This is the inaugural article of a new series that has grown out of my concern with the way trained professionals in a variety of fields are charged to make critical choices, but often do not have training in how to make valid decisions. In the Summer of 2004, I gave a seminar to a medical conference on how good medicine could lead to bad decisions. With relatively few changes, this same seminar was presented to a group of engineers engaged in security and homeland defense.

On a whim, I submitted a tutorial form of this basic presentation to Lockergnome to test the waters and see if anyone was interested. Much to my surprise, the interest generated by it quickly out-stripped the interest in my normal “Sherman’s Senior Service” feature. Two articles on the Monty Hall paradox similarly generated considerable feedback.

The essence of this series will be to explore amusing and entertaining puzzles with the intent of illuminating how to make good decisions, presumably with the intent of automating them on computers. All articles will have an element of programming insight.

The principles of decision theory need not be dry and boring. We all make decisions contiguously, and we think we know how to do it. The uproar over the Monty Hall paradox and the continued presence of Astrology columns in newspapers demonstrates that we should not decide that we know how to make decisions.

I don’t know how often I will be able to submit new articles in this category. It will depend in part on reader interest.

To start us off, here is an illuminating puzzle based on a common logical error. I found this in a new book, “The Philosophy Gym” by Stephen Law.

You are shown a spread of four cards. Each card has a letter on one side and a number on the other. They are arranged on a table with “E,” “F,” “2,” and “5″ showing. For example:

What is the quickest way to establish the truth of this statement: “Of the four cards shown, those with vowels on one side have even numbers on the other.”?

Obviously, you have to flip over some cards to see the other side. Flipping all of them so that you know what is on both sides of all cards will guarantee that you can prove or disprove the desired statement. However, that solution is not the quickest or most efficient way to prove or disprove it.

After you think about this for a while, you will most likely decide that only flipping the “E” and”2″ cards will do it. But that is wrong. If you fell for that trap, you are like most people.

As Stephen Law points out, you need to flip the “E” card to check that it has an even number on the back. If it doesn’t, you can stop there because the statement is false. Then you need to flip the “5″ card to see if it doesn’t have a vowel on the back because if it does, then the statement is false. As long as “E” has an even number and “5″ doesn’t have a vowel, the statement is true. What’s on the reverse of “F” and “2″ is irrelevant.

Why do people get this wrong? Because most people will try to confirm the hypothesis rather than disconfirm it. Yet disconfirming a hypothesis is often the more efficient way. More importantly, trying to confirm a hypothesis without equally trying to disconfirm it often leads to incorrect conclusions.

Law gives the example of a politician who believes that cutting taxes will lower the crime rate. There are many examples of cities that cut local taxes and had a subsequent lowering of the crime rate. Many politicians would stop right there, having just proven what they want to believe. However, without too much trouble, even more examples could be found with the opposite result. Establishing the truth of an statement often requires both trying to prove it and trying to disprove it.