Wednesday, July 1, 2009

Figures Don't Lie - But...

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Figures don’t lie, but liars figure. So do people who figure with good intentions but inadequate skill or thought.

It was all over the news. “U.S. gun stores and gun shows are the source of more than 90 percent of the weapons being used by Mexico's ruthless drug cartels, according to U.S. and Mexican law enforcement officials.” However the story had a bit of a problem – it was dead wrong, the result of misuse of data.

William La Jeunesse and Maxim Lott of Fox News published the facts. That number comes from a limited and abnormal sample of guns recovered by Mexican authorities. During 2007 and 2008 Mexico recovered 29,000 guns at crime scenes. They submitted 11,000 of those to the US for tracing. Only 6,000 could actually be traced with 90% of those 6,000 coming from the US. Over 23,000 of the guns either could not be traced or weren’t even submitted because there was no reason to do so. Many obviously came from Russia, South America, China etc

This is one example of the errors caused by poor understanding of what data means. The claim that 90% of those guns came from the US fooled a lot of people who should have known better, even the US secretary of state. Some may have been deliberately trying to mislead us, but most were probably just victims of the normal human failure to understand statistics. We tend to think that what is easily visible is representative of the whole.

Worse yet, we often think that anything precisely calculated must be correct. The claim that 90% of Mexican criminal weapons came from the U.S. was very precise – and very wrong. That number comes from equations that somebody manipulated to perfection, based on poor input. The source seems to have forgotten that applied mathematics is much more than the manipulation of equations, it requires understanding of the “physics” behind those equations and of the information fed to the equations. Even if the equations are perfect, they will give the wrong answer if the numbers used in the calculation are bad, Garbage In Garbage Out (GIGO).

This is not limited to politics. Two winners of the Nobel Memorial Prize for Economics served on the board of Long Term Capital Management, an investment firm which failed spectacularly. Their calculation was impeccable but accuracy in calculation was not enough to warn them of the oncoming problem.

I admit that I have a certain affinity for mathematics. I can enjoy grinding through equations and calculating results. However in this blog it would be a mistake to provide a treatise on how to calculate probabilities (though I would have fun doing that). First, I would probably bore any readers I have and lose them. Secondly, the bigger issue is not the actual calculation but determination of what goes into those equations. That is why Taleb* claims that “mathematics is a tool to meditate, not compute.” Anyone interested in the means of calculation can take any number of classes or read any of a variety of good books on the subject. Let us here confine ourselves to the “meditation” aspect of the problem.

What ought we to “meditate” on? First we should think about why we even consider any theory or model of the world in the first place. What makes it attractive to us? Its simplicity? Its usefulness? It’s beauty? (Make no mistake, scientists and mathematicians prefer beauty in their theories.) Are we being mislead because of our preferences?

Second, what other theories might explain the facts? Is there any reason to prefer one over another?

Third, are we considering all the facts? Are the facts we consider pertinent to the question at hand?

Forth, how can we know if the theory or model works? I’ve previously indicated that in any situation there are probably an unlimited number of theories that fit the facts. We need a way of distinguishing between those likely to be true and the rest of them. This is a knotty problem, one has troubled science for centuries and will almost certainly continue to cause trouble. The best answer we know comes from philosopher of science Karl Popper. His answer is that the theory must be falsifiable. By that me meant that it must make predictions that can be tested with clear results that might disagree with the theory.

For example, Newton’s famous second law of motion says that the acceleration of a body is directly proportional to the applied force. We can measure the force and the acceleration on a wide variety of objects under many circumstances. When we do so we find that in most cases the law holds to as accurately as we are able to measure. However at speeds approaching the velocity of light the data contradict that law. Newton’s second law is wrong, though it is very useful at ordinary speeds. At higher speeds we must use Einstein’s theory of relativity.

In the political arena we have many theories of how government should work. Frankly, none of them are perfect, probably because human beings are imperfect. However some work better than others. The unfortunate problem is that politicians seldom pay attention to the results when they try to modify a system. Market economies consistently out-produce controlled economies, yet politicians (and many voters) consistently ignore that fact as they increase government power and restrict individual and market freedom.

Next issue I intend to address one reason that government control causes problems with the economy.

*Nassim Nicholas Taleb, Fooled by Randomness, p216

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