Decision Theory In Everyday Life

In the last few articles, the topics were loosely organized around the idea of simplifying computations in various ways. One powerful method for simplifying data analysis is to find symmetries that help to organize observations in a way that allows one to more easily see information that might be hidden. Symmetries can be used for many purposes, for instance, we could store an image of a human in half the space by exploiting the bilateral symmetry that most of us have. Small deviations are not a problem since they could be handled as deviations and stored in a separate file.

Another way of organizing data is to empirically recognize a pattern. We need not know if the pattern is an artifact or indicative of the fundamental processes producing the data.

However, one must be careful when looking at raw data to detect symmetries or patterns. Our brains seem to have evolved to favor symmetry and find patterns in data as a way of simplifying our daily existence. After all, if one of our ancestors noticed a deviation from the pattern of the trees in a forest and ducked in time to avoid getting eaten, then the genes for pattern recognition would get passed on while the less fortunate fellow travelers helped nourish the predators.

Think of the stellar constellations. When we look at the night sky, we automatically associate stars that appear to be close to each other in groups even though later analysis shows that the stars have nothing to do with each other - they just happen to have a narrow separation when viewed from our current standpoint. (An exception is the Pleiades. There are others.) Organizing random distributions of stars into mythical constellations doesn’t hurt anybody, and even helps to refer to specific places quickly. However, the imposition of a perceived pattern can have unintended consequences. Much nonsense has been written about how the stars control our lives based on nothing more than recognition of arbitrary patterns.

Astrology is an example of the dangerous transition that arises from the subtle transition from observing patterns to attributing causes to the patterns. It’s one thing to say you see the image of a hunter chasing a lion in the sky and quite another to say it’s because the gods put the images up there because of heroic acts. Once a cause has assigned to a distribution, great harm can be done because we sometimes stop there and do not examine if the cause if truly justified.

Think of the nearly perfect correlation between being uneducated, poor, and black in certain areas of our country in the last century. It’s one thing to make that observation and something else to attribute it to genetic failure. We tend to accept explanations that make us feel good and neglect to examine those that make us feel bad. If you see a correlation and simultaneously form a conjecture about what caused that correlation, then you are likely to stop if the conjecture is in your favor. If the conjecture makes you look bad, you will be tempted to keep looking for a more favorable explanation. Most white people at that time were content with the genetic explanation for the disparity between the economic conditions of the races.

Relating the tools of mathematics back to everyday issues makes the effort of learning them more worthwhile. Pure mathematics for its own sake is a good thing, but if the pure math can find an application in such things as increasing effective storage space or combating inappropriate stereotypes, then so much the better. Decision theory should not be hobbled by relegating it to academic exercises. Many of the items discussed here can be effectively used in everyday life. Avoid falling into the pattern of self-censoring. There is no box labeled “Decision Theory” into which all this learning must be stuffed with no further social interaction.

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.

[tags]decision theory,symmetry,mathematics,symmetries,pattern recognition,data analysis,data organization[/tags]