A federal judge recently ruled that Sheriff Joe Arpaio was indulging in illegal racial profile. The blogs have been ablaze and a surprising number of people have been suggesting that the debate is between "political correctness" (a reference perhaps to the moral imperative and the constitutional requirement to be racially unbiased) and a very effective strategy. I have to admit that this isn't the first time I have heard this. People as diverse as Bill Maher, Rush Limbaugh and Ann Coulter have all advocated racial profiling - for illegal immigrants and terrorists. What is fascinating is how these people and the people on the blogs have been arguing for profiling. Their argument can basically be summarized as follows:
At issue are the underlying conditional probabilities.
To explain, let's do a thought experiment.
In 2011, according to the FBI, there were 4.7 murders per 100,000 people. Imagine for our experiment that all these murders are committed by African Americans. They are not. But, this extreme example will illustrate the point. If you follow the logic that Maher, Coulter and others employ, shouldn't you profile African Americans? After all, if you have a murder, by these statistics, the probability that the perpetrator is an African American is 100% - i.e. certain. Seems logical, right?
On the other hand, consider this. About 12.4% of US citizens are African American. That means in those 100,000 people, 12,400 are African American. So, in these statistics of every 12,400 people, <5 would be murderers and the remaining 12,395+ would not.
This is conditional probabilities in action. Even with a conditional probability of 100% for being African American given that we have a murder, the probability that you have a murderer given the person is African American is 0.038%, i.e. basically insignificant. 99.62% of African Americans in our extreme thought experiment would be innocent.
Since the percentage of African American perpetrators of murders is much smaller, the actual probability that an African American is innocent is much higher.
Let's consider another case. It turns out that if you have a mass shooting in the US, the perpetrator is more likely than not to be a white male. In fact, of the 14 mass shootings in 2012, 12 of them had a white male involved. Yet, the fact remains that no one is likely to want to round up all white men. For that matter, it is actually true that Asians are over represented in the list of mass shooters. Yet, of the millions of Asians in the US, as far as I can tell, the number of mass shooters is just a handful. That means that the probability that a randomly selected Asian is a mass shooter is probably less than 0.01%.
Or take another one. Let's say every terrorist attack all over the world was perpetrated by a Muslim (they aren't ... but again, this extreme version will help illustrate the point), i.e. we assume that the probability that the perpetrator is Muslim given that there has been a terrorist attack is 100%. There are over 1.6 billion Muslims in the world. There are likely not more than a few thousand terrorist attacks around the world a year. Assume there are 10,000 terrorist attacks a year (this is much much higher than the actual number which is rarely more than 1-2 per day). Over the last decade, there would have been about 100,000 attacks. Even then, the probability that a randomly selected Muslim would be a terrorist would be 0.006%, i.e. out of every 100,000 Muslims you screen, 99,994 would be innocent. Again, remember, I grossly overstated the number of terrorist attacks.
What does this mean?
This does not automatically mean that profiling can never work. It might. While most forms of profiling are likely to have minuscule predictive ability as standalone metrics for guilt, combined with other factors, it might have more of an implication. However, the question we should ask ourselves is whether the criteria we are using to identify likely criminals has sufficient nexus with the crime to be a strong indicator. If not, profiling is likely to be very inefficient, create obvious gaps in our security apparatus and due to a high false positive rate, will likely abrogate the Constitutional rights of the majority of those targeted. The mistake these commentators make is that they use the wrong conditional probability and therefore potentially draw the wrong conclusion about how to tackle the situation.
Most terrorists are Muslim so you should single out Muslims for extra scrutiny OR most illegal immigrants are Hispanic, so you should single out Hispanics for extra scrutiny.When I first encountered these arguments, I was amused but dismissed it, but having seen the frequency with which these arguments seem to arise, I decided to write about the framing of the argument.
At issue are the underlying conditional probabilities.
To explain, let's do a thought experiment.
In 2011, according to the FBI, there were 4.7 murders per 100,000 people. Imagine for our experiment that all these murders are committed by African Americans. They are not. But, this extreme example will illustrate the point. If you follow the logic that Maher, Coulter and others employ, shouldn't you profile African Americans? After all, if you have a murder, by these statistics, the probability that the perpetrator is an African American is 100% - i.e. certain. Seems logical, right?
On the other hand, consider this. About 12.4% of US citizens are African American. That means in those 100,000 people, 12,400 are African American. So, in these statistics of every 12,400 people, <5 would be murderers and the remaining 12,395+ would not.
This is conditional probabilities in action. Even with a conditional probability of 100% for being African American given that we have a murder, the probability that you have a murderer given the person is African American is 0.038%, i.e. basically insignificant. 99.62% of African Americans in our extreme thought experiment would be innocent.
Since the percentage of African American perpetrators of murders is much smaller, the actual probability that an African American is innocent is much higher.
Let's consider another case. It turns out that if you have a mass shooting in the US, the perpetrator is more likely than not to be a white male. In fact, of the 14 mass shootings in 2012, 12 of them had a white male involved. Yet, the fact remains that no one is likely to want to round up all white men. For that matter, it is actually true that Asians are over represented in the list of mass shooters. Yet, of the millions of Asians in the US, as far as I can tell, the number of mass shooters is just a handful. That means that the probability that a randomly selected Asian is a mass shooter is probably less than 0.01%.
Or take another one. Let's say every terrorist attack all over the world was perpetrated by a Muslim (they aren't ... but again, this extreme version will help illustrate the point), i.e. we assume that the probability that the perpetrator is Muslim given that there has been a terrorist attack is 100%. There are over 1.6 billion Muslims in the world. There are likely not more than a few thousand terrorist attacks around the world a year. Assume there are 10,000 terrorist attacks a year (this is much much higher than the actual number which is rarely more than 1-2 per day). Over the last decade, there would have been about 100,000 attacks. Even then, the probability that a randomly selected Muslim would be a terrorist would be 0.006%, i.e. out of every 100,000 Muslims you screen, 99,994 would be innocent. Again, remember, I grossly overstated the number of terrorist attacks.
What does this mean?
This does not automatically mean that profiling can never work. It might. While most forms of profiling are likely to have minuscule predictive ability as standalone metrics for guilt, combined with other factors, it might have more of an implication. However, the question we should ask ourselves is whether the criteria we are using to identify likely criminals has sufficient nexus with the crime to be a strong indicator. If not, profiling is likely to be very inefficient, create obvious gaps in our security apparatus and due to a high false positive rate, will likely abrogate the Constitutional rights of the majority of those targeted. The mistake these commentators make is that they use the wrong conditional probability and therefore potentially draw the wrong conclusion about how to tackle the situation.
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