While I try to intermix artificial puzzles with real-life uses of rational thinking, sometimes the incorrect use of words to win arguments in real life overwhelms me in waves. Of course this most often happens during the electioneering season, but since we have evolved from having periodic elections to a continuous campaign, political malpractice of logic has become too common to comment on.

My most recent episode of mental whiplash came when I turned on PBS in the middle of a diatribe by an obviously upset woman who was complaining that some allocation of a scarce resource had been made by matching the resource to the existing statistical distribution of need. Whether this was the best way to distribute the resource or not is unknown. However, the reason she was complaining is interesting. She wanted a rational distribution, not one based on stereotypes.

Since I was driving at the time, her argument almost got by me. I assume many in her audience were sympathetic to her anger. How could authorities be so crass as to base their largess on stereotypes? Many injustices are done by bigots and perverts who dehumanize their opponents by lumping them all into unsupported stereotypes and then doing bad things to them.

The problem is the subtle transition from statistics to stereotypes. We all do it to some degree or another, often without thinking about it. So what is a stereotype? From my Merriam-Webster:

Stereotype (noun)

1 : a plate cast from a printing surface

2 : something conforming to a fixed or general pattern; especially : a standardized mental picture that is held in common by members of a group and that represents an oversimplified opinion, prejudiced attitude, or uncritical judgment

The first definition carries the implication of a faithful copy, but nothing in the second definition requires a stereotype to be based on reality. In fact, there is a presumption (exploited by the upset woman on the radio) that a stereotype is by definition built at least partly on a false premise. If you can successfully accuse someone of thinking in stereotypes, then you have tarred your opponent with an implied falsehood.

Contrast this with statistics. Well-posed statistics do not lie, and do not predict. They tell what happened in the past to some accuracy. They do this without rancor or prejudice. That is, well-posed statistics do all these good things. Much that is passed off as statistics is really opinion or conjecture bolstered with nice sounding words. Even worse are the pseudo-statistics taken with a bias in mind and presented in a way that hides the bias.

Distorting what is called statistics would not necessarily cause a problem. But a major difficulty arises when people use statistics (the past) to predict future behavior. Statistics are a powerful tool for prediction — in fact our most powerful tool. But like any powerful tool, they can easily be misapplied.

What about stereotypes? Can they be honestly useful? Maybe some of them are useful. I think if they had no utility they would die out. But that gets us into a discussion of what is truly useful. The woman might have had a valid complaint about how the resources were distributed, but for me she weakened her case by using a sneaky transition from statistics to stereotypes to discredit her opponents. I wish she had done better.

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]stereotype, statistics, decision theory[/tags]