Let’s see now how likely would we observe a rational outcome if a decision maker acted randomly. Consider the case of three alternatives X, Y and Z. Assume that deciding between any two of these alternatives, e. g., X and Y, the decision maker rolls a die and depending on the outcome decides Y X or X Y or Y ~ X, each with equal probability. (More specifically, assume that a decision maker takes any two alternatives, say X and Y, and rolls a die; if one or two dots come up he decides that he is indifferent between X and Y, if three or four dots come up he decides that he prefers X over Y and if five or six dots come up he decides that he prefers Y over X. Then he does the same for X and Z and for Y and Z.)