Economists Do It With Models

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Before You Go Locking Up All Of Those “Crazy” People…

February 17th, 2010 · 5 Comments
Discrimination · Econ 101 · Fun With Math

I decided a long time ago that I didn’t want an academic career, at least in part because I didn’t want to deal with the whole tenure process. (For the record, academia may look all relaxed and thoughtful and tweed-jackety from the outside, but a lot of departments are way more cutthroat and political than they at first appear.) Apparently the tenure process makes people do strange things. (Unless you’ve been living under a rock for the last few weeks, you should have an idea of what that link is going to go to.)

Put aside the fact that just because some crazy lady shot people after she was denied tenure doesn’t necessarily mean that she shot people BECAUSE she was denied tenure for now and focus on a different issue. Let’s analyze some logic here. Crazy woman shoots some people, and the media jumps all over the fact that the woman had exhibited sketchy behavior in the past. For example, from Fox News:

I will ackowledge that the warning signs being talked about here are more extreme than usual. Nonetheless, let’s think about this notion of “people should have known” or “this should have been preventable.” It’s easy to see that people who commit violent crimes very often have things in their pasts that could be seen as warning signs. However, it’s also the case that plenty of people who exhibit these same warning signs turn out to be perfectly safe. This brings us to an important lesson in statistics.

Let’s say hypothetically that you take a pregnancy test. (Yep, even the guys. Just get on board here, ok?) From the test itself, there are two outcomes- negative and positive, meaning “not pregnant” and “pregnant,” respectively. In the larger scheme of things, however, there are actually four possibilities:

  • You’re not pregnant and the test comes back negative
  • You’re not pregnant and the test comes back positive
  • You’re pregnant and the test comes back negative
  • You’re pregnant and the test comes back positive

It’s easy to see that the test only gives a correct prediction in the first and last case, and the middle two cases represent different types of errors. In statistics terms, these errors are referred to as Type I and Type II errors. They can be summarized by the table below:

When the accuracy of a test is reported, it generally refers to the fraction of times that the outcome falls into one of the “correct” squares. So, for example, if a pregnancy test claims 99% accuracy, then you will get either a Type I or Type II error only 1% of the time. However, you don’t know how that 1% breaks down into the two error categories.

Let’s bring the conversation back to the crazy people and guns scenario. Suppose we listened to all of those people saying that this shooting was preventable because warning signs were there. The only way that we could take action (since I don’t know about you, but my crystal ball is on the fritz nowadays) would be to implement a policy that would affect ALL people who exhibit these warning signs. This is problematic, since, while most of the people who commit violent crimes exhibit some sort of warning signs (especially since it’s easy to find said signs once you go looking for them), it is not the case that most people who exhibit these warning signs go on to commit violent crimes. Again, let’s think about the four possibilities, this time with examples of people who made each type of error:

If we were to start locking up all of the people who exhibit warning signs for violent behavior, we would be committing a lot of Type I error, not to mention trouncing on people’s civil liberties. We’re then faced with a tradeoff- is it worth infringing on the rights of many people in order to prevent the few that turn out to be crazy from acting on their craziness? Given the often-made point that we all probably exhibit some sort of warning sign at one point or another, I’m guessing that that answer is a no. That said, the Huntsville woman shot her brother and wasn’t charged because her mom said it was an accident. Next time, maybe we’ll have a lesson on credibility and conflict of interest.

Derek Sivers made a similar point a few weeks ago when he wrote about the foolishness of punishing everyone for one person’s mistakes. The visual that he uses in the post pretty much says it all:

Something to think about next time you take off your shoes in the airport security line.

Tags: Discrimination · Econ 101 · Fun With Math

5 responses so far ↓

  • 1 Virginia // Feb 17, 2010 at 4:15 pm

    The first thing I said when I heard about the crazy professor and the “warning signs that were missed” and the “background checks that failed” was “Oh great, now anyone who’s ever been involved in an accidental shooting or investigated in relation to some serious incident can never be a college professor.”

    Then there’s all the talk about the fact that she owned a gun.

    Crap. I might want to be a college professor some day…but I own guns, so I probably have to cross that career option off the list.

  • 2 LL Cool A // Feb 17, 2010 at 4:47 pm

    Best part of the story you linked to in the first paragraph is that the hero of the story was none other than… Professor Moriarty!

  • 3 Tamara // Feb 17, 2010 at 9:24 pm

    the all tweed -jackedy comment was hilarious… who determines the level of craziness? who says hey this woman has a blog call economists do it with models so she must a be freak or hey that´s so genious and original.
    Everybody, as you mentioned, shows risky behaviour at some point in their lives that doesnt mean they are going to follow through the crazy evil nuts path.
    When I was younger I was kind of agressive and may have came across as violent. But, now Im so tolerant and sensible is amazing XD and thats because I channel my “crazyness” in a positive way; studying, sports,writing.

  • 4 dWj // Feb 17, 2010 at 9:59 pm

    My fiancee is in neuroscience, and this woman apparently tried to get a job at her lab (before she was there). The head of the lab recalls that he thought she wasn’t a very good scientist, but also that she was kind of crazy. Perhaps he would have recalled her differently a week ago, but I’d like to take your post on hindsight bias and nudge it toward adverse selection; if every neuroscience program except for one thought it shouldn’t employ her, she has a job.

    Incidentally, I understand that “hindsight bias” is much stronger in Western cultures than Eastern ones.

  • 5 Bane Coat Jacket // Oct 27, 2014 at 4:25 am

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