The cry for security theatre, once more, with feeling continues.  From the Atlantic piece:

The minute Abdulmutallab’s father walked into a U.S. Embassy with news that his son was a potential terrorist, the official in charge was duty-bound to see this through. Every scrap of paper and every byte of data on the suspect should have been called up and frozen. That’s why we have embassies. When the information was passed to the first special agent at the CIA, he or she was duty bound to see it through. When the information was passed to the first administrator at the National Counterterrorism Center, he or she, too, was duty bound to see it to the end.

Everyone who read the name “Umar Farouk Abdulmutallab” prior to December 25, 2009 should be reprimanded and fired.

Much has been made of the fact that Abdulmutallab’s father, in a modern Euthyphro dilemma, informed on his own son.  What has been made has generally taken one of two forms:  jokes about how hard it must be for a Nigerian banker to get his proposals taken seriously FOR OUR MUTUAL BENEFIT, and incredulity that when the man was turning in his son we didn’t immediately arrest the young man or at least put him on the no-fly list or revoke his visa.

The second form is an understandable reaction (his son!), but a moment’s reflection on our recent adventures in Afghanistan and Iraq should show the intelligent observer the perils of concluding that someone is a terrorist based on the say-so of a relative, colleague, or acquaintance.   If I recall, this is now one of the many lingering problems because it turns out that when you detain and torture someone based on the say-so of an informant, chances are that person is innocent, and your best case scenario is now hoping you didn’t radicalize a formerly innocent person who now has plenty of reason to hate you.

Now, obviously, no one’s suggested that Abdulmutallab should have been hauled off and tortured, but the point really needs to be made that just because someone says another person is a terrorist doesn’t necessarily mean that they are, and it’s a good thing if the United States doesn’t act like that.   That it was his father who informed on him is fascinating, but not proof of anything particularly.*

All that aside, there’s an interesting puzzle here that’s being overlooked.

Let’s treat the proposition someone is a terrorist as a proposition for which we can gather evidence that warrants belief that the proposition is true.   Let’s treat all the evidence that we can gather — parental informants, ties to radical imams, patterns of study, religion, country of origin, one way ticket, lack of checked luggage** — like a test, and let’s stipulate further that we have a very reliable terrorist test.  If we present the test with the profiles of 100 terrorists, it will correctly identify 99 of them as terrorists.   1% slip through. For simplicity’s sake, it also misidentifies, 1% of the time, an innocent person as a terrorist.

Now suppose a person about whom nothing is known comes to the attention of the powers that be, and they administer the test, and it’s positive for terrorism.

What is the chance that the person really is a terrorist?  Formulate your answer and then follow the jump.

You can’t formulate your answer!  You shouldn’t have tried! You don’t have enough information yet!  Why?  Because you need to know not just the rate of failure for the test, but also the percentage of terrorists in the relevant population!

I don’t know that number.  So let’s make one up.  Suppose out of every million and one hundred people whose cases come to the attention of the powers that be, one hundred of them are terrorists.  The powers that be apply the test to all of the cases very diligently (one might even say that their system works).  They will therefore identify ninety-nine of the terrorists…

… and ten thousand innocent people.

The chance that someone who is identified by the test as a terrorist is in fact a terrorist is, on this model, just under 1%.   Still think the “special agent at the CIA” [sic] is “duty-bound” to see every flag through?  (Won’t that mean he spends more time chasing innocent people and not enough time identifying the real terrorists, absent more information that helps him figure out who is naughty and nice?) Still want to put anyone like this on the no-fly-list automatically with a line of SQL?  There were 56 million international visitors to the U.S. in 2007. Won’t that mean a useless and bloated no-fly list?

The rarer terrorism is, the more false positives there will be.  (Compare: false positives on things like HIV tests.  If you hear hoofbeats, think horsies, not zebras.)

Now, maybe the terrorist tests are more reliable.  Maybe they’re 99.9% reliable.    Maybe 50% of the population who can get visas are terrorists.  (No.)  The point here is that if terrorism is relatively rare, quite a lot of what everyone thinks of as obvious tells will be more likely to pick out an innocent person than a terrorist.  This Nigerian panty-bomber seems like such an outlier (his dad turned him in!), but think of someone like the Ft. Hood shooter.  Well-educated, Muslim, posted angry things on the Internet, no history of violence… hmmm… Neddy?

I don’t say this to exonerate the administration or USCIS or the embassy or the various intelligence agencies, because I know only that I don’t know whether people should be fired, or what went wrong.   I find it an interesting question, however, to consider what happens if we simply don’t have the ability to separate the sheep from the goats. Do we ban people from Cuba to prevent Nigerian terrorists from boarding planes? Do we live with the occasional intelligence lapse and prepare for full-body scans at the airports?  How do we value the economic cost?  What if there really isn’t anyone to blame here?

The administration is calling this a systemic failure, and if they’re right, then firing everyone who came into contact with the name “Umar Farouk Abdulmutallab” plus Janet Napolitano just so we can demonstrate seriousness of mind and purpose is at best a useless idea, and at worst an actively harmful one.   If everyone did their jobs right, but a panty-bomber snuck through anyway, you’re firing the very people who are in a good position to tell you how the system failed and how to fix it so that when they do their jobs right in the future, they can catch the bad guy.

* Trivia: one thing USCIS has to deal with periodically is someone who reports their immigrant spouse as a fraud when the marriage sours, usually to get out of spousal support.  To the surprise of many citizens, USCIS doesn’t deport foreigners merely on the say-so of an embittered ex.  To my mind, this is a good thing.

**The Internet is very, very certain that being a young person traveling over the holidays without checked luggage is a classic sign of a terrorist, rather than a classic sign of a young person who really wants to arrive at his destination with his luggage.