Sometimes a decision problem can be solved without using probabilities or expected value at all. These are situations in which one strategy dominates all others, no matter what happens in the actual world. This is called dominance. It is illustrated by a very famous argument for acting as if you believed in God. Variations on that argument lead to other decision rules.
The expected value rule can be used only when some probabilities are available. Sometimes we are so ignorant that we are not inclined to talk even of the probabilities of different alternatives. That is the extreme end of uncertainty. Yet there may still be more or less reasonable decisions.
DOMINANCE
It was a dark and foggy night when Peter made his first trip to Holland, the homeland of his parents. His parents gave him enough money to rent a car to see the family, but after that he was practically broke. He was planning to stay with his distant relatives. So he was driving along a road, somewhat lost, when he came to an overhead signpost. Unfortunately, a garbage bag had blown over the front of the sign, obscuring the first three letters of each town. What he saw was:
▪ AVENHAGE ↑
▪ TERDAM →
Peter figured the topmost town must be “'s Gravenhage” (in English, “The Hague,” where the World Court is located). But the second town might be “Amsterdam” or “Rotterdam.” What should he do?
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