Ryan Wiley is another channel I'm subscribed to, whose videos I generally enjoy.
I was watching his video, "Sam Harris Still Sucks," giving Harris just criticism for his
support for the racial profiling of Muslims at airports.
Harris wrote this back in 2012, in his blog entry called "In Defense of Profiling."
Wiley did a good job of criticizing Harris, but once again, as a Bayesian I saw the blatant
flaw in Harris's thinking that most people might well fall for, but that any Bayesian
worth his salt should spot in a second.
I've heard it said that inside every non-Bayesian there's a Bayesian struggling to get out.
So if you'll allow me, let me help you get in touch with your Inner Bayes and discover
just what is wrong with racial profiling.
It all has to do with that all-important Likelihood Ratio, and how people get it completely backwards.
The idea of racial profiling is, "If I see a person at a US airport, and he's Mulsim,
then he's likely to be a terrorist, since most terrorists are Muslims."
The problem is, they're asking the WRONG question.
The question we want to be asking is, "Given that this person is Muslim, what is the probability
that he is a terrorist?"
But the question racial profiling is based on is, "Given that this person is a terrorist,
what is the probability that he is Muslim?"
Those are two completely different questions.
Let's examine this with some actual numbers.
I couldn't find any data on how many terrorists were actually Muslims, but let's go with the
perception of the profilers and say, hypothetically, that 99% of all terrorists are Muslims.
By making this assumption, we have NOT answered the question.
We've provided an answer to the question, if a person is a terrorist, what are the chances
that he's Muslim?
But the question we should be asking if we want to justify profiling is, if a person
is Mulsim, what are the chances that he's a terrorist?
I skimmed through some Google search results, and it seems like a high estimate of the number
of terrorists in the world (if we ignore people like Glenn Beck spouting off outrageous numbers)
is 500,000, or about .007% of the world's population.
So the prior probability of someone being a terrorist is .00007.
Now it's time to look at the all-important Likelihood Ratio.
In this case, we're using the fact that the person is Muslim as evidence that he's more
likely to be a terrorist--enough to make it necessary to profile him at an airport.
In our hypothetical, we've established that if he's a terrorist the chances that he's
a Muslim are .99.
So that's our numerator.
Wow, that must mean our result's going to be a HUGE percentage, isn't it?
Not so fast!
We still have to look at the all-important denominator.
What are the chances of a random passenger who is NOT a terrorist being a Muslim?
In the United States, Muslims make up about 8% of the population, so even though they're
a greater portion of the world's population, since we're dealing with American airports
it seems more reasonable to expect that 8% of travellers in America would be Muslim--which
again will weigh things in favor of the profilers.
So our denominator is .08.
Now it's time to do our calculation.
Use the online Bayesian calculator if you want to verify it with me:
p(H) = 0.00007 p(D|H) = 0.99
p(D|H') = 0.08
So if you see a Muslim at a US airport, eevn though 99% of terrorists are Muslims, the
likelihood that he is a terrorist is less than 1%, even less than .1%; it's about 0.0866%.
INCREDIBLY unlikely!
Does that surprise you?
Even if you're against racial profiling at airports, it's still very likely you didn't
think the probability would be THAT low!
But it is.
Why?
Well, there's a certain percentage of the world that are terrorists.
But although there's a bigger percentage of Muslims that are terrorists, there's an even
BIGGER number of Muslims that AREN'T, even if you limit it to just the Muslims in America.
Yes, the fact that 99% of terrorists (in our hypothetical) are Muslims pushes the number
up, but the fact that there are a lot MORE Muslims who AREN'T terrorists pulls it WAY
down!
The only way it would make sense to racially profile Muslims in US airports is if the number
of Muslim terrorists were a significant percentage compared to the number of Muslims in the US.
And they just aren't.
So although it seems counterintuitive, Bayesian probability shows the foolhardiness of racial
profiling.