The US Census shows that there are about 300 million people living in the USA.

Suppose that there are 1,000 terrorists there as well, which is probably a high estimate. The base-rate would be 1 terrorist per 300,000 people. In percentages, that is .00033%, which is way less than 1%. Suppose that NSA surveillance has an accuracy rate of .40, which means that 40% of real terrorists in the USA will be identified by NSA’s monitoring of everyone’s email and phone calls. This is probably a high estimate, considering that terrorists are doing their best to avoid detection. There is no evidence thus far that NSA has been so successful at finding terrorists. And suppose NSA’s misidentification rate is .0001, which means that .01% of innocent people will be misidentified as terrorists, at least until they are investigated, detained and interrogated. Note that .01% of the US population is 30,000 people. With these suppositions, then the probability that people are terrorists given that NSA’s system of surveillance identifies them as terrorists is only p=0.0132, which is near zero, very far from one. Ergo, NSA’s surveillance system is useless for finding terrorists.

Suppose that NSA’s system is more accurate than .40, let’s say, .70, which means that 70% of terrorists in the USA will be found by mass monitoring of phone calls and email messages. Then, by Bayes’ Theorem, the probability that a person is a terrorist if targeted by NSA is still only p=0.0228, which is near zero, far from one, and useless.

Suppose that NSA’s system is really, really, really good, really, really good, with an accuracy rate of .90, and a misidentification rate of .00001, which means that only 3,000 innocent people are misidentified as terrorists. With these suppositions, then the probability that people are terrorists given that NSA’s system of surveillance identifies them as terrorists is only p=0.2308, which is far from one and well below flipping a coin. NSA’s domestic monitoring of everyone’s email and phone calls is useless for finding terrorists.

NSA knows this. Bayes’ Theorem is elementary common knowledge. So, why does NSA spy on Americans knowing it’s not possible to find terrorists that way? Mass surveillance of the entire population is logically sensible only if there is a higher base-rate. Higher base-rates arise from two lines of thought, neither of them very nice:

1. McCarthy-type national paranoia;
2. political espionage.

The whole NSA domestic spying program will seem to work well, will seem logical and possible, if you are paranoid. Instead of presuming there are 1,000 terrorists in the USA, presume there are 1 million terrorists. Americans have gone paranoid before, for example, during the McCarthyism era of the 1950s. Imagining a million terrorists in America puts the base-rate at .00333, and now the probability that a person is a terrorist given that NSA’s system identifies them is p=.99, which is near certainty. But only if you are paranoid. If NSA’s surveillance requires a presumption of a million terrorists, and if in fact there are only 100 or only 10, then a lot of innocent people are going to be misidentified and confidently mislabeled as terrorists. […]

http://www.lewrockwell.com/orig7/rudmin1.html 

This entry was posted on Monday, July 10th, 2006 at 5:18 pm and is filed under Beautiful, The Facts.