As I posted previously, I am highly skeptical that any foolproof system can be developed to screen for potential threats. My previous argument was that in order to have a zero false negative rate for identifying terrorists, it would be impossible to not also have a relatively significant false positive rate. In other words, the only way to guarantee that a terrorist doesn’t board a plane is to not let anyone board. A way to visualize this graphically is with what is called a receiver operating characteristic or ROC curve, which is a plot of the true positive rate versus the false positive rate for a binary classification test as some parameter, usually a discrimination threshold, is changed. Ideally, one would like a curve that jumps to a true positive rate of 1 for zero false positive rate. The area under the ROC curve (AROC) is the usual measure for how good a discriminator is. So a perfect discriminator has AROC = 1. In my experience with biological systems, it is pretty difficult to make a test with an AROC of greater than 90%. Additionally, ROC curves are usually somewhat smooth so that they only reach true positve rate = 1 at false positive rate = 1.
Practicalities aside, is there any mathematical reason why a perfect or near perfect discriminator couldn’t be designed? This to me is the more interesting question. My guess is that deciding if a person is a terrorist is an NP hard question, which is why it is so insidious. For any NP problem, it is simple to verify the answer but hard to find one. Connecting all the dots to show that someone is a terrorist is a straightforward matter if you already know that they are a terrorist. This is also true of proving the Riemann Hypothesis or solving the 3D Ising model. The solution is obvious if you know the answer. If terrorist finding is NP hard, then that means for a large enough population and I think 5 billion qualifies, then no method nor achievable amount of computational power is sufficient to do the job perfectly.