Randomization in Decision-Making
This chapter looks at the role of randomness in decision-making and discusses the inclusion of a random factor in the solution to two-person, zero-sum games, which set the stage for the formal beginnings of game theory.
Decisions have long been made on the basis of randomness to be seen as transparently fair. “The tradition of making a decision by casting lots is ancient and has existed all over the world and at all times,” writes John Lindblum,1 as he notes its many uses in the Old Testament. Herodotus tells us that Darius of ancient Persia agreed to settle who would rule their great empire by meeting in a given place on a given day and seeing whose horse would neigh first, and his was first.2 In ancient democratic Athens, where democracy was equated in many ways with equality, selection by lot determined membership in the Council and filled positions on the courts as well as determining who would serve as public officials. While particularly associated in Greece with the radical democracy of the fifth and fourth centuries BC in Athens, casting lots can be found in the earliest Greek literature, with references to it in both Homer’s Iliad and Odyssey.3 The word “decimate” comes from a disciplinary practice in the Roman Army that involved random choice, when units found to have been cowardly or to have retreated in battle were marked for punishment, and one man in every ten in entire cohorts was selected by lot to be murdered by his fellow soldiers.
The transfer of difficult individual decisions to chance was justified as being fair. From the time of the Old Testament until the early modern age lotteries were also used for the purpose of discovering God’s will.4 With the rise of Christianity in Medieval Europe there was for a time a turn to this second strain of random decision, relying on divine judgment in difficult cases, in the use of trial by ordeal. For most simple matters procedures existed for resolving differences and determining guilt or responsibility, but it would not be until cities had grown and trade revived that law had the structure to deal with complex cases. Society was based on oaths and duties between unequals. In some cases of crimes and serious disputes it was considered best to leave the final decision in the hands of God. Trial by ordeal was the method. Among the ordeals were thrusting arms in boiling water to retrieve some item, burning by hot iron, dunking of suspected witches, and armed combat between parties with disagreements. Casting lots was a lesser ordeal. With the