25 March, 2004: But me no buts

[ Home page | Web log ]

It is a commonplace among racists of the `I'm not a racist, but...' variety to say things like, ``The police correctly say more black people commit crime so more are stopped.'' This is a misconception which needs to be squashed.

(Usually in this sort of discussion made-up attributes, for instance `tall' and `short', are used, rather than talking about actual ethnicities or whatever; presumably this is to avoid offending the easily-offended. Since the motto of this web log may as well be `offending the easily-offended since 2002', I won't bother.)

Suppose that there are w white people and b black people in some population. Suppose further that every so often a crime is committed, and that the victim is able accurately to report the ethnicity of the perpetrator (assume that these are muggings, or `hot' burglaries, or whatever). W crimes are recorded in which the perpetrator is white, and B in which the perpetrator is black.

Imagine that B > W; that is, more crimes are committed by black criminals than by white criminals. (In some areas of the country this is the case, we are told; these, presumably, are mostly areas with more black people than white people.) What does this tell us about the likelihood that an arbitrary black person -- such as might randomly be stopped by a police officer -- is a criminal, relative to the likelihood that an arbitrary white person is?

The answer: absolutely nothing.

The reason (which should be obvious) is that different criminals commit different numbers of crimes; the difference, that is, between `more black people commit crime' and `black people commit more crime'. These two statements are not the same.

As an extreme case, suppose that every white person commits one mugging a year, and one black person commits some large number N > w of muggings, while the rest are law-abiding. In this case, the probability of a randomly-selected white person being a criminal is 1, but the probability of a randomly-selected black person being a criminal is 1/b, a much smaller number. That is to say, in this case it is b times more likely that a random white person stopped by a police officer is a criminal than a black person is even if there are more crimes committed by black people than by white people. Without additional information about the numbers of crimes committed by individual criminals of each ethnicity, aggregate data about numbers of crimes won't tell us anything about the `propensity to crime' of white and black people.

In reality, the situation is not as extreme as in the example. Now we encounter a separate problem. Suppose that both black and white people commit crimes at the same rate, with the probabilities that an individual black or white person is a criminal being equal. In that case, the number of crimes committed by people of each ethnicity will be in proportion to the ratio of ethnicities in the general population.

Imagine that the police attempt to control crime by stopping and searching people at random (perhaps they look for stolen goods or something). Suppose further that the police are racist and stop ten times as many black people as white people. In this case, even if black and white people are equally likely to be criminals, the police will still find ten times as many black criminals as white, because everyone they stop has an equal chance of being a criminal, and they are stopping ten times as many black as white people. And, worse, their tactic is self-reinforcing, since an ill-informed police officer (or politician) might infer from the statistics that -- because so many black people are being arrested -- even more black people should be stopped and searched. But of course this is an incredibly inefficient (as well as unfair) way for the police to try to cut down on crime, since they are letting the (usually much larger) white segment of the population get away with much shallower scrutiny. And it might lead a lazy observer to conclude that black people are more likely to commit crime, while in fact what they're seeing is the effect of racist policing.

Now, all of this is just a model. The police don't investigate crime solely by stopping people at random, and there are lots of other relevant factors in criminality, some of which are correlated with race (for instance, poorer people are more likely to be criminals -- at least of the Bill the Burglar variety, if not the Martha Stewart kind -- and, sad to say, history has left black people on average poorer than white). As with so many things, the real situation is very complicated. But that's all the more reason not to make generalisations like the one which started me off on this rant.

Copyright (c) 2004 Chris Lightfoot; available under a Creative Commons License.