There is a saying to that out of the mouths of babes comes wisdom. I'm not sure about that, but children are well aware of a couple of the most important principles of decision theory - at least on an intuitive and practical level.

One of those important principles is admissibility. Maybe it should be called inadmissibility, because one alternative choice is inadmissible relative to a second alternative if no matter what actually happens, the second alternative leads to an outcome which is at least as good as the outcome from the first alternative. Well, children would never phrase it this way, but let's watch a child in action. The child wants something - maybe an in-between meal snack, maybe a new toy or a trip to the zoo. Shortly after the child acquires the ability to actually ask for this particular something, the child recognizes which parent it should ask, because the child knows which parent is more likely to grant the request.

Another important principle is the maximax principle, which states that if conditions are favorable, one should select the alternative which yields the maximum payoff. Want to watch a child employ the maximax principle? If the child asks his mother for a cookie and gets it, by far the most likely outcome is that after consuming the cookie, the child will request another. Even if the child is full, there's a very good chance that the child will request another cookie and then be unable to eat it all - a chain of events which in my family led to my mother saying, "Your eyes are bigger than your stomach."

However, I have never seen a child apply the Bayes' Criterion, which is the decision principle that urges one to choose the alternative that will result in the maximum payoffs in the long run. For instance, let's revisit the situation in the previous paragraph, where the child successfully scored a cookie, and then kept requesting them. The child is not sufficiently farsighted to realize that requesting too many cookies now will lead to the following result: the mother will remember that bad things happened when the child's request for additional cookies was granted. Consequently, the mother will view requests for additional cookies in the future with a jaundiced eye; she may even view the original cookie request in this light. As a result, the child might be better served in the long run by not requesting an additional cookie.

At least, I've never seen a child react in this fashion. If you do, I'd keep a really close eye on him or her, because you may be looking at a child prodigy, a Wolfgang Amadeus Mozart of practical decision theory.

About the Author

James Stein, Ph.D.

James Stein, Ph.D. is an author, but hanging on to the day job (math professor) in a trying economy.

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