THE PROBLEM

Imagine that you will shortly be asked to consciously select one of several urns and from this urn you will then be asked to randomly select one ball. For the moment, we assume that each urn contains exactly N balls (say, 1,000), and each ball in the selected urn is equally likely to be chosen. Each ball has a number on it which specifies the incremental monetary return to you for drawing that ball.

Suppose that you have the opportunity to examine the balls and their numbers in all the urns before deciding upon your choice of urn. How would you use that opportunity? A useful answer to this question would have to take some account of the length of time available for your examination. Here we will adopt the view that time is available for any extensive analysis that you would care to make.

We will present three different but related techniques for choosing among urns. In order to decide when and for whom these techniques are appropriate, we shall discuss various behavioral assumptions that underlie each of these techniques. In mathematical parlance, we shall discuss necessary and sufficient behavioral assumptions that justify each of these techniques.