedly, racial equality should evolve organically without prodding and therefore the over-representation in small groups described above (“political correctness gone mad” as the *Daily Heil* might say) should cease to be. In theory, representation *should* then occur naturally through sufficiently large sample sizes. At least, that’s what I’d *hope* he thinks, since that’s the only non-racially-motivated interpretation I can think of for Bloom’s bizarre tirade above (it couldn’t *possibly* be that he has no idea what he’s talking about…).

Do we have a sufficiently large sample size to try this on? A UKIP related one? Hell yes we do! Right there, above, 17 headshots wide and 16 headshots deep, the front cover of UKIP’s conference booklet shows a whopping 272 gurning faces (well, 269 if you count the three chopped off at the corner, 265 if you count the big gold sticker covering a few).

Next, it takes all of two seconds to look up the demographic information for the United Kingdom. The punchline being that the country is 85% White British, or about 90% White *Any*, with 10% being composed of myriad ethnic minorities.

I’ve often wondered what would happen, if anything, if we actually split “white” into further categories since it makes sense to sub-divide your largest categories to make them more useful and considering the cultural diversity exhibited between rural and urban England – and come on, Yorkshire is *totally* an ethnicity – but I digress.

Back to the punchline, this means around 1 in 10 people in the UK are non-white. This will vary from place to place, of course. If you’re lucky enough to hail from the desolate wastes North of The Wall, this will be 1 in 100, while in London it is about 1 in 2. So your expectations will certainly change, and if you grow up in certain areas you might think absolutely nothing of a grid of 100 faces that are all-white. However, we are talking about the ** United Kingdom** Independence Party here, not some regional separatist movement, and so the overall UK numbers are fit for purpose.

Anyway, taking Godfrey Bloom’s apparent take-home point at face value (“hey, we’re not racists, this is totally just random chance!”), this would give us an expectation value of 27 non-white faces on UKIP’s material (0.1 x 273, rounding off). But that’s an *expectation value*, if I roll 6D6 (that’s 6, six-sided dice, for the uninitiated) I should *expect* each number, 1 to 6, to come up once. But it’s not outside the realm of possibility to get three sixes pop up or two ones. If it wasn’t, *Yahtzee* would just suck. So instead we need to think of a *distribution* based on the odds of picking that many of a certain type of person. This is *not* an intuitive calculation, and I confess that before I popped the numbers into Google Calculator I didn’t expect to suddenly be talking orders of magnitude at this point.

So, what are the chances of UKIP making an all-white cover if they weren’t operating on some kind of racial prejudice? I.e., if they were completely motive-free and *representing the United Kingdom as a whole*. It’s simply a case of multiplying the 0.9 chance of picking a white person at random 272 times for each face. 0.9^{272}, in fact. This works out as a staggering 3.5×10^{-13}. In odds ratios this is 1 in 2.7×10^{12} – or 1 in 2.7 trillion. (in Northumberland, the equivalent calculation would produce 1 in 16, which is still low but not outside the realm of chance and might have produced a more interesting discussion below, while the London figures produce a “holy crap we’re talking number of particles in the universe” sort of figure – see what I mean about this being emphatically unintuitive?)

That’s the prior odds of this booklet cover happening by chance, and so we can say it’s pretty much beyond *mere chance*. If the party held a conference every day since the universe began, featuring random faces plucked from the UK’s ethnic make-up, we would expect to have seen this happen, by chance, about twice. So something else must be at work here, most likely UKIP’s internal racial demographic. But that does suggest that they don’t represent a significant chunk of the population, or actively go out of their way to *not* represent them. And that’s the point. Is it really a racist comment to question why a party allegedly representing the best interests of an entire country have zero representation, and apparently zero interest in such representation, of a tenth of its population?

### More nerding-out below

1 in 2.7 trillion, however, is merely a prior probability of such a poster happening at random. Does it say “UKIP are a bunch of racist fucks”? No it doesn’t; it *could* just be chance, and strictly speaking it only represents a particular frequency of that chance and the rest is inference. We can, however, go one further and figure out what the odds are that UKIP are a bunch of racist fucks *given* that they produced a conference poster of nearly 300 all-white faces. That’s the question we want answered, and yeah, you know where this is going…

To cut a long story short, P(A) is “the probability of [A] happening”, while P(A|B) is “the probability of [A] happening *given* that we know [B] is true”. Importantly, P(A|B) is not the same as P(B|A).

Here we do hit some hot water and have to do some handwaving. After all, the odds above are easy to calculate from demographic data and so P(B) is simply 1 in 2.7 trillion. But what are the prior odds that “UKIP are a bunch of racist fucks”? I’d say “pretty fucking high”, given that Godfrey Bloom was fired for calling women sluts, that their policies are firmly xenophobic, and that calling them “Diet BNP” is an insult to the concept of a diet/lite soft drink. They have questionable policies, and multiple prior convictions in the racism/xenophobia game. But let’s be generous and make it a true prior probability, given no other data, and say this value of P(A) is 1 in 1000 (not that it matters, it won’t be on the order of magnitude of trillions so it’s not going to mess with us too much).

It occurred to me a while after I originally wrote this that you could get an empirically informed value of P(A) by taking the total number of political parties in existence, and taking P(A) as the fraction of those that are considered, unambiguously, to be racially focused and motivated. Then I realised that doing this would probably mean P(A)>0.1, as opposed to P(A)=0.001. It doesn’t matter too much, you can ass-pull the priors as they also represent your *personal* prior biases – cf. *The Signal and the Noise* by Nate Silver, where this is discussed at great length.

Secondly, what are the prior odds that “UKIP will produce an all-white conference poster *given that* they’re a bunch of racist fucks”. Probably pretty high, but there is a probability that they might cover themselves or not express it in this way, so it won’t be 1. Somewhere in the region of 0.5 sound good to you? People are welcome to find more robust ways of working that bit out, though I doubt they’ll do much to the result below.

A lack of rigour is a red herring here, though. This sort of calculation is very good at taking you biases into account – and if you iterate with new data, you *should* converge on the same answer regardless of your prior biases. The practicalities of this are best left to people who treat Bayesian maths as more of a religious lifestyle choice rather than a tool for facetious trolling, though.

To complete the little trick, we need to change P(B) into something more useful, using the law of total probability to change it into (P(B|A)xP(A)) + (P(B|C)xP(C)) – where P(C) is the complementary value of “not a bunch of racist fucks”, which is 999 in 1000 given our other prior probability, P(A), of 1 in 1000. It should be obvious that with no racial prejudices that P(B|C), “the odds of an all-white conference poster coming from a non-racist-fuck party” will tend towards P(B), as it’s the one-in-trillions value of doing it by accident. So P(B|C) = P(B) or there abouts. As I said, this is facetious trolling.

For anyone confused by the above, P(B|A)P(A) + P(B|C)P(C) totals up all the possible sources for our piece of evidence, P(B). It either comes from a “racist fuck, intentionally”, P(B|A), or from a “not-a-racist-fuck, unintentionally”, P(B|C). It’s a necessary step to stop the numerator being larger than the denominator and producing a P(A|B) greater than 1, which is, of course, even more absurd than the notion that Godfrey Bloom has a functioning nervous system capable of operating his mouth. With me? No, never mind… let’s just move on.

The final expression to work out is, therefore, (0.5 x 0.001) / (0.5 x 0.001 + 1-in-2.7-trillion x 0.999). Bung that into Google calculator and you reach the conclusion that the probability that UKIP are a bunch of racist fucks given their conference poster is 0.99999999926. The odds that they’re *not* racist fucktards then works out to be 1 in 1.35 billion.

Hey, I don’t make the rules, blame the universal wavefunction and the boundary conditions of the universe.

Have you tried the same sums with the Lib Dems? Or the Lib Dems on sexual equality?

Politicians are disproportionately white and male in all parties not just the racist UKIP.

I can’t really see what that would illustrate. It’s fairly clear that politics is white male dominated, but in the a case of the Liberal Democrats they have sub-organisations in place to promote minority groups (EMLD) and improve their representation to compensate for an overall lack of diversity. That puts them in a very different boat to UKIP, who are actively pretending they don’t have a significantly xenophobic agenda and have a demographic to match. There’s no such pretence amongst most of the other mainstream UK parties.

But, sure, you could take a look at the first Lib Dem group shot that appears on Google Images (http://walthamforestlibdems.mycouncillor.org.uk/files/2008/11/lib-dems-group-3.jpg – it’s local, not national, though) and it’s clear that it’s about 20% non-white, which is slightly shy of the 45% non-white of Waltham Forest’s demographics. Make of that what you will, but it’s a significant improvement in representation over “fuck all”.

I don’t think there’s much question that UKIP are racist but if you’re going to claim that you can prove it mathematically then you need to consider the sample set. Those faces aren’t drawn from the population of the UK or from the population of UKIP supporters but rather from the UKIP’s elected representatives. It seems to me that if you’re going to make a mathematical argument for UKIP being racist then you need to use the UK’s elected representatives as your sample population at the very least.

I suspect any method would find, quite rapidly, that the Lib Dems – in particular – are racist and sexist and I’m choosing them as the target because I think it’s untrue.

I’m well aware of issues regarding the sample set, but the relevance of this is highly contingent on the claims being made. If the answer to “why are there no black faces on this poster?” was a simple and honest “we don’t have the ethnic diversity to draw it from”, then it wouldn’t be so much of a problem. And at least that would be honest. But then, the question simply skips back to “why does UKIP lack the diversity of the UK?” and I could simply re-frame the above based around that and lose nothing – indeed, the poster is actually a proxy for UKIP’s diversity (or lack thereof) and so that is what the above is really talking about. Why that matters is, of course, covered under the “social justice nerd” explanation about visibility. The parliamentary demographic is, therefore, a red herring in this situation.

But even so, that wasn’t the excuse given. Bloom’s hilarious mental breakdown seemed to want to shrug it off, to act all blameless as if the problem didn’t exist. To me, that says they think they supposedly don’t have any issues with race, so they

should– by Bloom’s own tirade – be the bastions of perfect representation. They don’t want to face up to the issues of under-representation, so I believe it is fair game to take the approach above, using the UK’s overall demographic figures, to underscore it. When comparing it to other parties, it’s essential to note that this demographic calculation is merely one single iteration of Bayes’ theorem; you repeat it and update P(A|B) for new evidence P(B). So even if repeating it for the Liberal Democrats initially shows that they under-represent compared to the population (a fact not widely disputed) then there is plenty of additional strong evidence against them being actively racist/xenophobic to take into account (which isn’t available for UKIP). So the methodwouldn’tarrive at the same conclusion at all as you cycle through the evidence available. It’s only the staggering magnitude of the odds against pulling 272 all white faces out of a hat that makes me stop there.Also, I don’t think taking Parliament’s ethnic diversity as the background changes things much. At 95%-white as the demographic, pulling off 272 white faces is still just about 1-in-a-million by chance alone. That tempers the hyperbole by a few orders of magnitude, for sure (and I’ll take that hit if you’re not convinced by my argument for taking the UK’s demographic for a party in denial about its prejudices), but really doesn’t affect the overall conclusions.

The major diversity issue with parliament, however, isn’t so much ethnicity as it is class; 90% are university educated (compared to 20% of the population) and a quarter are Oxbridge graduates (compared to a negligible proportion of the population). Though this is something else entirely and convolutes the issue even more.

“However, we are talking about the United Kingdom Independence Party here, not some regional separatist movement”

…yeah, but cmon, we sort of ARE talking about that, aren’t we?

Not that I would wish to influence any of Lincolnshire’s fine citizens to build a big wall around their county and not let anyone in or out.

I mean.

That would be equally awful for people on both sides of that wall, wouldn’t it?

I can only imagine the resulting nuclear war with The People’s Republic of Cornwall.