An Introduction to Decision Theory

On September 6, 1492, Christopher Columbus set off from the Canary Islands and sailed westward in an attempt to find a new trade route between Europe and the Far East. On October 12, after five weeks of sailing across the Atlantic, land was sighted. Columbus had never been to the Far East, so when he landed in Central America (“the West Indies”) he believed that he had indeed discovered a new route to the Far East. Not until twenty-nine years later did Magellan finally discover the westward route to the Far East by sailing south around South America.

Columbus’ decision to sail west from the Canary Islands was arguably one of the bravest decisions ever made by an explorer. But was it rational? Unlike some of his contemporaries, Columbus believed that the earth is a rather small sphere. Based on his geographical assumptions, he estimated the distance from Europe to East India to total 2,300 miles. The actual distance is about 12,200 miles, which is more than five times farther than Columbus thought. In the fifteenth century, no ship would have been able to carry provisions for such a long journey. Had America not existed, or had the earth been flat, Columbus would certainly have faced a painful death. Was it really worth risking everything for the sake of finding a new trade route?

This book is about decision theory. Decision theory is the theory of rational decision making. Columbus’ decision to set off westwards across an unknown ocean serves as a fascinating illustration of what decision theory is all about. A decision maker, in this case Columbus, chooses an act from a set of alternatives, such as sailing westwards or staying at home. The outcome depends on the true state of the world, which in many cases is only partially known to the decision maker. For example, had the earth been a modest-sized sphere mostly covered by land and a relatively small and navigable sea, Columbus’ decision to sail westwards would have made him rich and famous, because the King and Queen of Spain had promised him 10% of all revenue gained from a new trade route. However, Columbus’ geographical hypothesis turned out to be false.