Art Carden  

Sundry Observations on Statistical Discrimination and Terrorism

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There are a lot of great comments on my last post, "Better Living Through Statistics: Muslim Terrorists Edition." A few observations:

That Muslims are far more likely to be terrorists than others is barely relevant to our day-to-day lives given that we live in a world where almost no one is a terrorist. p(Terrorist|Muslim) might be much, much higher than p(Terrorist|non-Muslim), but in a world where both are maybe a few one-hundredths or one-thousandths of one percent, that information probably isn't very informative or a sufficient justification for looking skeptically at someone wearing traditional Muslim garb in a grocery store or on a plane. The fundamental problem is that people dramatically over-estimate the likelihood of terrorism.

If p(Muslim|Terrorist) is 95.3%--the number from Easterly's post; I haven't verified it, but for the sake of the argument, let's assume it's accurate--and there has been a terrorist attack, then yes, the terrorist was probably a Muslim. Some commenters are absolutely right to point this out, but this doesn't mean we should be suspicious of Muslims in immigration policy, security policy, or day-to-day life.

Consider sex crimes like child molestation or rape. I don't have estimates in front of me but my impression is that p(male|child molester) and p(male|rapist) are both pretty high. Therefore, it's probable that the perpetrator was a male given that a child has been molested or given that someone has been raped. Given that there are so many men and so few child molesters and rapists among them, you're looking for a needle in a very large haystack. Similarly, Muslim terrorists are needles in very large haystacks given that there are so many Muslim non-terrorists.

Unfortunately, I agree with Tyler Cowen's claim even though I hope he's wrong: "There is a good chance these events doom immigration reform, by the way." Given that there are so few terrorists to begin with, there's no reason it should.

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COMMENTS (22 to date)
Ken B writes:

You mentioned profiling. The word has connotations, it suggests situations unlike "ordinary life", things like boarding planes. So "ordinary life" points are frankly otiose.

Your first post purported to be about good statistical reasoning. That is what I objected to. To suggest that anyone who really understands Bayes's Theorem would on that basis oppose profiling is a remarkable argument.

ed writes:

I'm still confused by your argument.

If, say, P(Muslim-immigrant|terrorist) = 90%, then doesn't it follow that we could cut future terrorism by close to 90% by not letting in any Muslim immigrants?

Perhaps you are arguing that terrorism is just not important enough to justify keeping all those people out, from a moral standpoint?

What if there is a cap on total immigration, so that denying Muslim immigrants would allow us to accept more non-Muslim immigrants, would that change your argument?

(Yes I realize that native-born Muslims can also be terrorists, and that it is not always easy to prevent people from entering the country. I'm just trying to clarify the argument in the post.)

Faré writes:

What that means is that being muslim might make you slightly more suspect but by itself still pretty non-suspect. Constantly following radical islamic websites might make you somewhat more suspect. Hopefully, whatever profiling happens should happen based on a collection of traits that together bring significant probability of suspicion, rather than on one slim indicator.

More interesting is the fact that the elder terrorist was reportedly investigated by the FBI based on profiling, and they had many interviews with him over the years. Assuming they aren't complicit, this didn't help them stop him on time. All that invasion of privacy was for nothing!

Delphin writes:

So we learn this guy had accomplices. It's a waste to spend more police resources looking into his young Muslim male acquaintances rather than his old female Amish ones? That seems to be your argument, because if it's wrong to use his religion, since by itself it has low correlation, it must be wrong to use age, sex, nationality, or location as they all have low correlations too.

Pseu writes:

In the calculation, one must factor in severity as well as frequency. One additional terrorist cancels out the benefits of rather a large number of decent, hard-working immigrants.

BC writes:

It's unnecessary to consider sex crimes to find analogies to finding Muslim terrorist needles in Muslim haystacks. p(male|terrorist) is probably higher than p(male|molester) and probably higher than p(Muslim|terrorist) for that matter. What would be the rationale for being suspicious of Muslims in, say, immigration policy but not for being suspicious of males? For that matter, p(non-handicapped|terrorist) is probably even higher than p(male|terrorist) and p(Muslim|terrorist). Does that mean that only handicapped people should be allowed to immigrate?

The true irrationality is not in mis-application of Bayes rule. It's in the selection of classification criteria (religion, ethnicity, gender, ideology, occupation, handicapped status, etc.). If a terrorist or mass killer happens to be a white Muslim, as was the case for the Boston Marathon bombers, then he's Muslim. If he happened to be a black Christian, then he would be black, not Christian. If he happened to be a white Christian postal worker, then he would be a postal worker. Because one can classify people along a myriad of dimensions, it is almost always possible to select a classification criteria by which someone exhibiting a negative characteristic (e.g., terrorist) belongs to a group that does not include oneself. Then, one can rationalize discriminating against that group based on "objective" evidence.

For those old enough to remember, Ben Johnson was a great Canadian sprinter who shattered world records in the 100-meter dash...until he tested positive for steroids. Then, he became Jamaican-born sprinter Ben Johnson.

Steve Sailer writes:

No, sorry, but you need to think this through in a more sophisticated manner. Consider a probability distribution of evidence of acts demonstrating hostility toward the host country, with blowing up the Boston Marathon at the far, far right edge of the curve. That Muslims, especially Muslims of certain ethnicities, such as Chechen, are wildly overrepresented on the right side of this bell curve suggests that their overall population is shifted to the right on the underlying bell curve of hatred for the host population.

Similarly, Muslim suicide bombers in England are just extreme examples of the high hostility and bad behavior of Muslims toward the English.

Steve Sailer writes:

Jacob A. Geller writes:

The bombers' uncle, Ruslan Tsarni, gave reporters a forceful and passionate defense of immigration, whether he knew it or not, when they asked him about how he felt about America.

He said: "I respect this country, I love this country, this country, which gives a chance to everybody else to be treated as a human being, and just to BE human being, to FEEL yourself human being. That's what I feel about this country."

You can watch the video here):

Also notice his response to the reporters' silly question about why his brother's family lived in Cambridge: "They LIVED there."

Jacob A. Geller writes:


You write on your blog that since 2 out of 200 Chechens in the United states are apparent terrorists, that figure (1%) constitutes a "rebunking" of the stereotype that Chechens are terrorists.

Two questions:

1) Wouldn't you agree that 1% is far too tiny a figure to "rebunk" a "stereotype"? Doesn't a stereotype, in order to have *any* validity, have to apply to a much larger fraction of the population than 1%?

2) Austria has 30,000 Chechens. How many terrorist attacks has Austria suffered at the hands of Chechens, and what does that say about the usefulness of the Chechen-terrorist stereotype?


Justin writes:

By invoking the low apriori probability of a person being a terrorist you're conflating the profiling subject with whether one should screen for terrorists at all.

But *given* that one screens for terrorists, how does one allocate resources?

Given that an adoption agency is screening for child molesters, how do they allocate resources? They are more suspicious of males, and rightfully so.

Richard writes:

On the one hand, terrorism is so incredibly rare that it simply wouldn't matter much if all terrorists were Muslim. How many Americans have been killed by Muslim terrorists in the last 20 years? We have 9/11, this Boston bombing, Fort Hood. So let's estimate 3,500 excess deaths. Let's say that the average life is worth $4 million, which is within the normal range for analysis of regulations.

How much has Muslim immigration cost the United States in lives? My calculations give me $14 billion over twenty years, or $700 million a year. The benefits of Muslim immigration would have to be balanced at least against that $700 million/year costs. (this doesn't consider the indirect costs of terrorism like less civil liberties protection, the Iraq War, etc., but the overreaction can be seen as the result of bad policy more than terrorism itself).

Now, if you take 9/11 out of the equation, the number drops a lot. Let's limit our analysis to the last ten years. 4 were killed by the Chehen terrorists, 13 at Fort Hood, and that's about it. Fort Hood and the Chechens also wounded a lot of people. So let's say that Muslim terrorism has caused the equivalent of 50 deaths over the last ten years, and still use $4 million as the value of a life. Then Muslim immigration has cost us $200 million over the last ten years, or $20 million a year. That number also should be taken into account in any cost/benefit analysis of Muslim immigration, though it's obviously much less than the $700 million/year figure we get by including 9/11.

So I think that one could quite plausibly argue that the threat of terrorism justifies more restrictions on Muslim immigration. How much it should matter depends to a great extent on how likely you think another 9/11-like attack is.

Jeff writes:

Richard, your analysis understates the cost of 9/11 quite a bit by only including lives lost. How much would the World Trade Center have fetched if you put it on the market back in September 2001? Billions, I'm sure. That's some pretty valuable real estate in lower Manhattan. Not to mention the cost of cleaning up the wreckage. The four jets that crashed were worth quite a bit of money, also; tens of millions, at least. Throw in the cost of the subsequent investigation, and you're talking billions more, maybe hundreds of billions. You could also include the cost of the DHS, created in response to 9/11 and carrying a budget of ~61 billion for 2013...things are looking pretty expensive.

If those are the costs, it'd be nice if a Muslim immigrant or three invented a new stem cell therapy or perfected cryogenics or steered an asteroid off a collision course with earth or something.

Richard writes:

Yeah, that's a good point. It therefore seems that even a tiny chance of major terrorist attacks leads one to the conclusion that the country should restrict Muslim immigration, especially when their numbers can easily be made up by non-Muslim immigrants if someone truly believes that the nation needs immigrants.

This entire analysis assumes, of course, that one only cares about the well-being of current Americans. If one takes Bryan Caplan's position that we should care about all people of the world roughly equally, than the benefits to Muslim immigrants may outweigh the costs to the United States. On the other hand, even if one agrees with Caplan on this point, you could still say that if the total number of immigrants were to remain constant, we may decide to let in fewer Muslims and more Christians, Buddhists, etc. based on statistical discrimination. But I think Caplan would probably favor an immigration policy that let in the neediest people in the world even if the total number of migrants was kept limited.

NZ writes:

As I said in my comment to a previous post--and this sort of ties in with Steve Sailer's comment above--the Muslims who actually do the terrorizing are only one part of the equation.

Child molesters are usually able to act alone, even with close friends and family who staunchly oppose child molestation and would report the child molester (or worse) if they knew about his deeds.

Acts of terrorism, however, frequently require planning, materials, funding, direction, etc. and this often comes from outside parties and networks. Therefore, you can't just ask "What's the probability that a given Muslim is a terrorist?" You have to ask "What's the probability that a given Muslim will either support or fail to make an effort to stop terrorism by a fellow Muslim?"

Steve Sailer writes:

"1) Wouldn't you agree that 1% is far too tiny a figure to "rebunk" a "stereotype"?"

What's your Bayesian prior?

We ought to know a lot about Chechens before this: they have long been considered among the most archetypal examples of the mountain bandit culture archetype. Pushkin, Lermontov, and Tolstoy all admired them as brave psychos. Over the last generation, this tiny nationality has built a track record of impressively daring and/or suicidal/homicidal attacks on great powers, such as numerous spectacular raids on Russia like the seizing all those little kids in Beslan. Chechen volunteers appear to have been the core of the courageous rearguard who inflicted a massive strategic defeat upon the United States at Tora Bora a decade ago, allowing Osama bin Laden to escape.

Now, we have a spectacular example of a full 1% of all Chechens in America acting Checheny.

Steve Sailer writes:

The other dimension is that a propensity toward terrorism correlates with propensities toward gangsterism, violence, and fraud. There are large skill sets that overlap among terrorist, freedom fighter, and gangster.

And, unsurprisingly, that turns out to be true for Chechens, who have nasty mafias in Russia.

The Bomb Brothers family has a long track record of domestic violence, shoplifting, and perhaps hit-and-run. Add a few more Chechens in the country, and there would be a very scary Chechen Mafia.

Look, the Obama Administration accepts my logic -- they've had a policy of largely keeping Chechens out of the United States.

Brian writes:


But you have to count the $4-million value added per Muslim immigrant who enters the U.S. Given that the number of Muslims who enter far outweighs the number they kill, it follows that there's no justification for keeping them out. And that's true for any group that creates more value than it destroys, which would be, well, every group, including Chechens. The only valid discriminator would be on specific individuals, who can very easily have a high probability of doing more harm than good.

Methinks writes:

When an event like this befalls us poor humans, I have observed that four things follow closely and afflict even those who ought to know better:

1.) The probability of you or your loved ones becoming victims of such acts of violence becomes severely exaggerated in one's imagination.

2.) The probability of being able to stop similar events in the future becomes severely exaggerated in one's imagination.

3.) The cost of attempting to reduce an infinitesimally small probability to something slightly more infinitesimally small is hugely diminished in one's imagination.

4.) Every barbaric feeling toward members of other tribes is loving nurtured.

Reality be damned.

pyroseed13 writes:

To buttress Jeff’s point, I would add that you also need to another major cost of 9/11, one that Garrett Jones aptly pointed out on this blog: fighting a war. If we have the capabilities to foil terrorist plots, such as through profiling, then we might find that our society would have less of collective desire to “get the bad guys” by invading other countries.

I also think Art is straw-manning a bit in this post. He seems to assume, like many other anti-profilers, that profile advocates only want to screen based on one characteristic. However, the profile is not simply “Muslim” but “young, Muslim, and male.” Determining who is Muslim requires the ability to profile based on several characteristics (clothing, skin color, ethnicity, country of origin). We could also expand our profile to include behaviors (does this person seem unusually nervous?).

I assume that Art would be in favor of abolishing the TSA, and would prefer to leave security in airports to the private sector. What I would like to know is if he thinks this would actually lead to his preferred outcome (no ethnic or religious profiling, perhaps no screening at all?) or would instead to lead to a market in which airports respond to their customers “irrational” fears of terrorism by profiling those who are more likely than others to be terrorists? I find it difficult to believe that airports would be able to profitably subject all of their customers to a rigorous screening process, but since people post-9/11 value safety when they travel, I don’t think airports would eliminate all security checkpoints.

Krishna writes:

Say, as a boy you were given $10 to go get 10 lottery tickets, all tickets being priced at $1 each. The shop sells two types of lottery tickets, both carrying the same amount of prize money, the probablility of winning is indeed minuscule on both, but one offers a probability of winning which is 247000 times the probability of winning the other. How would you split the $10 between the two types of lottery tickets?

ohwilleke writes:

A big part of the 1% of Chechens are terrorists analysis is that it involves look elsewhere effects. Coincidences in general, look coincidental, in part because you haven't considered all of the possible ways in which events that would look equally coincidental and improbable can come up. For example, two brothers who carry out of a terrorist act have to come from some country. Even if that country is totally random, the percentage involvement of people from any given country will seem much greater after the fact because you ignore all of the other countries where a similar coincident could have taken place. You ignore Chechen ex-pat populations elsewhere.

Conversely, if you wanted to make the 1% larger, you could confine it to ethnically Chechen men, aged 19 to 26, born abroad, who have a family member who has lived in the Caucasus mountains region the last twelve months who have martial pass-times like boxing and wrestling - maybe that gets you to 33% to 50%.

One also ignores the fact that even pro-terrorist Chechen Islamists may be scratching their heads to figure out what bombing the Boston Marathon without a claim of responsiblity does to advance their cause. There is no symbolic link there. The only people who really seem convinced that this made any sense are the Westboro Baptists. Criminals and would be terrorists routinely do stupid things that make sense only to them which makes them inherently unpredictable.

There is a percentage in predicting things only when the data set is large enough to make statistically powerful predictions which we have for all sorts of ills in our society (from workplace accidents to drunk driving deaths to teen pregnancies) but when the data sets are small, this approach falls apart.

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