# Racial Profiling vs Description of the Suspect

You are a policeman in a car chase of a criminal wearing globes and a mask, the most likely scenario according to statistics is that the criminal is a white person. Then the car stops in front of a bar and the criminal rushes in getting rid of the globes, mask and changing his clothing. You enter the bar and you see a white guy and a non-white guy. Who should you question first? The non-white guy. Racism? No, Bayes’ Theorem.

According to the US Department of Justice racial profiling is defined as:

Any police-initiated action that relies on the race, ethnicity, or national origin rather than the behavior of an individual or information that leads the police to a particular individual who has been identified as being, or having been, engaged in criminal activity.

A key part in this definition is where it justifies the police-initiated action when there is information that leads to a particular individual. In other words, if there are witnesses saying that the thief was a barefooted blond white little girl wearing a green blouse and a red tutu then going after girls looking like that would not be considered racial profiling but simply checking on the description of the suspect.

But how about if the police-initiated action is not based on information coming from witnesses but in information coming from statistics? Is information coming from statistics still information according to the definition of the US Department?

Is it racial profiling when police double check in the airports guys coming from Middle East countries based on statistical evidences from recent history? There are situations where profiling works amazingly well; for example, if China had a problem with illegal white men immigration in their country, asking white men for papers would be a very efficient strategy to solve the problem since very few white men happen to be Chinese citizens. Would anyone reasonable say it is racist to ask white men for papers in this scenario? Yet, this is exactly what happens in Germany: it is illegal to ask the passport to someone just because he or she does not look German; it’s racist.

But instead going into an endless debate on whether racial profiling is moral or immoral I’d rather figure out first whether it works for general crimes and, if it does, how well it does work since, in fact, checking out how well it works might help us to figure out how immoral it is.

So to find out how well racial profiling works for general crimes it would be good to know the probability to be a criminal if you belong to a particular racial group, that is:

$P(Criminal | Race)$

Some might feel tempted to extract those probabilities from the inmate population statistics but those statistics give us an estimation of the probability to belong to a particular race group if you are already a criminal, that is:

$P(Race | Criminal)$

Nonetheless, using Bayes Theorem we have that:

$P(Criminal | Race) = P(Race | Criminal) P(Criminal) / P(Race)$

Unfortunately it is not easy to estimate P(Criminal). Though we know how many people we have in jail we do not know how many are applying for a place in it. But fortunately, since its value is a constant it still will allow us to calculate the proportions among those probabilities, that is, we will know how much likely is to be a criminal given a race compared to other races.

Sometimes data happens to be not politically correct and in many places gather statistics about race is consider itself racist. Fortunately it seems to be fine to gather statistics about nationality and, since many countries are racially quite homogeneous, using nationalities will give us a good estimation of how good racial profiling is.

# Results for the Spanish region of Catalonia

Here are the results for the year 2011 in the Spanish region of Catalonia. The data used for the calculations was gathered from official sources.

*In Spain Africans are mainly from the Maghreb region, Americans from Latin American Countries and Asians from China.

 Spain Europe EU Europe Non-Eu Africa* America* Asia* Nationality if Criminal 54.5% 6.5% 2.6% 20.1% 15.3% 1.1% Criminal if Nationality 1.1 2.6 5.9 7.9 5.1 1

This results show that If the only thing we know about a person is that he/she is a criminal in Catalonia, then there is a 54.5% chances that his/her nationality is Spanish. However, if we have come down to two suspects (remember the example in the intro) and one of them is Asian and the other one is from North Africa, then the probability that the North African is guilty is 7.9 higher than the Asian suspect.

# The Calculations

We will assume that criminality is homogeneous among nationalities to simplify the interpretation, otherwise we should consider facts like pickpocketing or drug related crimes are more common among some nationalities than others.

The formula we would like to have is:

$P(Criminal | Race) = P(Race | Criminal) P(Criminal) / P(Race)$

But since we don’t have statistics about race we will approximate this with

$P(Criminal | Nationality) = P(Nationality | Criminal) P(Criminal) / P(Nationality)$

As I explained before we cannot calculate P(Criminal | Nationality) because we cannot easily estimate P(Criminal) but, we do not actually need this to compare nationalities among them. To calculate the criminality proportion given nationalities N1 and N2 we simply need divide their ratios:

$\frac{P(C|N2)}{P(C|N1)} = \frac{P(N2/C)P(C)/P(N2)}{P(N1/C)P(C)/P(N1)} = \frac{P(N2/C)/P(N2)}{P(N1/C)/P(N1)}$

And therefore we do not need P(C) anymore. So following the proportions calculated this way and shown in the table and pie chart above, we should inquire people in the following order to maximize the chances to catch a criminal per inquire: Africans, Europeans (Non-EU), Americans, European (EU), Spaniards, Asians.

# Profiling Strategy

So, if the only thing you know about a person is that he is a criminal then the most likely nationality is Spaniard with a 54.5% chances to be so. Knowing this, should we investigate first Spaniards? No, and this is why.

An investigation is a resource limited task, meaning that you cannot investigate a whole nation but just a few candidates. Since this is so, what we want is to maximize the chances to catch a criminal with every inquire.

When police question someone they don’t know whether he is a criminal or not, so P(Nationality | Criminal) has no use, we need  P(Criminal | Nationality) and, with this information and the formula for the expected value of a Geometric Distribution, we would know that the expected number of times we have to check a nationality before we catch a criminal would be 1/P(Criminal | Nationality).

A practical example; let’s imaging we have to trust someone in Barcelona (for example with our camera to take a picture) and we only know his nationality, no other background check is allowed, then our safest option would be an Asian or a Spanish guy since they are around eight times less likely to be a criminal than a African (Note that Africans in this context means mainly Maghreb region, black Africans happen to be a rather peaceful community in Spain) , 6 times less likely than an European from a non EU country, five times less likely than an American and three times less likely than other Europeans.

It is important to realize that whether racial profiling has any practical use depends on how big P(Criminal) is, for example, if the probability for a Chinese person to be a criminal is 10% and for an African is 80% then racial profiling totally pays off and it would be absolutely reasonable. On the other hand, if the probabilities were 0.000001% vs 0.000008%, though it would still be 8 times more likely for an African to be a criminal, the chances for either suspect to be one would be really low and, therefore, we could begin considering social issues; in this case racial profiling could be hardly justified and consequently it could be argued it is racist.

But P(Criminal) does not only change from country to country or even from city to city, it does change a lot from neighborhood to neighborhood! Which makes difficult for anyone to switch off the racial profiling mindset.