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.
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).
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
- 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.
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.
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.
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:
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.
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.
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.
[send him mail] is Professor
of Social & Community Psychology at the University of Tromsø