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What Are the Chances That a Muslim Is a Terrorist? – Article by Sanford Ikeda

## What Are the Chances That a Muslim Is a Terrorist? – Article by Sanford Ikeda

Sanford Ikeda
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It’s flu season and for the past two days you’ve had a headache and sore throat. You learn that 90% of people who actually have the flu also have those symptoms, which makes you worry.  Does that mean the chances of your having the flu is 90%?  In other words, if there’s a 90% chance of having a headache and sore throat given that you have the flu, does that mean there’s a 90% chance having the flu given that you have a headache and sore throat?We can use symbols to express this question as follows: Pr(Flu | Symptoms) = Pr(Symptoms | Flu) = 90%?

If you think about it you’ll realize that there are other things besides the flu that can give you a combination of a headache and sore throat, such as a cold or an allergy, so that having those symptoms is certainly not the same thing as having the flu.  Similarly, while fire produces smoke, the old saying that “where there’s smoke there’s fire” is wrong because it’s quite possible to produce smoke without fire.

Fortunately, there’s a nice way to account for this.

How Bayes’ Theorem Works

Suppose you learn that, in addition to Pr(Symptoms | Flu) = 90%, that the probability of a randomly chosen person having a headache and sore throat this season, regardless of the cause, is 10% – i.e. Pr(Symptoms) = 10% – and that only one person in 100 will get the flu this season – i.e. Pr(Flu) = 1%.  How does this information help?

Again, what we want to know are the chances of having the flu, given these symptoms Pr(Flu | Symptom).  To find that we’ll need to know first the probability of having those symptoms if we have the flu (90%) times the probability of having the flu (1%).  In other words, there’s a 90% chance of having those symptoms if in fact we do have the flu, and the chances of having the flu is only 1%. That means Pr(Symptoms | Flu) x Pr(Flu) = 0.90 x 0.01 = 0.009 or 0.9% or a bit less than one chance in 100.

Finally, we need to divide that result by the probability of having a headache and sore throat regardless of the cause Pr(Symptoms), which is 10% or 0.10, because we need to know if your headache and sore throat are flu Symptoms out of all headache-and-sore symptoms that have occurred.

So, putting it all together, the answer to the question, “What is the probability that your Symptoms are caused by the Flu?” is as follows:

Pr(Flu | Symptoms) = [Pr(Symptoms | Flu) x Pr(Flu)] ÷ Pr(Symptoms) = 0.90 x 0.01 ÷ 0.10 = 0.09 or 9%.

So if you have a headache and sore throat there’s only a 9% chance, not 90%, that you have the flu, which I’m sure will come as a relief!

This particular approach to calculating “conditional probabilities” is called Bayes’ Theorem, after Thomas Bayes, the 18th century Presbyterian minister who came up with it. The example above is one that I got out this wonderful little book.

Muslims and Terrorism

Now, according to some sources (here and here), 10% of Terrorists are Muslim. Does this mean that there’s a 10% chance that a Muslim person you meet at random is a terrorist?  Again, the answer is emphatically no.

To see why, let’s apply Bayes’ theorem to the question, “What is the probability that a Muslim person is a Terrorist?” Or, stated more formally, “What is the probability that a person is a Terrorist, given that she is a Muslim?” or Pr(Terrorist | Muslim)?

Let’s calculate this the same way we did for the flu using some sources that I Googled and that appeared to be reliable.  I haven’t done a thorough search, however, so I won’t claim my result here to be anything but a ballpark figure.

So I want to find Pr(Terrorist | Muslim), which according to Bayes’ Theorem is equal to…

1) Pr(Muslim | Terrorist):  The probability that a person is a Muslim given that she’s a Terrorist is about 10% according to the sources I cited above, which report that around 90% of Terrorists are Non-Muslims.

Multiplied by…

2) Pr(Terrorist):  The probability that someone in the United States is a Terrorist of any kind, which I calculated first by taking the total number of known terrorist incidents in the U.S. back through 2000 which I tallied as 121 from this source  and as 49 from this source. At the risk of over-stating the incidence of terrorism, I took the higher figure and rounded it to 120.  Next, I multiplied this times 10 under the assumption that on average 10 persons lent material support for each terrorist act (which may be high), and then multiplied that result by 5 under the assumption that only one-in-five planned attacks are actually carried out (which may be low).  (I just made up these multipliers because the data are hard to find and these numbers seem to be at the higher and lower ends of what is likely the case and I’m trying to make the connection as strong as I can; but I’m certainly willing to entertain evidence showing different numbers.)  This equals 6,000 Terrorists in America between 2000 and 2016, which assumes that no person participated in more than one terrorist attempt (not likely) and that all these persons were active terrorists in the U.S. during those 17 years (not likely), all of which means 6,000 is probably an over-estimate of the number of Terrorists.

If we then divide 6,000 by 300 million people in the U.S. during this period (again, I’ll over-state the probability by not counting tourists and visitors) that gives us a Pr(Terrorist) = 0.00002 or 0.002% or 2 chances out of a hundred-thousand.

Now, divide this by…

3) The probability that someone in the U.S. is a Muslim, which is about 1%.

Putting it all together gives the following:

Pr(Terrorist | Muslim) = [Pr(Muslim | Terrorist) x Pr(Terrorist)] ÷ Pr(Muslim) = 10% x 0.002% ÷ 1% = 0.0002 or 0.02%.

One interpretation of this result is that the probability that a Muslim person, whom you encounter at random in the U.S., is a terrorist is about 1/50th of one-percent. In other words, around one in 5,000 Muslim persons you meet at random is a terrorist.  And keep in mind that the values I chose to make this calculation deliberately over-state, probably by a lot, that probability, so that the probability that a Muslim person is a Terrorist is likely much lower than 0.02%.

Moreover, the probability that a Muslim person is a Terrorist (0.002%) is 500 times lower than the probability that a Terrorist is a Muslim (10%).

(William Easterly of New York University applies Bayes’ theorem to the same question, using estimates that don’t over-state as much as mine do, and calculates the difference not at 500 times but 13,000 times lower!)

Other Considerations

As low as the probability of a Muslim person being a Terrorist is, the same data do indicate that a Non-Muslim person is much less likely to be a Terrorist.  By substituting values where appropriate – Pr(Non-Muslim | Terrorist) = 90% and Pr(Non-Muslim) = 99% – Bayes’ theorem gives us the following:

Pr(Terrorist | Non-Muslim) = [Pr(Non-Muslim | Terrorist) x Pr(Terrorist) ÷ Pr(Non-Muslim) = 90% x 0.002% ÷ 99% = 0.00002 or 0.002%.

So one interpretation of this is that a randomly chosen Non-Muslim person is around one-tenth as likely to be a Terrorist than a Muslim person (i.e. 0.2%/0.002%).  Naturally, the probabilities will be higher or lower if you’re at a terrorist convention or at an anti-terrorist peace rally; or if you have additional data that further differentiates among various groups – such as Wahhabi Sunni Muslims versus Salafist Muslim or Tamil Buddhists versus Tibetan Buddhists – the results again will be more accurate.

But whether you’re trying to educate yourself about the flu or terrorism, common sense suggests using relevant information as best you can. Bayes’ theorem is a good way to do that.

(I wish to thank Roger Koppl for helping me with an earlier version of this essay. Any remaining errors, however, are mine, alone.)

Sanford (Sandy) Ikeda is a professor of economics at Purchase College, SUNY, and the author of The Dynamics of the Mixed Economy: Toward a Theory of Interventionism. He is a member of the FEE Faculty Network.

America’s Concentration Camps Are a Warning, Not a Model – Article by Gary McGath

## America’s Concentration Camps Are a Warning, Not a Model – Article by Gary McGath

Gary McGath
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But some politicians are trying to revive their legacy

Woodrow Wilson’s reputation has recently taken a well-deserved beating because of his racial policies. He restored segregation in the federal civil service, and the infamous movie Birth of a Nation highlights his support for the Ku Klux Klan. Those policies are dead today, with very few advocates.

However, a more recent president implemented an even worse race-based policy against Americans, and some politicians say we should emulate it today. Franklin D. Roosevelt’s executive order forcibly removed about 120,000 Japanese-Americans, mostly US citizens, from their homes.

After the bombing of Pearl Harbor, people feared a Japanese attack on the West Coast, and many regarded the Japanese American population in California as disloyal. On February 19, 1942, Roosevelt issued Executive Order 9066, which authorized the military to remove people from designated military areas.

As explained in Greg Robinson’s By Order of the President, Roosevelt’s language was broad, but everyone understood “any and all persons” to mean Japanese-Americans and “military areas” to mean the West Coast. The removals included “Issei” — resident immigrants — as well as “Nisei” — native-born Americans with Japanese parents. Immigration from Japan had been banned since 1924, and all Japanese immigrants were ineligible for citizenship, although all had been living in America for at least eighteen years.

They were forcibly removed to ten concentration camps. The government officially called them “relocation centers,” but Roosevelt himself used the words “concentration camp” in a recommendation as early as 1936, as did a military proposal in 1942. The occupants were kept behind barbed wire, and armed guards kept them from leaving.

The mass displacement of Japanese-Americans, but not people of German or Italian extraction, was the result of racial rather than security considerations. Roosevelt showed a lifelong hostility toward the Japanese. Robinson states:

FDR had a long and unvaried history of viewing Japanese-Americans in racialized terms, that is, as essentially Japanese in their identity and emotional allegiance, and of expressing hostility toward them on that basis.

In the years before World War I, Roosevelt considered immigration part of the Japanese threat to the West Coast. During the 1920s, when Roosevelt urged better relations with Japan, he supported immigration restriction and legal discrimination in order to deter Japanese-American settlement.

A report commissioned by Congress concluded that

Executive Order 9066 was not justified by military necessity, and the decisions that followed from it — exclusion, detention, the ending of detention and the ending of exclusion — were not founded upon military considerations. The broad historical causes that shaped these decisions were race prejudice, war hysteria and a failure of political leadership.

As documented by Thomas Fleming in The New Dealers’ War, Roosevelt proposed removing an even larger number of Japanese and Japanese-Americans in Hawaii. The military objected because so many of them were skilled workers who were necessary to the war effort.

The order banning Japanese-Americans from the West Coast was lifted in January of 1945, and the camps were shut down soon afterward. Many returned to find they couldn’t reclaim their property or return to their homes.

These events should be a shameful chapter in America’s past, but even today people cite them as an example to follow. David Bowers, mayor of Roanoke, Virginia, ordered the city government to stop helping Syrian refugees, citing Roosevelt’s internment order as justification.

Al Baldasaro, a New Hampshire state representative and co-chair of Donald Trump’s state veterans’ coalition, has defended Trump’s proposal to ban Muslim immigration by citing World War II internment: “What he’s saying is no different than the situation during World War II, when we put the Japanese in camps.”

Trump has made the connection between his call for banning Muslim immigrants and creating a national registry and FDR’s policies explicit:

What I’m doing is no different than FDR’s solution for German, Italian, Japanese, you know… They stripped them of their naturalization proceedings. They went through a whole list of things; they couldn’t go five miles from their homes. They weren’t allowed to use radios, flashlights. I mean, you know, take a look at what FDR did many years ago and he’s one of the most highly respected presidents.

Trump evaded the question of whether he would have supported Japanese internment, saying, “I would have had to be there at the time to give you a proper answer.” He wasn’t there, but there are still living Americans who were. One was George Takei, who played Lt. Sulu on Star Trek and was sent off at the age of five. He recalls how it happened:

Without charges, without trial, without due process — the fundamental pillar of our justice system — we were summarily rounded up, all Japanese-Americans on the West Coast, where we were primarily resident, and sent off to 10 barb wire internment camps — prison camps, really, with sentry towers, machine guns pointed at us — in some of the most desolate places in this country.

For the sake of a false sense of security, the US government ruined countless lives, imprisoned tens of thousands without charges, without even accusation, with only the mere fact of their skin color and ancestry. The internment stoked hatred against a minority group, squandered potential assets in the war, and fueled the Axis’s anti-American propaganda.

The lesson that America’s concentration camps should have burned into our national consciousness that we must never do that again — not to a racial, national, or a religious minority, nor anyone else — no matter how afraid we are. They are a warning, not a model.

Gary McGath is a freelance software engineer living in Nashua, New Hampshire.