Last week I wrote about receiving a political quiz that used quotes from Hillary. Several people commented unfavorably on it because of the subject matter. That is, this column is advertised as being about decision theory, statistics, and probability. What am I doing writing about a political hit piece (without regard to which side is writing or the target)?

These comments and questions miss the essential point of this series. Decision making is not an academic exercise. I cannot in good conscience limit the content of columns to puzzles involving truth-tellers and liars on an isolated island or the Sultan’s daughters. Every day we make serious decisions based on grossly inadequate data, insufficient analysis, and lack of real understanding. It is a wonder we do as well as we do in living our largely uneventful lives. Daily decisions range from the small — such as what to have for breakfast, to large issues — such as politics and religion. In between are the decisions about responding to advertising.

My example of applying some rational thought to a political hit piece did not involve any equations or advanced math. If making better decisions required us to be able to solve differential equations analytically in our heads while driving cars, we would be doomed. Instead, I am trying to show “Patterns of Plausible Inference” (see the book by Polya of the same name). With a little practice, one can listen to a commercial, a sermon, or a speech and parse it into logical statements to see just what is being offered. Failure to do this can lead to behavioral aberrations. For instance, I have no mental model of how people can become convinced that blowing up themselves and innocent people is a holy act. Coercion might work, but deliberately educating candidates to make the wrong decisions certainly works better. Voting for a totalitarian regime might result in a temporarily better life for a fraction of the population, but is the society as a whole improved by a non-democratic government? Buying a new HDTV would improve my television viewing experience, but what are the tradeoffs?

Lack of simple thought often leads to less than optimal decisions. But there is another side to the coin. Searching for an absolute optimum can also lead to bad decisions. Sometimes there simply is no single maximum. We can make decisions about which roads to take to drive from A to B and probably find an optimum giving present knowledge. A GPS does it better if we ignore traffic conditions. We can override the GPS directions if we hear about a traffic jam ahead. We have more current knowledge than the GPS and the optimum route changes.

But what decisions do you make to lead the best life? That question is not well-posed, so the answer cannot be exact. The best you can do is hone in on a better life by eliminating obvious bad choices.

Even very bright people get confused on this point. Arthur Laffer famously argued that income to a government from taxes is a simple function of the tax rate. At zero tax rate, the government takes in zero dollars. At 100% tax rate, he argued that the government would also take in no money. However, at an intermediate rate, the government obviously takes in money. The function is bounded at two ends of a domain with at least one positive point and thus has a maximum value. Therefore, Laffer argued, there is a single tax rate at which the income to the government is maximized and with some more arguments, pleaded for reduced taxes (primarily benefiting wealthy people) to increase the net income. There are at least two fallacies in his argument. Can you pick them out? Of course who should get taxed and how much is a very political question, and I should probably not discuss it here.

In response to the interest my original tutorial generated, I have completely rewritten and expanded it. Check out the tutorial availability through Lockergnome. The new version is over 100 pages long with chapters that alternate between discussion of the theoretical aspects and puzzles just for the fun of it. Puzzle lovers will be glad to know that I included an answers section that includes discussions as to why the answer is correct and how it was obtained. Most of the material has appeared in these columns, but some is new. Most of the discussions are expanded compared to what they were in the original column format.