Megan McArdle

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P(A|B)!=P(B|A)

25 Jun 2008 05:14 pm

As predicted by a friend over IM this morning, the remark about Timothy McVeigh wannabes probably being in Afghanistan or Iraq right now was wildly misinterpreted as an attack on our troops.

I am second to none in my admiration for the military. I do not think that being in the military makes you more likely to be a nutty, militia-style potential home-grown terrorist. At a guess, there are perhaps a couple hundred people in the United States who would like to take violent action against our government in a frantic attempt to ward off the New World Order. There are about 3 million members of the active and reserve military right now. Even if every single one of our homegrown nuts was a service member, the probability that any member of the military was a potential terrorist would be entirely negligible. Most people who are serving in the military do so for honorable, or at the very least respectable, reasons like wanting to serve their country, or get money for school.

But the probability of A, given B is not the same thing as the probability of B, given A. That's what the notation in the title means. To put it more concretely: the probability that you are Jewish, given that you are a rabbi, is 100%. The probability that you are a rabbi, given that you are Jewish, is a small fraction of 1%.

So even though almost no one in the military is a raving nativist loon, many of the raving nativist loons may be in the military. My understanding is that many serial killers are attracted to law enforcement; similarly, people with fantasies about striking a violent blow against the forces of evil may be seeking vocational education in the armed forces. This is no more a smear against the military than it is a smear against firemen to note that many arsonists seek to join their ranks.

Comments (32)

"To put it more concretely: the probability that you are Jewish, given that you are a rabbi, is 100%. The probability that you are a rabbi, given that you are Jewish, is a small fraction of 1%."

So now you're comparing rabbis to raving nativist loon whacko terrorists?

I am second to none in my admiration for the military.

Whoa, really? Bold. Daring. You sure you want to go on the record with that statement?

FISA?

"My understanding is that many serial killers are attracted to law enforcement": dear lady, stop digging.

BlackOrchid

And what of disgraced, disgraceful puppy-tossing Marine David Motari?

It fits what Megan is saying. He's an awful monster, and it was terrible that he was a Marine (for the USA and our military). But he was a Marine. He clearly enjoyed being a Marine, for his own sometimes sadistic purposes.

Its like pointing out that a child's eye color is neither of the parents in the room.

I didn't take it personally because I've met some pretty crazy racists in 5 years of US Army Active service. It isn't like you pulled a Kerry and said I was stuck in Iraq. I would advise though, remember no matter how you qualify it, people will hear what they want to.

Megan McArdle

No, really, it's true--many of them try to join the police force. That's apparently why Ted Bundy became a law student. It's also true that many arsonists try to join the fire department. They are still a trivial percentage of all firemen.

P(John McCain is second to MM in admiration for the military)

Megan,

Having been in the military for 5 years, my experience is that we represent a fair cross-section of society in terms of behavior. We have some absolutely stellar folks, a large majority who have never committed a major crime (but perhaps a number who break the speed limit or fudge their taxes), and a proportionally small number of screw-ups. The latter are, thankfully, usually caught and either rehabilitated or removed.

Megan,

Having been in the military for 5 years, my experience is that we represent a fair cross-section of society in terms of behavior. We have some absolutely stellar folks, a large majority who have never committed a major crime (but perhaps a number who break the speed limit or fudge their taxes), and a proportionally small number of screw-ups. The latter are, thankfully, usually caught and either rehabilitated or removed.

ken magalnik

While not particularly insulting to military the remark was pretty foolish, if you dont mind my saying so. Not only is it practically begging to be interpreted the wrong way (at least enough to require an explanation), but it is also saying that virtually all capable nutcases have not only joined the military but also managed to get themselves deployed. All the ones that are left couldn't mix fertilizer if their lives depended on it, or dont have the organizing skills to put something like this together. Also, they never get anytime off, and will be stop-lossed for the next decade, since that was the arbitrary length of time you have picked for your post.
Couldn't you have just left it at domestic right wing terrorists not being an existential threat because most at least claim to want to preserve the republic?

Megan-

I'm not saying your observation are incorrect. By the way this whole thing is funny, given where your intent was and where the interpretation is. But you let the cat out of the bag pointing this stuff out:)

Thorley Winston

Megan, I think of think you could have avoided this problem if you’d actually just addressed what McCain actually was reported to have said (you misstated it in your original post and you may not have noticed but a couple of your readers tried to correct you on that). McCain never said that he thought that “terrorism” was an existential threat – he said that he thought that “radical Islamic extremism” was the greatest long term threat facing the United States.

If you had written a response about why you thought that McCain was wrong about what he was actually reported to have said, you would have covered much of the same territory (e.g. terrorist attacks, nuclear terrorism) as in your second post and probably a lot more issue as well – WMD proliferation to non-State actors, destabilization of allied and/or friendly governments, a nuclear Iran, what happens when this technology and information to make chemical, nuclear and biological weapons becomes even more widely available in a part of the world where someone may have both the resources and the will to make (or use or lose control of it), the effects on the world’s oil supply, etc.

It’s doubtful IMO that in discussing why you disagreed with Senator McCain’s actual reported statement that he thought that “radical Islamic extremism” – as opposed to just “terrorism” as you incorrectly reported – was an existential threat, that you would have ever gone down the path of talking about Timothy McVeigh and the military.

I suppose that like in a lot of lines of work that one achieves a contract for in a free society, the members of the military generally try to put the best of themselves into their work and that, at times, the work is somehow related to the regressed elements of their personality which may be expresed in various ways in off hours. At times the regression wins but probably more likely, the combination of the contribution made in work and their 'confession' and direction in the military community leads to a more mature personality.

Tim McVeigh was ex-military. But by the time he got to hating the US government enough to blow up buildings, he'd been out of the military a while, and wasn't keen to join up again.

Last I checked on what the raving nativist loons had to say about themselves, they mostly thought the US government, including the military, was being controlled by the Zionist Occupation Government. They're not pro-American, nor pro-military, as most of us understand those concepts. August Kreis is a big fan of militant Islam these days, for example. I looked in on David Duke's web site a couple years ago, and while half of it was the usual crap about hating black people, the stuff about foreign policy was pretty much straight Chomsky, with a side of explicit anti-Semitism.

These folks aren't just overenthusiastic flag-wavers. They're genuinely nuts.

God I love this blog. Thanks for explaining, in statistical notation, exactly why this common misperception is totally wrong.

If only the average reporter were this mathematically literate.

Dear Megan, that's your second defensive post today.

It's the curse of someone who craves a certain level of respectability, which I don't begrudge you in the least, that you've resisted telling the minority who insist on misinterpreting you to simply sod off.

But keep in mind the subtext here, that left-wing nutjobs, you know like the ex-Marines who kill presidents in Dallas, never join the Marines.

Nope. And ignore that left-wing terror groups are not unknown either, but she never mentioned them in her list of threats...you know like the guys who bombed a recruiting office or the Weathermen. Or in Europe where left-wing terror groups far outweigh right wing wackos.

Malignant Bouffant

Aaron:

Left wing terror groups committing terror acts in the last, say, twenty years: Not many. Body count: 0.

Right wing terror groups (or individuals) committing terror acts in the same time period:
A lot, w/ a body count of 168 (OKC) plus however many abortion providers have been shot or bombed, the Atlanta Olympics., etc.

"Bombed a recruiting office or the Weathermen?" Let's compare Oklahoma City to a small blast at a recruiting office at three in the a. m., that wouldn't have made the news if it hadn't been in Times Square & recorded on a surveillance camera. The Weathermen, who mostly managed to blow themelves up, haven't been active for over thirty years.

But everytime anyone left of Attila the Hun becomes president, the RW bombers/snipers crawl back out of the woodwork. Chances are good to excellent that the next terror incident in the U. S. will be perpetrated by a right winger, & not a redical Islamist right winger, but a home-grown radical Xtian right winger.

David Skurnick

I believe the number of American troops in Afghanistan and Iraq is around 200,000. That's around 1/1500 of the US population. So Megan's assertion that "Their most terroristically useful members are probably in Iraq or Afghanistan right now" implies that terrorist nutcases are more than 1500 times more likely to be in active military than not. That's an awfully high ratio, particularly since it's based on no data.

I am second to none in my admiration for the military.

Others, above, have been sarcastic about this comment of yours but I really do wonder if you know how tone deaf this makes you sound? If you had a good gig blogging & writing at Atlantic and became pissy that there was not enough advertising for the U.S. Military services at Atlantic, and you abandoned the Atlantic, but used your fame as an ex-Atlantic editor to start another blog, and you offered 100% free advertising for all Military services on your new magazine-ish blog...

then, you might have a basis for extolling your own admiration for the military.

Even such actions as this might be debatable that it shows "second to none" admiration, but at least it would be plausible.

If I were you, I would sneak back into the post and delete that line.

aMouseforallSeasons

But everytime anyone left of Attila the Hun becomes president, the RW bombers/snipers crawl back out of the woodwork. Chances are good to excellent that the next terror incident in the U. S. will be perpetrated by a right winger, & not a redical Islamist right winger, but a home-grown radical Xtian right winger.

This, kids, is the kind of wacky fiction you'll come up with after descending into the dark and soul-sucking depths of partisanship. To start with the low-hanging fruit, ALF, Earth First!, and ELF are three identifiably left-wing organizations that have chalked up at least as much of a recent record as any right-wing antiabortion or antigovernment group one might care to name.

Meanwhile, the recent large-scale homeland incidents are almost exclusively perpetrated by foreign-bred terrorists, OKC being a lonely exception in a list that includes the WTC bombing (which wasn't worse only because the perpetrators misjudged both the WTC foundation structure and the capacity of cyanide to be oxidized in a blast), the foiled tunnels & bridges plot thereafter, and 9/11.

MarcInSeattle

"My understanding is that many serial killers are attracted to law enforcement;"
--And I have it from the highest authority that that man SOLD HIS SOUL TO THE DEVIL!!

Just kidding...

The probability non-equation in the title is known as the "Prosecutor's Fallacy".

The probability of the evidence, assuming the prisoner's guilt, is not equal to the probability of guilt, given the evidence. Courts are concerned with the second quantity.

The correct version is given by Bayes' Theorem:

P(A|B)=P(B|A)P(A)/P(B)

So if A is the event "T. McVeigh wannabee" & B is "Serving in the armed forces, the probably that one is a TMV crazy, given one is in the armed forces is proportional to P(A), the probability that one is a TMV crazy in the first place. That will be very small.

So the numbers of TMV wannabees in the armed forces will be small and in proportion to the number in the general population. I presume that all branches of the forces try to spot and weed out hardened sociopaths and psychopaths. Many should end up in the stockade.

BTW, if I recall the Timothy McVeigh story, it was his experiences in the Gulf War that drove him to the edge. He did not join the army to learn how to blow up federal buildings and kill innocent people.

Left wing terror groups committing terror acts in the last, say, twenty years: Not many. Body count: 0.
Right wing terror groups (or individuals) committing terror acts in the same time period:
A lot, w/ a body count of 168 (OKC) plus however many abortion providers have been shot or bombed, the Atlanta Olympics., etc.

Unabomber? Or was there a reason you listed Left wing terror groups and Right wing terror groups AND individuals

Is it true that a disproportionate number of narcissists seek tenured University posts? Child-molesters want to be journalists on the New York Times? Drunks seek political office? Torturers become social workers? Innumerate illiterates apply to be schoolteachers? Fruitcakes become psychiatrists? What about lawyering - disproportionately attractive to whom? Liars? Fantasists? Thieves?

Left wing terror groups committing terror acts in the last, say, twenty years: Not many. Body count: 0.

MB, You're mostly incorrect. ELF/ALF is considered to be the largest US domestic terror threat by the FBI with well over 1,000 criminal incidents all within the past 20 years. They haven't killed anyone yet, but that's just blind luck and eventually some arson attack will get out of control and kill somebody.

Terrorism requires both the willingness and the ability to use violence in pursuit of one's political aims.

The US army doesn't teach you to be a disaffected nut (some things you just have to figure out on your own), but do provide the world's greatest education in applied violence. Hence, it is commonplace to find that the more succesful and deadly brand of terrorist, such as the DC snipers or McVeigh, have some degree of military training

This (I believe) was the point Megan was trying to make, and I'll second the point that anyone who believes otherwise really ought to read up on Bayes theorem.

Squeaky Fromme and John Hinkley were right wingers? Who knew? What about Sirhan Sirhan - or doesn't he count because Bobby kennedy wasn't elected yet.

Malignant, indeed. Don't let facts get in the way of a good hypothesis.

Charlie (Colorado)

The real question is whether the probability that a particular individual being a potential terrorist etc is greater among members of the military than among members of the more general population of military age people. Given as large a population as we have in the military, the likelihood that there exist potential McVeighs in the military probably approaches 1; ditto the general population.

The null hypothesis, however, is that they're no more common in the military than outside the miltary, and my suspicion is that they're probably less common among people who have completed basic training, just because people with authority issues often don't do well.

David Skurnick wrote:

I believe the number of American troops in Afghanistan and Iraq is around 200,000. That's around 1/1500 of the US population. So Megan's assertion that "Their most terroristically useful members are probably in Iraq or Afghanistan right now" implies that terrorist nutcases are more than 1500 times more likely to be in active military than not. That's an awfully high ratio, particularly since it's based on no data.

Note: She said "useful." She didn't say such individuals were common in the military, or even that they made up most terroristically inclined individuals. The vast majority of soldiers won't do anything like Tim McVeigh. But successful terrorists generally need to learn their skills somewhere. The 911 hijackers learned theirs at Osama U--Afghanistan Campus; this school got closed down. Another poster noted that the US Army gives you pretty much the best training in applied violence available to most people.

According to a friend of mine who did two tours in Iraq in the Marines, one during the Battle of Fallujah, the most dangerous enemy combatants were the Chechen mercs, many of whom learned their trade in the Russian military before being radicalized by the Chechen war. Where do you think the next domestic terrorist is likely to learn his?


Mark wrote:

So now you're comparing rabbis to raving nativist loon whacko terrorists?

No, she's making a totally appropriate analogy to illustrate the fact that P(A|B) != P(B|A). You're the one casting politically correct innuendo here. The only thing I think we can accuse Megan of being here is a tad bit incautious in her choice of words.

My complaint is about the assumption that only right-wingers commit terrorism.

Then we have the pipe bomber who wanted to create the smiley face on the newspaper maps of his hits.

I think terrorists' agenda is often just an excuse for a psychopath.

Jens Fiederer

Somebody else pointed out the full version of the Bayes Theorem.

It follows that our headline is true if and only if P(A) != P(B).

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