The Bush administration

and the National Security Agency (NSA) have been secretly monitoring

the email messages and phone calls of all Americans. They are doing

this, they say, for our own good. To find terrorists. Many people

have criticized NSA’s domestic spying as unlawful invasion of privacy,

as search without search warrant, as abuse of power, as misuse of

the NSA’s resources, as unConstitutional, as something the communists

would do, something very unAmerican.

In addition,

however, mass surveillance of an entire population cannot find terrorists.

It is a probabilistic impossibility. It cannot work.

What is the

probability that people are terrorists given that NSA’s mass surveillance

identifies them as terrorists? If the probability is zero (p=0.00),

then they certainly are not terrorists, and NSA was wasting resources

and damaging the lives of innocent citizens. If the probability

is one (p=1.00), then they definitely are terrorists, and NSA has

saved the day. If the probability is fifty-fifty (p=0.50), that

is the same as guessing the flip of a coin. The conditional probability

that people are terrorists given that the NSA surveillance system

says they are, that had better be very near to one (p=1.00) and

very far from zero (p=0.00).

The mathematics

of conditional probability were figured out by the Scottish logician

Thomas Bayes. If you Google "Bayes’ Theorem", you will

get more than a million hits. Bayes’ Theorem is taught in all elementary

statistics classes. Everyone at NSA certainly knows Bayes’ Theorem.

To know if

mass surveillance will work, Bayes’ theorem requires three estimations:

- The base-rate

for terrorists, i.e. what proportion of the population are terrorists; - The accuracy

rate, i.e., the probability that real terrorists will be identified

by NSA; - The misidentification

rate, i.e., the probability that innocent citizens will be misidentified

by NSA as terrorists.

No matter how

sophisticated and super-duper are NSA’s methods for identifying

terrorists, no matter how big and fast are NSA’s computers, NSA’s

accuracy rate will never be 100% and their misidentification rate

will never be 0%. That fact, plus the extremely low base-rate for

terrorists, means it is logically impossible for mass surveillance

to be an effective way to find terrorists.

I will not

put Bayes’ computational formula here. It is available in all elementary

statistics books and is on the web should any readers be interested.

But I will compute some conditional probabilities that people are

terrorists given that NSA’s system of mass surveillance identifies

them to be terrorists.

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:

- McCarthy-type

national paranoia; - 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.

The ratio of

real terrorists to innocent people in the prison camps of Guantanamo,

Abu Ghraib, and Kandahar shows that the US is paranoid and is not

bothered by mistaken identifications of innocent people. The ratio

of real terrorists to innocent people on Bush’s no-fly lists shows

that the Bush administration is not bothered by mistaken identifications

of innocent Americans.

Also, mass

surveillance of the entire population is logically plausible if

NSA’s domestic spying is not looking for terrorists, but looking

for something else, something that is not so rare as terrorists.

For example, the May 19 Fox News opinion poll of 900 registered

voters found that 30% dislike the Bush administration so much they

want him impeached. If NSA were monitoring email and phone calls

to identify pro-impeachment people, and if the accuracy rate were

.90 and the error rate were .01, then the probability that people

are pro-impeachment given that NSA surveillance system identified

them as such, would be p=.98, which is coming close to certainty

(p=1.00). Mass surveillance by NSA of all Americans’ phone calls

and emails would be very effective for domestic political intelligence.

But finding

a few terrorists by mass surveillance of the phone calls and email

messages of 300 million Americans is mathematically impossible,

and NSA certainly knows that.

May

26, 2006

Floyd Rudmin

[send him mail] is Professor

of Social & Community Psychology at the University of Tromsø

in Norway.