Bryan Caplan posts, insightfully as ever, on statistical discrimination. There’s one issue here, though, that troubles me. Just how robust is the distinction between statistical discrimination - generalizing from personal experience to form stereotypes about the members of different ethnic groups - and narrow-minded prejudice?
The problem arises because very few people reason correctly about statistics.
One big problem is that the media almost never report statistics accurately. Take this from the Sunday Times:
Although black people make up around 10% of London's population, they are involved (sic) in a staggering 70% of the city's shooting incidents.
We’re invited to infer that blacks are hugely involved in gun crime. Let’s unbundle the numbers.
In the last 12 months, the Met reckons there were 3819 crimes involving guns. These include offences where a firearm was seen – let alone used – and where the firearm was fake or an airgun.
Let’s assume two people – a target and an aggressor - were “involved” in each incident, and that there were no repeat targets or aggressors*. That gives us a total of 7638 people involved in gun crime. On the Sunday Times numbers, 5347 of these were black and 2291 non-black.
Now, there are 7,421,228 people in London. On the Sunday Times figures, 742,123 are black and 6,679,105 non-black.
So, the proportion of blacks “involved” in gun crime in the last 12 months is 5347 out of 742,123 – 721 per 100,000.
The proportion of non-blacks involved is 2291 in 6,679,105 – 34 per 100,000.
So, blacks are indeed more likely to be “involved” in gun crime – 21 times more likely in dead-tree-speak, or by 687 per 100,000 in more reasonable terms.
Statistical discrimination tells us to associate blacks, more than non-blacks, with gun crime.
But is this a big difference? In another sense, blacks and non-blacks have an enormous amount in common, in that neither are likely to see either end of a gun. 99,279 out of 100,000 blacks were not “involved” in gun crime last year. And 99,966 non-blacks were not “involved.”
But then, the line “blacks overwhelmingly unlikely to be involved in gun crime” isn’t much of a headline.
We shouldn’t, though, blame only the media for encouraging excessive statistical discrimination. There are other biases involved
1. The salience heuristic. People draw stronger inferences than they should from prominent information. So, if a black man shoots someone, they infer that blacks are more likely to shoot people. But they fail to draw inferences from the millions of everyday ordinary acts of black people. This problem becomes especially severe if groups are segregated from each other. Then, acts of violence are likely to be disproportionately the only times that whites see blacks, or Jews see Arabs.
2. Framing effects. Say a 6’4” black man who works as doorman shoots someone. People will call this a “black crime,” and draw inferences. But why not call it a “tall crime”, and infer that tall people are a menace? Or a "doorman crime"? There are fewer tall people or doormen than black ones, so – on this datum – the proportion of tall people or doormen who are criminals is higher than the proportion of blacks. Why focus on colour, unless it is because there's some back-story to warrant doing so?
3. Conservatism bias. Once people have a view, they stick to it to a greater extent that they should. The man who believes blacks are likely to be muggers ignores the huge majority of blacks who don’t mug him.
In practice, then, many instances of statistical discrimination are intellectually wrong. In particular, they exaggerate the differences between blacks and whites.
Which raises the question. Is there a point at which intellectual error becomes a moral error?
* this is unrealistic, but it probably biases the figures against my point. And I’ll take the Sunday Times figures on blacks at face value, rather than get into issues of racial categorization.