Riots, Islamism and Bayes theorem

The chuntering class is demonstrating its talent for fact-free theorizing over the question: what , if anything, have the French riots to do with Islam?
David Aaronovitch says: nothing. Melanie Phillips  says that's a "big lie."
In principle, though, this is a simple empirical question. We should be able to use Bayes theorem to judge the relative importance of Islam, unemployment, or anything else, in the riots.
It works like this. Consider the young residents of a suburb afflicted by a riot. Say there were 1000 of them. Let's say these are split 500-500 between Muslims and non-Muslims and that there were 200 rioters, of which 150 were Muslims and 50 non-Muslims.
Simple manipulation then tells us that 30% of  Muslims (150 of 500) rioted compared with 10% (50 of 500) of non-Muslims.
We could repeat this exercise, replacing Muslim with unemployed (or unskilled, or previous criminals or any other category)  to assess the relative strength of the  links between Islam, unemployment, or anything else, and the riots.
Of course, I've plucked these numbers out of the air just for illustration; I picked them merely to show that it's possible for there to be a link between Islam and rioting even when the majority of Muslims don't riot.
The key point, though, is that the facts are in principle knowable. What's needed is hard numbers on who the rioters were, relative to the population they were drawn from.
What's not useful is idle arm-waving. The one thing we know for certain is that we all make terrible judgments about things that are uncertain. We see correlations where we expect them, rather than where they are, we over-infer from single salient incidents, and we see evidence that corroborates our prejudice more readily than we see disconfirming evidence. The fact that a few rioters mutter something about "jihad" does not establish that the riots were caused by Islamism, any more than the fact that many other riots have nothing to do with Islam means that Islam was irrelevant in this case.
Aaronovitch and Phillips are merely demonstrating that the dead tree industry is sometimes little more than a catalogue of cognitive biases, used to entrench people's preconceptions.
Another thing: FWIW, my gut feel is with Aaronovitch. But I try not to think with my gut. And I certainly wouldn't expect anyone to pay me for doing so.

Comments

[Deb]

Nice post. When talking about cognitive biases related to Bayes Theorem, it's worth including the "confusion of the inverse" - when people confuse p(evidence/hypothesis) with p(hypothesis/evidence).

The probability that Saddam Hussein would refuse UN inspectors given that he had weapons of mass destruction is very high. Americans mistakenly assumed that p(WMD/refuse UN inspectors) was equally high. Bad inference.

Cognitive biases can be very costly.

[stu]

Such forms of quantative analysis also have their limitations (not as many as melanie phillips, i know) and so we need to be careful when dealing with them not to read too much into the data.

If you count a rioter as a being muslim, you could too easily deduce that he is rioting because he is a disaffected muslim (or unemployed etc). - i am sure you have a cognative bias that explains this?

While it may be a useful lesson for journalists who report that "Muslim Youths are rioting in Paris" to establish quantifiable evidence (heaven's forbid) but understanding causes of social discource is a little more complicated than a headcount.

[chris]

Stu - you're exactly right. The fact that a rioter is a Muslim doesn't mean he's rioting because he's a Muslim; correlation doesn't imply causality. But causality does imply correlation. So if there's no correlation, there's no causality. All I'm saying is: let's have the correlations, so we can at least start thinking about causality.
Deb - you're right too. But if I were to list every cognitive bias, I'd quickly exceed Typepad's allowed diskspace usage.

[sean morris]

Maybe both are right, Racism, ghettoisation, and exclusion from mainstream or prosperous french life, gives the aims of political Islam and the Islamists more willing foot soldiers and supporters. Afterall the Saudis dont send much in the way of development aid to the Palestinians but they do send plenty of guns and ammo.

[Backword Dave]

Again, nice post, Chris. Other possible hypotheses: Muslim population in France, and suburbs/inner-cities which did not see riots. Also, of course, Islam is not an homogenous belief system, so religion is not the only factor, but which mosque one attends. Germany has quite a large Muslim immigrant population (I remember ads on a U-Bahn 20 years ago about welcoming neighbours and understanding their differences). Germany is roughly as prosperous as France (I realise that reading Sean's comment above that I don't think of the French as "well off" economically, merely comfortable in a shabby epicurean style; the Germans, or some Germans, seem conspicuously rich to me). There's a comparison there, too.

David Aaronovitch picked the right answer, btw, even if for the wrong reasons. The opposite conclusion, ie "everything", is tantamount to "burn down your local mosque as they're all plotting against you". There's far too much of that around, apart from being paranoid, it's also wrong. And I may be wrong about the sort of Bayesian analyses you're talking about, but I seem to remember that they only exclude certain conclusions; they don't actually give you the right one (because of the correlation/causality thing explained earlier). DA's job is to back something. People don't read political columnists to learn, say, that MMR *isn't* connected to autism. They know it's not connected to the sun rising in the east either. They want short cuts to answers. But I agree that less ignorant columnists would be a very good thing. However, there are many statistically literate graduates pouring out of science courses, and newspaper columns are well-paid and subject (to an extent, as the real market is whether the editor likes you) to market forces, so this is as good as it's likely to get.

If Sean meant to imply that Saudi Arabia is waging a sort of war by proxy, I second that. My thoughts on this come down to: we made them rich, and they hate us for it. I know that's nuts, of course.

[dearieme]

"if there's no correlation, there's no causality": doesn't that assume a perfect ability to think of possible causes and then allow for them perfectly in your calculations? Wouldn't some of the Simpson's Paradox examples disprove your point?

[Andrew]

Chris - I'm always fascinated when you discuss cognitive biases, and wondered if you knew of a decent book on the topic in general?

[chris]

Andrew - the classic book on this subject, that kicked off the whole thing, is Judgment under Uncertainty, edited by Kahneman, Slovic and Tversky.
I'd also recommend Everyday Irrationality by Robyn Dawes and Reckoning with Risk by Gerd Gigerenzer.

[Simstim]

Isn't this post also just fact-free (albeit somewhat more analytically nuanced) theorising?